| version 1.6, 2006/12/14 17:57:33 |
version 1.13, 2007/01/23 20:05:31 |
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| <s><lb/>Si motus violentus e&longs;&longs;et æquabilis, percurreret proiectum &longs;patium <lb/>ferè duplum eo tempore, quo retardato percurrit &longs;ubduplum: hinc <lb/>&longs;onus tam citò auditur; quia propagatur cum particulis aëris æqua­<lb/>bili ferè motu: e&longs;&longs;e autem &longs;patium ferè duplum, probatur ex eo, <pb xlink:href="026/01/015.jpg"/>quòd &longs;patium motu æquabili decur&longs;um re&longs;pondet rectangulo; de­<lb/>cur&longs;um verò motu retardato, re&longs;pondet triangulo, &longs;ubduplo rectan­<lb/>guli: a&longs;&longs;umpto &longs;cilicet, æquali tempore. </s></p><p type="main"> | <s><lb/>Si motus violentus e&longs;&longs;et æquabilis, percurreret proiectum &longs;patium <lb/>ferè duplum eo tempore, quo retardato percurrit &longs;ubduplum: hinc <lb/>&longs;onus tam citò auditur; quia propagatur cum particulis aëris æqua­<lb/>bili ferè motu: e&longs;&longs;e autem &longs;patium ferè duplum, probatur ex eo, <pb xlink:href="026/01/015.jpg"/>quòd &longs;patium motu æquabili decur&longs;um re&longs;pondet rectangulo; de­<lb/>cur&longs;um verò motu retardato, re&longs;pondet triangulo, &longs;ubduplo rectan­<lb/>guli: a&longs;&longs;umpto &longs;cilicet, æquali tempore. </s></p><p type="main"> |
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| <s>9. Vites potentiæ proiicientis toto ni&longs;u re&longs;pondent velocitati <lb/>acqui&longs;itæ in toto de&longs;cen&longs;u corporis proiecti; tantumdem enim <lb/>impetus in de&longs;cen&longs;u acquiritur, quantùm in a&longs;cen&longs;u deperditur. </s> | <s>9. Vites potentiæ proiicientis toto ni&longs;u re&longs;pondent velocitati <lb/>acqui&longs;itæ in toto de&longs;cen&longs;u corporis proiecti; <expan abbr="tantũdem">tantundem</expan> enim <lb/>impetus in de&longs;cen&longs;u acquiritur, quantùm in a&longs;cen&longs;u deperditur. </s> |
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| <s><lb/>Impetus primo in&longs;tanti, quo e&longs;t, agit, &longs;i e&longs;t aliquod impedimen­<lb/>tum; e&longs;t enim cau&longs;a nece&longs;&longs;aria: primo in&longs;tanti motus aliquid im­<lb/>petus de&longs;truitur: &longs;iue præce&longs;&longs;erit motus violentus, &longs;iue non præce&longs;­<lb/>&longs;erit, corpus graue æquali motu deor&longs;um cadit: re&longs;i&longs;tentia aëris e&longs;t <lb/>quidem maior initio; &longs;ed etiam &longs;unt maiores vires. </s></p><figure id="id.026.01.015.1.jpg" xlink:href="026/01/015/1.jpg"/><p type="main"> | <s><lb/>Impetus primo in&longs;tanti, quo e&longs;t, agit, &longs;i e&longs;t aliquod impedimen­<lb/>tum; e&longs;t enim cau&longs;a nece&longs;&longs;aria: primo in&longs;tanti motus aliquid im­<lb/>petus de&longs;truitur: &longs;iue præce&longs;&longs;erit motus violentus, &longs;iue non præce&longs;­<lb/>&longs;erit, corpus graue æquali motu deor&longs;um cadit: re&longs;i&longs;tentia aëris e&longs;t <lb/>quidem maior initio; &longs;ed etiam &longs;unt maiores vires. </s></p><figure id="id.026.01.015.1.jpg" xlink:href="026/01/015/1.jpg"/><p type="main"> |
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| <s>Tertiò probatur; pila di&longs;iuncta à manu proiicientis diu adhuc mo­<lb/>uetur per hypoth.6. igitur hic motus habet cau&longs;am per Ax. 8. quælibet <lb/>enim pars motus de nouo e&longs;t, neque duæ illius partes &longs;imul e&longs;&longs;e po&longs;&longs;unt. </s> | <s>Tertiò probatur; pila di&longs;iuncta à manu proiicientis diu adhuc mo­<lb/>uetur per hypoth.6. igitur hic motus habet cau&longs;am per Ax. 8. quælibet <lb/>enim pars motus de nouo e&longs;t, neque duæ illius partes &longs;imul e&longs;&longs;e po&longs;&longs;unt. </s> |
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| <s><lb/>atqui potentia motrix non e&longs;t can&longs;a per Ax.10. immò pote&longs;t e&longs;&longs;e de&longs;tru­<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. <!--neuer Satz-->Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pilæ <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s> | <s><lb/>atqui potentia motrix non e&longs;t cau&longs;a per Ax.10. immò pote&longs;t e&longs;&longs;e de&longs;tru­<lb/>cta; igitur non e&longs;t cau&longs;a per Ax. 9. <!--neuer Satz-->Non e&longs;t etiam cau&longs;a &longs;ub&longs;tantia pilæ <lb/>mobilis per Th.5.5. nec priores pattes motus per re&longs;p. </s> |
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| <s>ad primam in­<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s></p><p type="main"> | <s>ad primam in­<lb/>&longs;tantiam Th 5. igitur aliquid aliud; voco impetum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 24.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Omne corpus, quod e&longs;t capax motus, e&longs;t capax impetus, & vici&longs;&longs;im.<emph.end type="italics"/><lb/>Probatur 1. pars; quia impetus in eo non e&longs;&longs;et fru&longs;trà; haberet enim <lb/>fuum effectum formalem, & finem intrin&longs;ecum. </s> | <s><emph type="italics"/>Omne corpus, quod e&longs;t capax motus, e&longs;t capax impetus, & vici&longs;&longs;im.<emph.end type="italics"/><lb/>Probatur 1. pars; quia impetus in eo non e&longs;&longs;et fru&longs;trà; haberet enim <lb/>&longs;uum effectum formalem, & finem intrin&longs;ecum. </s> |
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| <s>Probatur 2.pars; quia in <lb/>eo impetus non e&longs;&longs;et fru&longs;trà per Ax. 6. igitur haberet &longs;uum effectum; <lb/>igitur motum. </s></p><p type="main"> | <s>Probatur 2.pars; quia in <lb/>eo impetus non e&longs;&longs;et fru&longs;trà per Ax. 6. igitur haberet &longs;uum effectum; <lb/>igitur motum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis primò ex dictis præclarum naturæ in&longs;titutum; cum enim <lb/>corpus moueri &longs;emper non debeat, (quippe hoc e&longs;&longs;et maximè incom­<lb/>modum) certè per &longs;uam entitatem moueri non exigit; alioquin &longs;emper <lb/>moueretur; igitur per aliud ab entitate di&longs;tinctum, id e&longs;t per impetum; <lb/>itaque licet per &longs;uam entitatem exigat fluxum in tempore, id e&longs;t con&longs;er­<lb/>nari, & durare; id e&longs;t nouam &longs;emper actionem con&longs;eruatiuam; quia <lb/>maximum eius bonum e&longs;t durare vel exi&longs;tere; Igitur per &longs;e ip&longs;um illud <lb/>exigit; quia &longs;emper exigit, non tamen per &longs;e ip&longs;um exigit fluxum in <lb/>loco, id e&longs;t motum; quia moueri non &longs;emper e&longs;t bonum. </s></p><p type="main"> | <s>Ob&longs;eruabis primò ex dictis præclarum naturæ in&longs;titutum; cum enim <lb/>corpus moueri &longs;emper non debeat, (quippe hoc e&longs;&longs;et maximè incom­<lb/>modum) certè per &longs;uam entitatem moueri non exigit; alioquin &longs;emper <lb/>moueretur; igitur per aliud ab entitate di&longs;tinctum, id e&longs;t per impetum; <lb/>itaque licet per &longs;uam entitatem exigat fluxum in tempore, id e&longs;t con&longs;er­<lb/>uari, & durare; id e&longs;t nouam &longs;emper actionem con&longs;eruatiuam; quia <lb/>maximum eius bonum e&longs;t durare vel exi&longs;tere; Igitur per &longs;e ip&longs;um illud <lb/>exigit; quia &longs;emper exigit, non tamen per &longs;e ip&longs;um exigit fluxum in <lb/>loco, id e&longs;t motum; quia moueri non &longs;emper e&longs;t bonum. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis &longs;ecundò, cum idem corpus aliquando velociùs, tardiùs <lb/>aliquando moueri exigat; &longs;i per &longs;uam entitatem moueri exigeret, eo­<lb/>dem &longs;emper ferretur motu; quia eadem &longs;emper e&longs;&longs;et exigentia; igitur <lb/>debet e&longs;&longs;e aliquid aliud; illud autem e&longs;t impetus, qui aliquando maior <lb/>&longs;eu perfectior, aliquando verò minor e&longs;t; igitur maiorem &longs;eu velcio­<lb/>rem motum aliquando exigit, aliquando minorem, &longs;eu tardiorem; <lb/>cum enim motus &longs;it eius finis intrin&longs;ecus, vt re&longs;olutio e&longs;t finis caloris <lb/>vel rarefactio; quemadmodum maior calor maiorem exigit, &longs;eu præ­<lb/>&longs;tat re&longs;olutionem; ita & maior, &longs;eu perfectior impetus maiorem, &longs;eu <lb/>velociorem motum exigit. </s></p><p type="main"> | <s>Ob&longs;eruabis &longs;ecundò, cum idem corpus aliquando velociùs, tardiùs <lb/>aliquando moueri exigat; &longs;i per &longs;uam entitatem moueri exigeret, eo­<lb/>dem &longs;emper ferretur motu; quia eadem &longs;emper e&longs;&longs;et exigentia; igitur <lb/>debet e&longs;&longs;e aliquid aliud; illud autem e&longs;t impetus, qui aliquando maior <lb/>&longs;eu perfectior, aliquando verò minor e&longs;t; igitur maiorem &longs;eu <expan abbr="velcio­rem">velocio­<lb/>rem</expan> motum aliquando exigit, aliquando minorem, &longs;eu tardiorem; <lb/>cum enim motus &longs;it eius finis intrin&longs;ecus, vt re&longs;olutio e&longs;t finis caloris <lb/>vel rarefactio; quemadmodum maior calor maiorem exigit, &longs;eu præ­<lb/>&longs;tat re&longs;olutionem; ita & maior, &longs;eu perfectior impetus maiorem, &longs;eu <lb/>velociorem motum exigit. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis tertiò aliud naturæ in&longs;titutum, quo &longs;cilicet in eo tan­<lb/>tùm &longs;ubiecto recipi pote&longs;t cau&longs;a formalis, in quo recipi pote&longs;t eius effe­<lb/>ctus formalis &longs;ecundarius: nec alia regula, præter eam excogitari pote&longs;t; <lb/>cum enim aliqua forma ad talem, vel talem finem à natura in&longs;tituta e&longs;t; <lb/>certè propter illum finem e&longs;t, igitur in eo non e&longs;t, in quo &longs;uum finem <lb/>con&longs;equi non pote&longs;t; alioquin fru&longs;trà e&longs;&longs;et; & contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;trà non e&longs;t; cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; ad­<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no­<lb/>uus effectus e&longs;t; atqui nouus effectus &longs;ine &longs;ua cau&longs;a e&longs;&longs;e non pote&longs;t, neque <lb/>cau&longs;a nece&longs;&longs;aria &longs;ine e&longs;&longs;ectu; igitur ibi, &longs;cilicet in hoc &longs;ubiecto, in quo <lb/>e&longs;t, vel e&longs;&longs;e pote&longs;t effectus formalis, cau&longs;a formalis e&longs;t, vel e&longs;&longs;e pote&longs;t, <lb/>e&longs;t inquam citra miraculum. </s></p><p type="main"> | <s>Ob&longs;eruabis tertiò aliud naturæ in&longs;titutum, quo &longs;cilicet in eo tan­<lb/>tùm &longs;ubiecto recipi pote&longs;t cau&longs;a formalis, in quo recipi pote&longs;t eius effe­<lb/>ctus formalis &longs;ecundarius: nec alia regula, præter eam excogitari pote&longs;t; <lb/>cum enim aliqua forma ad talem, vel talem finem à natura in&longs;tituta e&longs;t; <lb/>certè propter illum finem e&longs;t, igitur in eo non e&longs;t, in quo &longs;uum finem <lb/>con&longs;equi non pote&longs;t; alioquin fru&longs;trà e&longs;&longs;et; & contra in eo e&longs;&longs;e pote&longs;t, <lb/>in quo fru&longs;trà non e&longs;t; cum &longs;cilicet in eo &longs;uum finem con&longs;equatur; ad­<lb/>de quod finis ille intrin&longs;ecus phy&longs;icus &longs;cilicet, non moralis, aliquis no­<lb/>uus effectus e&longs;t; atqui nouus effectus &longs;ine &longs;ua cau&longs;a e&longs;&longs;e non pote&longs;t, neque <lb/>cau&longs;a nece&longs;&longs;aria &longs;ine effectu; igitur ibi, &longs;cilicet in hoc &longs;ubiecto, in quo <lb/>e&longs;t, vel e&longs;&longs;e pote&longs;t effectus formalis, cau&longs;a formalis e&longs;t, vel e&longs;&longs;e pote&longs;t, <lb/>e&longs;t inquam citra miraculum. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis quartò egregiam rationem; propter quam res eadem in <lb/>pluribus locis naturaliter e&longs;&longs;e non pote&longs;t; quippe cum res fuerit primo <lb/>producta in aliquo loco, illa certè nouum locum acquirere non pote&longs;t <lb/>naturaliter; ni&longs;i per motum, atqui motus dicit nece&longs;&longs;ario priorem lo­<lb/>tum relictum, & nouum acqui&longs;itum; igitur cum tot acquirantur loca <lb/>per motum, quot relinquuntur; &longs;i ante motum vnus tantùm erat eiu&longs;­<lb/>dem rci locus, po&longs;t motum etiam vnus e&longs;t: quod autem producatur tan-<pb xlink:href="026/01/056.jpg" pagenum="24"/>tùm res in vno loco patet; vel enim à cau&longs;a prima vel ab aliqua 2. pro­<lb/>ducitur; &longs;i à 2. ergo ab aliqua aplicata; igitur ex &longs;uppo&longs;itione quòd il­<lb/>la cau&longs;a 2. in vno tantùm loco producta &longs;it, vni tantum applicari po­<lb/>te&longs;t; quod autem cau&longs;a 1. in pluribus locis naturaliter eundem effectum <lb/>non producat, certum e&longs;t, & demon&longs;trabimus in Metaphy&longs;. quia &longs;in­<lb/>gulis effectibus &longs;ingulæ &longs;ufficiunt actiones; &longs;ingulis terminis &longs;ingulæ <lb/>viæ; immò hoc requiri videtur, &longs;eu &longs;pectare ad huius vniuer&longs;itatis or­<lb/>dinem; quippe &longs;i res eadem in pluribus locis e&longs;&longs;et; cur potius in duo­<lb/>bus quam in tribus? </s> | <s>Ob&longs;eruabis quartò egregiam rationem; propter quam res eadem in <lb/>pluribus locis naturaliter e&longs;&longs;e non pote&longs;t; quippe cum res fuerit primo <lb/>producta in aliquo loco, illa certè nouum locum acquirere non pote&longs;t <lb/>naturaliter; ni&longs;i per motum, atqui motus dicit nece&longs;&longs;ario priorem lo­<lb/>tum relictum, & nouum acqui&longs;itum; igitur cum tot acquirantur loca <lb/>per motum, quot relinquuntur; &longs;i ante motum vnus tantùm erat eiu&longs;­<lb/>dem rei locus, po&longs;t motum etiam vnus e&longs;t: quod autem producatur tan-<pb xlink:href="026/01/056.jpg" pagenum="24"/>tùm res in vno loco patet; vel enim à cau&longs;a prima vel ab aliqua 2. pro­<lb/>ducitur; &longs;i à 2. ergo ab aliqua aplicata; igitur ex &longs;uppo&longs;itione quòd il­<lb/>la cau&longs;a 2. in vno tantùm loco producta &longs;it, vni tantum applicari po­<lb/>te&longs;t; quod autem cau&longs;a 1. in pluribus locis naturaliter eundem effectum <lb/>non producat, certum e&longs;t, & demon&longs;trabimus in Metaphy&longs;. quia &longs;in­<lb/>gulis effectibus &longs;ingulæ &longs;ufficiunt actiones; &longs;ingulis terminis &longs;ingulæ <lb/>viæ; immò hoc requiri videtur, &longs;eu &longs;pectare ad huius vniuer&longs;itatis or­<lb/>dinem; quippe &longs;i res eadem in pluribus locis e&longs;&longs;et; cur potius in duo­<lb/>bus quam in tribus? </s> |
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| <s>deinde multiplex iure po&longs;&longs;et exi&longs;timari; denique <lb/>quod vnum e&longs;t in entitate creata, &longs;eu dependente ab eadem cau&longs;a, vnum <lb/>e&longs;t etiam in dependentia; quæ e&longs;t actio, per quam dependet; &longs;ed de his <lb/>aliàs. </s></p><p type="main"> | <s>deinde multiplex iure po&longs;&longs;et exi&longs;timari; denique <lb/>quod vnum e&longs;t in entitate creata, &longs;eu dependente ab eadem cau&longs;a, vnum <lb/>e&longs;t etiam in dependentia; quæ e&longs;t actio, per quam dependet; &longs;ed de his <lb/>aliàs. </s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus non producitur in eo mobili, quod moueri non pote&longs;t à potentia <lb/>motrice applicata, licèt à fortiori moueri po&longs;&longs;it.<emph.end type="italics"/></s><s> Probatur, quia impetus <lb/>e&longs;t tantùm propter motum, qui eius effectus e&longs;t, & finis, per Th. 15. <lb/>& 16. Igitur vbi non e&longs;t motus, fru&longs;trà e&longs;t impetus; &longs;ed quod fru&longs;trà <lb/>e&longs;t, non e&longs;t; id e&longs;t non e&longs;t, quod fru&longs;trà e&longs;&longs;et, &longs;i e&longs;&longs;et per Ax. 6. Exci­<lb/>pio tamen impetum naturalem innatum, qui nunquam e&longs;t fru&longs;trà, vt <lb/>dictum e&longs;t &longs;uprà in Theorem. <!-- KEEP S--></s> | <s><emph type="italics"/>Impetus non producitur in eo mobili, quod moueri non pote&longs;t à potentia <lb/>motrice applicata, licèt à fortiori moueri po&longs;&longs;it.<emph.end type="italics"/></s><s> Probatur, quia impetus <lb/>e&longs;t tantùm propter motum, qui eius effectus e&longs;t, & finis, per Th. 15. <lb/>& 16. Igitur vbi non e&longs;t motus, fru&longs;trà e&longs;t impetus; &longs;ed quod fru&longs;trà <lb/>e&longs;t, non e&longs;t; id e&longs;t non e&longs;t, quod fru&longs;trà e&longs;&longs;et, &longs;i e&longs;&longs;et per Ax. 6. Exci­<lb/>pio tamen impetum naturalem innatum, qui nunquam e&longs;t fru&longs;trà, vt <lb/>dictum e&longs;t &longs;uprà in Theorem. <!-- KEEP S--></s> |
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| <s>17. adde quod non pote&longs;t cogno&longs;oi <lb/>impetus, ni&longs;i vel ex motu, vel ex ictu, vel ex contrario ni&longs;u, vel <lb/>impul&longs;u; &longs;ed nihil horum cernitur in rupe quam ferio; Igitur non <lb/>e&longs;t dicendum in ea produci impetum, cuius rationem afferemus infrà; <lb/>nunc&longs;atis e&longs;t Ax. 3. id manife&longs;tè probari; nam qui diceret in rupe im­<lb/>mobili impetum imprimi; certè po&longs;itiuo argumento probare tenere­<lb/>tur, quod tantùm duci pote&longs;t, vel ab experimento; atqui hîc nullum e&longs;t; <lb/>vel à nece&longs;&longs;itate, quæ nulla e&longs;t; vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; &longs;ed maiorem lucem huic Th. 3. ex proximè <lb/>&longs;equentibus accer&longs;emus; nec e&longs;t quòd aliqui dicant produci impetum <lb/>inefficacem; qui cum fru&longs;trà &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: ad­<lb/>de quòd de&longs;truitur impetus, ne &longs;it fru&longs;trà; Igitur non producitur, ne &longs;it <lb/>fru&longs;trà; nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; Igitur &longs;i <lb/>hæc non ponitur, ne aliquid &longs;it fru&longs;trà; etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s></p><p type="main"> | <s>17. adde quod non pote&longs;t cogno&longs;ci <lb/>impetus, ni&longs;i vel ex motu, vel ex ictu, vel ex contrario ni&longs;u, vel <lb/>impul&longs;u; &longs;ed nihil horum cernitur in rupe quam ferio; Igitur non <lb/>e&longs;t dicendum in ea produci impetum, cuius rationem afferemus infrà; <lb/>nunc &longs;atis e&longs;t Ax. 3. id manife&longs;tè probari; nam qui diceret in rupe im­<lb/>mobili impetum imprimi; certè po&longs;itiuo argumento probare tenere­<lb/>tur, quod tantùm duci pote&longs;t, vel ab experimento; atqui hîc nullum e&longs;t; <lb/>vel à nece&longs;&longs;itate, quæ nulla e&longs;t; vel ex alio quocumque capite, quod <lb/>nullum excogitari pote&longs;t; &longs;ed maiorem lucem huic Th. 3. ex proximè <lb/>&longs;equentibus accer&longs;emus; nec e&longs;t quòd aliqui dicant produci impetum <lb/>inefficacem; qui cum fru&longs;trà &longs;it, &longs;i e&longs;t, ex nullo capite probari pote&longs;t: ad­<lb/>de quòd de&longs;truitur impetus, ne &longs;it fru&longs;trà; Igitur non producitur, ne &longs;it <lb/>fru&longs;trà; nam con&longs;eruatio e&longs;t vera actio, vt dicemus &longs;uo loco; Igitur &longs;i <lb/>hæc non ponitur, ne aliquid &longs;it fru&longs;trà; etiam 1. productio poni non <lb/>debet; vnde commentum illud impetus inefficacis pror&longs;us inefficax e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Ideo potentia motrix non producit impetum in pradicta rupe.<emph.end type="italics"/> v.g. <emph type="italics"/>quia de­<lb/>bilior e&longs;t.<emph.end type="italics"/></s><s> Probatur, & explicatur; quippedebilior potentia minorem ef­<lb/>fectum producit per. </s> | <s><emph type="italics"/>Ideo potentia motrix non producit impetum in prædicta rupe.<emph.end type="italics"/> v.g. <emph type="italics"/>quia de­<lb/>bilior e&longs;t.<emph.end type="italics"/></s><s> Probatur, & explicatur; quippe debilior potentia minorem ef­<lb/>fectum producit per. </s> |
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| <s>Ax. 13. <emph type="italics"/>num.<emph.end type="italics"/> 2. igitur pauciores partes impetus <lb/>æquales vni certæper idem <emph type="italics"/>num.<emph.end type="italics"/> 1. igitur &longs;i &longs;int plures partes &longs;ubiecti <lb/>mobilis, &longs;eu rupis, quàm impetus; cum vna pars impetus duobus parti­<lb/>bus &longs;ubiecti ine&longs;&longs;e non po&longs;&longs;it; licet plures vni &longs;imul in e&longs;&longs;e po&longs;&longs;int; <lb/>non e&longs;t mirum &longs;i nullus impetus producatur; cum non po&longs;&longs;int tot partes <lb/>illius produci, quot e&longs;&longs;ent nece&longs;&longs;ariæ; vt &longs;altem &longs;ingulæ &longs;ingulis &longs;ubie­<lb/>cti, &longs;eu rupis partibus di&longs;tribuerentur. </s></p><pb xlink:href="026/01/057.jpg" pagenum="25"/><p type="main"> | <s>Ax. 13. <emph type="italics"/>num.<emph.end type="italics"/> 2. igitur pauciores partes impetus <lb/>æquales vni certæper idem <emph type="italics"/>num.<emph.end type="italics"/> 1. igitur &longs;i &longs;int plures partes &longs;ubiecti <lb/>mobilis, &longs;eu rupis, quàm impetus; cum vna pars impetus duobus parti­<lb/>bus &longs;ubiecti ine&longs;&longs;e non po&longs;&longs;it; licet plures vni &longs;imul in e&longs;&longs;e po&longs;&longs;int; <lb/>non e&longs;t mirum &longs;i nullus impetus producatur; cum non po&longs;&longs;int tot partes <lb/>illius produci, quot e&longs;&longs;ent nece&longs;&longs;ariæ; vt &longs;altem &longs;ingulæ &longs;ingulis &longs;ubie­<lb/>cti, &longs;eu rupis partibus di&longs;tribuerentur. </s></p><pb xlink:href="026/01/057.jpg" pagenum="25"/><p type="main"> |
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| <s><emph type="italics"/>Vel producitur impetus in omnibus &longs;ubiecti partibus vnitis, vel in nulla; <lb/>modò nulla fiat &longs;eparatio, neque compre&longs;&longs;io<emph.end type="italics"/>: Certum e&longs;t enim in ijs omni­<lb/>bus partibus, quæ auolant ab ictu, produci impetum. </s> | <s><emph type="italics"/>Vel producitur impetus in omnibus &longs;ubiecti partibus vnitis, vel in nulla; <lb/>modò nulla fiat &longs;eparatio, neque compre&longs;&longs;io<emph.end type="italics"/>: Certum e&longs;t enim in ijs omni­<lb/>bus partibus, quæ auolant ab ictu, produci impetum. </s> |
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| <s>Probatur igitur <lb/>1. quia &longs;i non producatur in omnibus partibus, & nulla &longs;eparetur ab <lb/>alijs; certè nulla mouetur, vt certum e&longs;t; igitur nulla habet impetum; <lb/>quia ibi non e&longs;t cau&longs;a formalis, vbi non e&longs;t effectus formalis; alicquin <lb/>e&longs;&longs;et fru&longs;trà, contra Ax. 6.2. Tu dicis produci impetum in aliquot parti­<lb/>hus; hoc dicis, hoc proba? </s> | <s>Probatur igitur <lb/>1. quia &longs;i non producatur in omnibus partibus, & nulla &longs;eparetur ab <lb/>alijs; certè nulla mouetur, vt certum e&longs;t; igitur nulla habet impetum; <lb/>quia ibi non e&longs;t cau&longs;a formalis, vbi non e&longs;t effectus formalis; alioquin <lb/>e&longs;&longs;et fru&longs;trà, contra Ax. 6.2. </s> |
| | <s>Tu dicis produci impetum in aliquot parti­<lb/>bus; hoc dicis, hoc proba? </s> |
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| <s>an potes digno&longs;cere impetum ni&longs;i ex motu? </s> | <s>an potes digno&longs;cere impetum ni&longs;i ex motu? </s> |
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| <s>Igitur certum e&longs;tvel produci in omnibus, vel <lb/>in nulla, ni&longs;i forte aliquæ auolent, &longs;ed tunc &longs;eparantur. </s></p><p type="main"> | <s>Igitur certum e&longs;tvel produci in omnibus, vel <lb/>in nulla, ni&longs;i forte aliquæ auolent, &longs;ed tunc &longs;eparantur. </s></p><p type="main"> |
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| <s>Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap­<lb/>to: igitur agit per Ax. 12. Re&longs;pondeo e&longs;&longs;e impeditam; nam re&longs;i&longs;tentia <lb/>&longs;ubiecti &longs;uperat vires potentiæ vt dictum e&longs;t; immò in ip&longs;o motu re­<lb/>torqueo argumentum; licèt enim &longs;it applicata cau&longs;a nec&longs;&longs;aria mouens, <lb/>non tamen mouet. </s></p><p type="main"> | <s>Obiiciet aliquis 1. e&longs;&longs;e cau&longs;am nece&longs;&longs;ariam applicatam &longs;ubiecto ap­<lb/>to: igitur agit per Ax. 12. Re&longs;pondeo e&longs;&longs;e impeditam; nam re&longs;i&longs;tentia <lb/>&longs;ubiecti &longs;uperat vires potentiæ vt dictum e&longs;t; immò in ip&longs;o motu re­<lb/>torqueo argumentum; licèt enim &longs;it applicata cau&longs;a nece&longs;&longs;aria mouens, <lb/>non tamen mouet. </s></p><p type="main"> |
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| <s>Obiiciet 2. Ignis applicatus agit in nonnullas partes fubiecti, licèt <lb/>non agat in omnes; igitur & potentia motrix. </s> | <s>Obiiciet 2. Ignis applicatus agit in nonnullas partes fubiecti, licèt <lb/>non agat in omnes; igitur & potentia motrix. </s> |
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| <s>Obiiciet. </s> | <s>Obiiciet. </s> |
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| <s>3. &longs;int duo trahentes idem mobile; ita vt &longs;eor&longs;im neuter <lb/>trahere po&longs;&longs;it, coniunctim verò vterque po&longs;&longs;it; certè &longs;i alter non pro­<lb/>ducit impetum &longs;cor&longs;un, nec etiam coniunctim producet; nec enim au­<lb/>gentur eius vires ab altero: Re&longs;pondeo vtrunque agere actione com­<lb/>muni; igitur non e&longs;t mirum &longs;i effectus maior e&longs;t, quem tamen neuter <pb xlink:href="026/01/058.jpg" pagenum="26"/>&longs;eor&longs;im producere pote&longs;t. </s></p><p type="main"> | <s>3. &longs;int duo trahentes idem mobile; ita vt &longs;eor&longs;im neuter <lb/>trahere po&longs;&longs;it, coniunctim verò vterque po&longs;&longs;it; certè &longs;i alter non pro­<lb/>ducit impetum &longs;eor&longs;im, nec etiam coniunctim producet; nec enim au­<lb/>gentur eius vires ab altero: Re&longs;pondeo vtrunque agere actione com­<lb/>muni; igitur non e&longs;t mirum &longs;i effectus maior e&longs;t, quem tamen neuter <pb xlink:href="026/01/058.jpg" pagenum="26"/>&longs;eor&longs;im producere pote&longs;t. </s></p><p type="main"> |
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| <s>Dices &longs;i vterque coniunctim producit effectum: &longs;int v. <!-- REMOVE S-->g. <!-- REMOVE S-->100. par­<lb/>tes impetus; Igitur &longs;inguli producunt tantùm 50. Igitur cur potiùs in <lb/>in his partibus &longs;ubiecti, quàm in alijs, cum vtriu&longs;que potentia eidem <lb/>&longs;ubiecti parti po&longs;&longs;et e&longs;&longs;e applicata? </s> | <s>Dices &longs;i vterque coniunctim producit effectum: &longs;int v. <!-- REMOVE S-->g. <!-- REMOVE S-->100. par­<lb/>tes impetus; Igitur &longs;inguli producunt tantùm 50. Igitur cur potiùs in <lb/>in his partibus &longs;ubiecti, quàm in alijs, cum vtriu&longs;que potentia eidem <lb/>&longs;ubiecti parti po&longs;&longs;et e&longs;&longs;e applicata? </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Obiicies 4. producitur &longs;onus &longs;i ferias rupem; igitur & impetus; Re&longs;­<lb/>pondeo ad &longs;onum &longs;olam aëris colli&longs;ionem &longs;ufficere, quam fieri certum <lb/>e&longs;t à prædicto ictu; deinde mallej motus impacti in rupem facit &longs;onum; <lb/>quidquid tandem &longs;it &longs;onus, de quo hîc non di&longs;puto: adde qnod in ru­<lb/>pe &longs;unt &longs;emper aliquæ partes trem ulæ, quæ modico tantùm, coque flexi­<lb/>bili nexu cum alijs partibus copu lantur; adde aliquam compre&longs;&longs;ionem, <lb/>ex qua modicæ vibrationes &longs;equuntur. </s></p><p type="main"> | <s>Obiicies 4. producitur &longs;onus &longs;i ferias rupem; igitur & impetus; Re&longs;­<lb/>pondeo ad &longs;onum &longs;olam aëris colli&longs;ionem &longs;ufficere, quam fieri certum <lb/>e&longs;t à prædicto ictu; deinde mallej motus impacti in rupem facit &longs;onum; <lb/>quidquid tandem &longs;it &longs;onus, de quo hîc non di&longs;puto: adde quod in ru­<lb/>pe &longs;unt &longs;emper aliquæ partes tremulæ, quæ modico tantùm, eoque flexi­<lb/>bili nexu cum alijs partibus copulantur; adde aliquam compre&longs;&longs;ionem, <lb/>ex qua modicæ vibrationes &longs;equuntur. </s></p><p type="main"> |
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| <s>Obiicies 5. Quando aliquæ partes auolant ab ictu, haud dubiè auo­<lb/>lant propter impetum impre&longs;&longs;um: Igitur prius e&longs;t imprimi impetum, <lb/>quàm auolare; igitur productus e&longs;t impetus in nonnullis partibus, & <lb/>non in aliis, cum quibus illæ &longs;unt coniunctæ. </s> | <s>Obiicies 5. Quando aliquæ partes auolant ab ictu, haud dubiè auo­<lb/>lant propter impetum impre&longs;&longs;um: Igitur prius e&longs;t imprimi impetum, <lb/>quàm auolare; igitur productus e&longs;t impetus in nonnullis partibus, & <lb/>non in aliis, cum quibus illæ &longs;unt coniunctæ. </s> |
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| <s>Re&longs;pondeo equidem im­<lb/>petum produci in illis partibus antequam auolent; &longs;ed ideo produci vt <lb/>deinde auolent nam tota ratio cur non producatur, e&longs;t ne &longs;it fru&longs;trà; &longs;ed <lb/>&longs;i auolent aliquæ partes: certè in ijs non e&longs;t fru&longs;trà, in quibus habet <lb/>&longs;uum effectum, id e&longs;t, motum. </s></p><p type="main"> | <s>Re&longs;pondeo equidem im­<lb/>petum produci in illis partibus antequam auolent; &longs;ed ideo produci vt <lb/>deinde auolent nam tota ratio cur non producatur, e&longs;t ne &longs;it fru&longs;trà; &longs;ed <lb/>&longs;i auolent aliquæ partes: certè in ijs non e&longs;t fru&longs;trà, in quibus habet <lb/>&longs;uum effectum, id e&longs;t, motum. </s></p><p type="main"> |
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| <s>Dices; igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;trà; in quo non <lb/>habet &longs;uum effectum; Re&longs;pondeo nunquam primo in&longs;tanti e&longs;&longs;e fru&longs;trà, <lb/>modò &longs;it motus &longs;ecundo cum etiam primo in&longs;tanti, quo e&longs;t impetus, <lb/>non po&longs;&longs;it e&longs;&longs;e motus, vt demon&longs;trabo infrà; immò ideo ponitur im­<lb/>petus primo vt &longs;it motus &longs;ecundo exigendo pro i n&longs;tant i &longs;equenti, de <lb/>cum impetus ponat tantùm motum quo aliàs. </s></p><p type="main"> | <s>Dices; igitur primo in&longs;tanti impetus ille e&longs;t fru&longs;trà; in quo non <lb/>habet &longs;uum effectum; Re&longs;pondeo nunquam primo in&longs;tanti e&longs;&longs;e fru&longs;trà, <lb/>modò &longs;it motus &longs;ecundo cum etiam primo in&longs;tanti, quo e&longs;t impetus, <lb/>non po&longs;&longs;it e&longs;&longs;e motus, vt demon&longs;trabo infrà; immò ideo ponitur im­<lb/>petus primo vt &longs;it motus &longs;ecundo exigendo pro in&longs;tant &longs;equenti, de <lb/>cum impetus ponat tantùm motum quo aliàs. </s></p><p type="main"> |
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| <s>Dices; &longs;ed potentia motrix ne&longs;cit an po&longs;&longs;it pars aliqua mobilis &longs;epa­<lb/>rari; igitur non e&longs;t quòd aliquando producat impetum, aliquando <lb/>non producat. </s> | <s>Dices; &longs;ed potentia motrix ne&longs;cit an po&longs;&longs;it pars aliqua mobilis &longs;epa­<lb/>rari; igitur non e&longs;t quòd aliquando producat impetum, aliquando <lb/>non producat. </s> |
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| <s>Re&longs;pondeo non &longs;tare per cau&longs;am nece&longs;&longs;ariam, quin &longs;em­<lb/>per agat; &longs;ed per &longs;ubiectum, quod &longs;i aptum e&longs;t, & capax e&longs;&longs;ectus; haud <lb/>dubiè eo ip&longs;o cau&longs;a nece&longs;&longs;aria applicata in ip&longs;um aget; &longs;i verò ineptum. </s> | <s>Re&longs;pondeo non &longs;tare per cau&longs;am nece&longs;&longs;ariam, quin &longs;em­<lb/>per agat; &longs;ed per &longs;ubiectum, quod &longs;i aptum e&longs;t, & capax effectus; haud <lb/>dubiè eo ip&longs;o cau&longs;a nece&longs;&longs;aria applicata in ip&longs;um aget; &longs;i verò ineptum. </s> |
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| <s><lb/>haud dubiè non aget; nam ad hoc vt producatur effectus in &longs;ubiecto; <lb/>non &longs;atis e&longs;t cau&longs;am po&longs;&longs;e producere, ni&longs;i etiam &longs;ubiectum po&longs;&longs;it recipe­<lb/>re; igitur cum &longs;it talis ordo à natura in&longs;titutus, ne aliquid &longs;it fru&longs;trà; <lb/>certè &longs;i impetus producibilis &longs;it futurus fru&longs;trà, hauddubiè non produ­<lb/>cetur; &longs;ecus verò &longs;i fru&longs;trà non &longs;it futurus, in quo non e&longs;t difficultas. </s></p><p type="main"> | <s><lb/>haud dubiè non aget; nam ad hoc vt producatur effectus in &longs;ubiecto; <lb/>non &longs;atis e&longs;t cau&longs;am po&longs;&longs;e producere, ni&longs;i etiam &longs;ubiectum po&longs;&longs;it recipe­<lb/>re; igitur cum &longs;it talis ordo à natura in&longs;titutus, ne aliquid &longs;it fru&longs;trà; <lb/>certè &longs;i impetus producibilis &longs;it futurus fru&longs;trà, hauddubiè non produ­<lb/>cetur; &longs;ecus verò &longs;i fru&longs;trà non &longs;it futurus, in quo non e&longs;t difficultas. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles à debili po­<lb/>tenria loco moueri non po&longs;&longs;it; cum enim tot &longs;altem requirantur partes <lb/>impetus, quot &longs;unt partes &longs;ubiecti: quia vel in omnibus, vel in nulla <lb/>producitur; certè cum &longs;int plures partes &longs;ubiecti, quàm vt in &longs;ingulis <lb/>ab ea dumtaxat potentiâ impetus produci po&longs;&longs;it; quid mirum e&longs;t, &longs;i mo­<lb/>ueri non po&longs;&longs;it. </s></p><p type="main"> | <s>Hinc egregia ratio erui pote&longs;t, cur ingens corporis moles à debili po­<lb/>tentia loco moueri non po&longs;&longs;it; cum enim tot &longs;altem requirantur partes <lb/>impetus, quot &longs;unt partes &longs;ubiecti: quia vel in omnibus, vel in nulla <lb/>producitur; certè cum &longs;int plures partes &longs;ubiecti, quàm vt in &longs;ingulis <lb/>ab ea dumtaxat potentiâ impetus produci po&longs;&longs;it; quid mirum e&longs;t, &longs;i mo­<lb/>ueri non po&longs;&longs;it. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc certa ratio alterius vulgaris effectus potentiæ motricis, quæ lapi­<lb/>dem 40. librarum tardo tantùm motu impellit, etiam cum &longs;ummo ni&longs;u, <lb/>cum tamen &longs;axo vnius libræ velocioremmotum imprimat; quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma­<lb/>iori lapide, & paucioribus in minori; igitur &longs;ingulæ partes minoris <lb/>habent plures partes impetus, vt manife&longs;tè coa&longs;tat; ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <!-- REMOVE S--><lb/>13. num.2. </s> | <s>Hinc certa ratio alterius vulgaris effectus potentiæ motricis, quæ lapi­<lb/>dem 40. librarum tardo tantùm motu impellit, etiam cum &longs;ummo ni&longs;u, <lb/>cum tamen &longs;axo vnius libræ velociorem motum imprimat; quia &longs;cilicet <lb/>partes impetus producti di&longs;tribuuntur pluribus partibus &longs;ubiecti in ma­<lb/>iori lapide, & paucioribus in minori; igitur &longs;ingulæ partes minoris <lb/>habent plures partes impetus, vt manife&longs;tè con&longs;tat; ergo ille impetus <lb/>inten&longs;ior e&longs;t; igitur maiorem exigit &longs;eu perfectiorem motum per Ax. <!-- REMOVE S--><lb/>13. num.2. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc &longs;ublata ratione diuer&longs;æ re&longs;i&longs;tentiæ medij, dato pondere <lb/>mobilis vtriu&longs;que, datoque ni&longs;u communi potentiæ, pote&longs;t de­<lb/>terminari certus velocitatis gradus vtriu&longs;que; nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it pondùs 4. librarum; fit etiam 2. librarum <lb/>&longs;it impetus impre&longs;&longs;us vtrique &longs;uppo&longs;ito communi, & æquali ni&longs;u <lb/>potentiæ, & æquali tempore; haud dubiè velocitas mobilis 2. libra­<lb/>rum erit dupla velocitatis mobilis 4. librarum; quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili quàm in illo (accipio enim vtrum­<lb/>que eiu&longs;dem mareriæ, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; dixi, &longs;i fiat æquali <lb/>ni&longs;u, & æquali tempore; quia reuerâ non fit in tempore æquali, &longs;ed <lb/>inæquali, &longs;i &longs;upponatur idem arcus brachij v. <!-- REMOVE S-->g. <!-- REMOVE S-->iacientis; nam tempo­<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib. | <s>Hinc &longs;ublata ratione diuer&longs;æ re&longs;i&longs;tentiæ medij, dato pondere <lb/>mobilis vtriu&longs;que, datoque ni&longs;u communi potentiæ, pote&longs;t de­<lb/>terminari certus velocitatis gradus vtriu&longs;que; nam ratio velocitatum <lb/>e&longs;t inuer&longs;a ponderum v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it pondùs 4. librarum; fit etiam 2. librarum <lb/>&longs;it impetus impre&longs;&longs;us vtrique &longs;uppo&longs;ito communi, & æquali ni&longs;u <lb/>potentiæ, & æquali tempore; haud dubiè velocitas mobilis 2. libra­<lb/>rum erit dupla velocitatis mobilis 4. librarum; quia cum &longs;int duplo <lb/>plures partes &longs;ubiecti in hoc mobili quàm in illo (accipio enim vtrum­<lb/>que eiu&longs;dem materiæ, vt omnes lites fugiam) igitur in minori e&longs;t duplo <lb/>inten&longs;ior impetus: Igitur duplo velocior motus; dixi, &longs;i fiat æquali <lb/>ni&longs;u, & æquali tempore; quia reuerâ non fit in tempore æquali, &longs;ed <lb/>inæquali, &longs;i &longs;upponatur idem arcus brachij v. <!-- REMOVE S-->g. <!-- REMOVE S-->iacientis; nam tempo­<lb/>ra &longs;unt in ratione &longs;ubduplicata ponderum; vt demon&longs;trabimus lib. |
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| 10. <lb/>& velocitates &longs;unt vt tempora permutando. </s> | 10. <lb/>& velocitates &longs;unt vt tempora permutando. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Collorarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc facilè determinari pote&longs;t proportio impetus impre&longs;&longs;i cognitâ <lb/>grauitate mobilium; v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it mobile grauc vt4. & aliud graue vt 2. haud <lb/>dubiè vt moucatur æquali gradu velocitatis, debet produci duplo <lb/>maior impetus in maiori mobili, hoc e&longs;t, iuxta rationem maioris ad mi­<lb/>nus, quod clari&longs;&longs;imè &longs;cquitur ex dictis; vt enim tot&longs;int gradus impetus <pb xlink:href="026/01/060.jpg" pagenum="28"/>in qualibet parte minoris, quot &longs;unt in qualibet parte minoris; haud <lb/>dubiè impetus maioris habet eandem rationem ad impetum minoris; <lb/>quam habet maius ad minus. </s> | <s>Hinc facilè determinari pote&longs;t proportio impetus impre&longs;&longs;i cognitâ <lb/>grauitate mobilium; v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it mobile graue vt4. & aliud graue vt 2. haud <lb/>dubiè vt moueatur æquali gradu velocitatis, debet produci duplo <lb/>maior impetus in maiori mobili, hoc e&longs;t, iuxta rationem maioris ad mi­<lb/>nus, quod clari&longs;&longs;imè &longs;equitur ex dictis; vt enim tot&longs;int gradus impetus <pb xlink:href="026/01/060.jpg" pagenum="28"/>in qualibet parte minoris, quot &longs;unt in qualibet parte minoris; haud <lb/>dubiè impetus maioris habet eandem rationem ad impetum minoris; <lb/>quam habet maius ad minus. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Potest impetus aliquo in&longs;tanti non moueri quo mouetur ip&longs;um mobile, in <lb/>quo est.<emph.end type="italics"/></s><s> Nam moueatur mobile quodlibet; & dum mouetur, impella­<lb/>tur, factâ &longs;cilicet acce&longs;&longs;ione noui impetus; haud dubiè hoc primo in­<lb/>&longs;tanti, quo producitur impetus in dato mobili non mouetur per Th. <!-- REMOVE S--><lb/>35. quo tamen in&longs;tanti mouetur prædictum mobilc. </s> | <s><emph type="italics"/>Potest impetus aliquo in&longs;tanti non moueri quo mouetur ip&longs;um mobile, in <lb/>quo est.<emph.end type="italics"/></s><s> Nam moueatur mobile quodlibet; & dum mouetur, impella­<lb/>tur, factâ &longs;cilicet acce&longs;&longs;ione noui impetus; haud dubiè hoc primo in­<lb/>&longs;tanti, quo producitur impetus in dato mobili non mouetur per Th. <!-- REMOVE S--><lb/>35. quo tamen in&longs;tanti mouetur prædictum mobile. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc corpus grauius per&longs;e, &longs;altem eiu&longs;dem materiæ, non cadit velo­<lb/>ciùs, quàm leuius, vti globus plumbeus 100. librarum, quàm globus <lb/>vnius libræ plumbeus; quia &longs;cilicet impetus vnius partis non iuuat mo­<lb/>tum alterius: præterca tam facilè 2, partes impetus in 2. partibus &longs;ubie­<lb/>cti receptæ ca&longs;dem mouent, quàm 100. alias 100. dixi per &longs;e; nam di­<lb/>uer&longs;a e&longs;&longs;e pote&longs;t medij re&longs;i&longs;tentia; &longs;ed de his fu&longs;e in 2. lib. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main"> | <s>Hinc corpus grauius per&longs;e, &longs;altem eiu&longs;dem materiæ, non cadit velo­<lb/>ciùs, quàm leuius, vti globus plumbeus 100. librarum, quàm globus <lb/>vnius libræ plumbeus; quia &longs;cilicet impetus vnius partis non iuuat mo­<lb/>tum alterius: præterea tam facilè 2, partes impetus in 2. partibus &longs;ubie­<lb/>cti receptæ ea&longs;dem mouent, quàm 100. alias 100. dixi per &longs;e; nam di­<lb/>uer&longs;a e&longs;&longs;e pote&longs;t medij re&longs;i&longs;tentia; &longs;ed de his fu&longs;e in 2. lib. <!-- REMOVE S--><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus recipitur tantùm in ip&longs;a &longs;ub&longs;tantia &longs;ubiecti naturaliter.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>mobile &longs;it ferrum calidum, recipitur in ip&longs;a &longs;ub&longs;tantia ferri; non verò <lb/>in ip&longs;o calore (ex &longs;uppo&longs;itione quod calor &longs;it accidens, vt aliàs demon­<lb/>&longs;trabimus; nec in alijs accidentibus, &longs;i quæ &longs;unt, in eodem &longs;ubiecto; pro­<lb/>batur 1. quia &longs;i produceretur etiam impetus in accidentibus, quo plu­<lb/>ra e&longs;&longs;ent accidentia in aliquo &longs;ubiecto; plures quoque partes impetus <lb/>producendæ e&longs;&longs;ent; igitur maiori potentiâ opus e&longs;&longs;et per Ax. 13. n. </s> | <s><emph type="italics"/>Impetus recipitur tantùm in ip&longs;a &longs;ub&longs;tantia &longs;ubiecti naturaliter.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>mobile &longs;it ferrum calidum, recipitur in ip&longs;a &longs;ub&longs;tantia ferri; non verò <lb/>in ip&longs;o calore (ex &longs;uppo&longs;itione quod calor &longs;it accidens, vt aliàs demon­<lb/>&longs;trabimus; nec in alijs accidentibus, &longs;i quæ &longs;unt, in eodem &longs;ubiecto; pro­<lb/>batur 1. quia &longs;i produceretur etiam impetus in accidentibus, quo plu­<lb/>ra e&longs;&longs;ent accidentia in aliquo &longs;ubiecto; plures quoque partes impetus <lb/>producendæ e&longs;&longs;ent; igitur maiori potentiâ opus e&longs;&longs;et per Ax. 13. n. </s> |
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| <s>Diceret fortè ali­<lb/>quis eundem impetum recipi &longs;imul in &longs;ub&longs;tantia & in ip&longs;is accidenti­<lb/>bus; &longs;ed contra, nam reuera, &longs;i hoc e&longs;&longs;et, dum proijcitur ferrum cali­<lb/>dum, & &longs;tatim frigefit, de&longs;trueretur totus impetus, de&longs;tructo &longs;cilicet <lb/>eius &longs;ubiecto: 2. qui hoc diceret, deberet probare; nam codem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipiin illis impetum, nec etiam ratio, <lb/>vt dicam paulò po&longs;t. </s> | <s>Diceret fortè ali­<lb/>quis eundem impetum recipi &longs;imul in &longs;ub&longs;tantia & in ip&longs;is accidenti­<lb/>bus; &longs;ed contra, nam reuera, &longs;i hoc e&longs;&longs;et, dum proijcitur ferrum cali­<lb/>dum, & &longs;tatim frigefit, de&longs;trueretur totus impetus, de&longs;tructo &longs;cilicet <lb/>eius &longs;ubiecto: 2. qui hoc diceret, deberet probare; nam codem modo <lb/>mouetur corpus &longs;iue afficiatur pluribus accidentibus, &longs;iue paucioribus; <lb/>igitur non euincit experientia recipiin illis impetum, nec etiam ratio, <lb/>vt dicam paulò po&longs;t. </s> |
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| <s>Ratio à priori e&longs;&longs;e pote&longs;t; quia accidens cum &longs;uo <lb/>&longs;ubiecto coniunctum exigit &longs;emper e&longs;&longs;e præ&longs;ens &longs;ubiecto, cum natura­<lb/>liter extra &longs;ubiectum exi&longs;tere non po&longs;&longs;it; igitur cum exigat con&longs;erua­<lb/>ri, & exi&longs;tere; eo tantùm modo, quo pote&longs;t naturaliter con&longs;eruari & <lb/>exi&longs;tere; certè exigit con&longs;eruari, & ine&longs;&longs;e &longs;ubiecto; igitur exi&longs;tere in <lb/>eo loco, in quo exi&longs;tit &longs;ubiectum, vt patet; igitur, &longs;i &longs;ubiectum mutet <lb/>locum etiam accidens cnm eo coniu nctum mutare debet. </s></p><p type="main"> | <s>Ratio à priori e&longs;&longs;e pote&longs;t; quia accidens cum &longs;uo <lb/>&longs;ubiecto coniunctum exigit &longs;emper e&longs;&longs;e præ&longs;ens &longs;ubiecto, cum natura­<lb/>liter extra &longs;ubiectum exi&longs;tere non po&longs;&longs;it; igitur cum exigat con&longs;erua­<lb/>ri, & exi&longs;tere; eo tantùm modo, quo pote&longs;t naturaliter con&longs;eruari & <lb/>exi&longs;tere; certè exigit con&longs;eruari, & ine&longs;&longs;e &longs;ubiecto; igitur exi&longs;tere in <lb/>eo loco, in quo exi&longs;tit &longs;ubiectum, vt patet; igitur, &longs;i &longs;ubiectum mutet <lb/>locum etiam accidens cum eo coniunctum mutare debet. </s></p><p type="main"> |
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| <s>Dices, igitur &longs;imiliter dici pote&longs;t non recipi impetum in omni­<lb/>bus partibus &longs;ubiecti mobilis, &longs;ed in vnâ dumtaxat; cui cum <lb/>aliæ &longs;int vnitæ, exigunt moueri &longs;ine impetu ad illius motum? </s> | <s>Dices, igitur &longs;imiliter dici pote&longs;t non recipi impetum in omni­<lb/>bus partibus &longs;ubiecti mobilis, &longs;ed in vnâ dumtaxat; cui cum <lb/>aliæ &longs;int vnitæ, exigunt moueri &longs;ine impetu ad illius motum? </s> |
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| <s>cum <lb/>hoc ip&longs;um ad omnem vnionem &longs;pectare videatur; Re&longs;pondeo vnam <pb xlink:href="026/01/062.jpg" pagenum="30"/>partem plumbi ita coniungi cum alia, vt etiam &longs;eparata naturaliter <lb/>exi&longs;tere po&longs;&longs;it; igitur non e&longs;t par ratio; præterea vna pars plumbi non <lb/>e&longs;t in loco alterius; nec enim inuicem penetrantur cum &longs;it compene­<lb/>tratio accidentium cum &longs;ubiecto; deinde, quò plures &longs;unt partes vnitæ, <lb/>maior e&longs;t re&longs;i&longs;tentia, quæ ip&longs;o etiam &longs;en&longs;u percipitur; denique non vide­<lb/>rur cur potius produceretur in vna parte, quam in alia; quæ omnia <lb/>iam &longs;uprà Th. 33. demon&longs;trauimus. </s></p><p type="main"> | <s>cum <lb/>hoc ip&longs;um ad omnem vnionem &longs;pectare videatur; Re&longs;pondeo vnam <pb xlink:href="026/01/062.jpg" pagenum="30"/>partem plumbi ita coniungi cum alia, vt etiam &longs;eparata naturaliter <lb/>exi&longs;tere po&longs;&longs;it; igitur non e&longs;t par ratio; præterea vna pars plumbi non <lb/>e&longs;t in loco alterius; nec enim inuicem penetrantur cum &longs;it compene­<lb/>tratio accidentium cum &longs;ubiecto; deinde, quò plures &longs;unt partes vnitæ, <lb/>maior e&longs;t re&longs;i&longs;tentia, quæ ip&longs;o etiam &longs;en&longs;u percipitur; denique non vide­<lb/>tur cur potius produceretur in vna parte, quam in alia; quæ omnia <lb/>iam &longs;uprà Th. 33. demon&longs;trauimus. </s></p><p type="main"> |
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| <s>Adde quod &longs;i impetus produceretur in ip&longs;is accidentibus, etiam in <lb/>ip&longs;o impetu prius producto alius impetus produceretur; cum &longs;cilicet <lb/>noua fit impetus acce&longs;&longs;io; quod &longs;atis ridiculum e&longs;t; qua&longs;i verò impetus <lb/>indigeat impetu &c. </s> | <s>Adde quod &longs;i impetus produceretur in ip&longs;is accidentibus, etiam in <lb/>ip&longs;o impetu prius producto alius impetus produceretur; cum &longs;cilicet <lb/>noua fit impetus acce&longs;&longs;io; quod &longs;atis ridiculum e&longs;t; qua&longs;i verò impetus <lb/>indigeat impetu &c. </s> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc manife&longs;tè patet, quid dicendum &longs;it de anima bruti, quæ mouc­<lb/>tur etiam &longs;ine impetu; quia exigit &longs;emper e&longs;&longs;e coniuncta corpori, à <lb/>quo di&longs;iuncta naturaliter exi&longs;tere non pote&longs;t, vt &longs;uo loco dicemus; igi­<lb/>tur ad motum corporis, &longs;eu &longs;ubiecti moueri deber. </s></p><p type="main"> | <s>Hinc manife&longs;tè patet, quid dicendum &longs;it de anima bruti, quæ moue­<lb/>tur etiam &longs;ine impetu; quia exigit &longs;emper e&longs;&longs;e coniuncta corpori, à <lb/>quo di&longs;iuncta naturaliter exi&longs;tere non pote&longs;t, vt &longs;uo loco dicemus; igi­<lb/>tur ad motum corporis, &longs;eu &longs;ubiecti moueri deber. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Idem quoque de Anima rationali dicendum e&longs;&longs;e videtur; licèt <lb/>enim à corpore &longs;eparata naturaliter exi&longs;tere po&longs;&longs;it; tandiù tamen cum <lb/>corpore manet coniuncta, quandiu agere pote&longs;t in organis corporcis; <lb/>ac proinde exigit con&longs;eruari in corpore ip&longs;o, quandiu &longs;uas operatio­<lb/>nes organicas in eo exercere pote&longs;t. </s></p><p type="main"> | <s>Idem quoque de Anima rationali dicendum e&longs;&longs;e videtur; licèt <lb/>enim à corpore &longs;eparata naturaliter exi&longs;tere po&longs;&longs;it; tandiù tamen cum <lb/>corpore manet coniuncta, quandiu agere pote&longs;t in organis corporeis; <lb/>ac proinde exigit con&longs;eruari in corpore ip&longs;o, quandiu &longs;uas operatio­<lb/>nes organicas in eo exercere pote&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 39.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 39.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Quando corpus pellitur ab alio corpore per impetum impre&longs;&longs;um; band da­<lb/>biè impetus ille impre&longs;&longs;us ab aliqua cau&longs;a efficiente producijur<emph.end type="italics"/>; patet <lb/>per Ax. 8. </s></p><pb xlink:href="026/01/063.jpg" pagenum="31"/><p type="main"> | <s><emph type="italics"/>Quando corpus pellitur ab alio corpore per impetum impre&longs;&longs;um; haud du­<lb/>biè impetus ille impre&longs;&longs;us ab aliqua cau&longs;a efficiente producitur<emph.end type="italics"/>; patet <lb/>per Ax. 8. </s></p><pb xlink:href="026/01/063.jpg" pagenum="31"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main"> |
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| <s><lb/>Dicunt aliqui requiri <expan abbr="motũ">motum</expan> præuium, vt agat; &longs;ed contra; nam motus <lb/>præuius non requiritur vt cau&longs;a, vt patet; quia cau&longs;a vt agat debet exi­<lb/>&longs;tere per Ax. 9. Igitur requiritur, vt conditio, quod dici non pote&longs;t; <lb/>quia primo etiam conditio debet e&longs;&longs;e præ&longs;ens; &longs;ed motus præuius de <lb/>nihil pre&longs;enti e&longs;t &longs;ecundo quia non pote&longs;t excogitari aliud munus con­<lb/>ditionis; ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie­<lb/>cto apto; præterea motus præuius non e&longs;t; igitur codem modo &longs;e <lb/>habet, ac &longs;i nunquam extiti&longs;&longs;et; & &longs;i eo in&longs;tanti quo corpus impa­<lb/>ctum primo tangit, amitteret totum impetum, ita vt expræterito motu <lb/>nihil reliquum e&longs;&longs;et, haud dubiè corpus aliud non pelleret. </s></p><p type="main"> | <s><lb/>Dicunt aliqui requiri <expan abbr="motũ">motum</expan> præuium, vt agat; &longs;ed contra; nam motus <lb/>præuius non requiritur vt cau&longs;a, vt patet; quia cau&longs;a vt agat debet exi­<lb/>&longs;tere per Ax. 9. Igitur requiritur, vt conditio, quod dici non pote&longs;t; <lb/>quia primo etiam conditio debet e&longs;&longs;e præ&longs;ens; &longs;ed motus præuius de <lb/>nihil pre&longs;enti e&longs;t &longs;ecundo quia non pote&longs;t excogitari aliud munus con­<lb/>ditionis; ni&longs;i vel vt tollat impedimentum, vel vt applicet cau&longs;am &longs;ubie­<lb/>cto apto; præterea motus præuius non e&longs;t; igitur codem modo &longs;e <lb/>habet, ac &longs;i nunquam extiti&longs;&longs;et; & &longs;i eo in&longs;tanti quo corpus impa­<lb/>ctum primo tangit, amitteret totum impetum, ita vt expræterito motu <lb/>nihil reliquum e&longs;&longs;et, haud dubiè corpus aliud non pelleret. </s></p><p type="main"> |
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| <s>Diceret alius impetum e&longs;&longs;e tantùm conditionem, quæ &longs;emper e&longs;t <lb/>de præ&longs;enti: ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; & certè <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; haud dubiè <lb/>maior e&longs;&longs;et ictus; licèt cum codem motu præuio, & tamen idem e&longs;&longs;et <lb/>corpus <expan abbr="impactũ">impactum</expan>, Igitnr ad hanc <expan abbr="in&longs;tantiã">in&longs;tantiam</expan> alio modo re&longs;pondeo, ex appli­<lb/>catione impetus &longs;emper &longs;equitur productio alterius impetus; dum &longs;cili­<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s> | <s>Diceret alius impetum e&longs;&longs;e tantùm conditionem, quæ &longs;emper e&longs;t <lb/>de præ&longs;enti: ad hanc in&longs;tantiam non valet &longs;uperior re&longs;pon&longs;io; & certè <lb/>&longs;i eo ip&longs;o in&longs;tanti contactus noua fieret impetus acce&longs;&longs;io; haud dubiè <lb/>maior e&longs;&longs;et ictus; licèt cum codem motu præuio, & tamen idem e&longs;&longs;et <lb/>corpus <expan abbr="impactũ">impactum</expan>, Igitur ad hanc <expan abbr="in&longs;tantiã">in&longs;tantiam</expan> alio modo re&longs;pondeo, ex appli­<lb/>catione impetus &longs;emper &longs;equitur productio alterius impetus; dum &longs;cili­<lb/>cet &longs;ubiectum, cui applicatur &longs;it capax motus; ex applicatione corporis <lb/>&longs;eu &longs;ubiecti ip&longs;ius non &longs;emper &longs;equitur; igitur dicendum e&longs;t impetum <lb/>ip&longs;um e&longs;&longs;e cau&longs;am alterius per Ax. 11. n. </s> |
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| <s>1. voco enim illud cau&longs;am, <lb/>ex cuius applicatione &longs;emper &longs;equitur &longs;imilis effectus; alioquin &longs;i hoc <lb/>neges; proba mihi aliter ignem accendi ab alio igne; dicam enim tibi <lb/>ignem applicatum e&longs;&longs;e tantùm conditionem, & produci à cœlo; proba <lb/>mihi aliter calorem produci à calore? </s> | <s>1. voco enim illud cau&longs;am, <lb/>ex cuius applicatione &longs;emper &longs;equitur &longs;imilis effectus; alioquin &longs;i hoc <lb/>neges; proba mihi aliter ignem accendi ab alio igne; dicam enim tibi <lb/>ignem applicatum e&longs;&longs;e tantùm conditionem, & produci à cœlo; proba <lb/>mihi aliter calorem produci à calore? </s> |
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| <s>igitur illius e&longs;t tollere impedimentnm, cuius e&longs;t exigere motum, <lb/>corpus ip&longs;um graue non exigit motum &longs;ur&longs;um, &longs;ed impetus; igitur im­<lb/>petus e&longs;t tollerc impedimentum &longs;ui effectus; igitur producere impetum, <lb/>quo vno tolli tantùm pote&longs;t: En tibi rationem à priori, cutum nullam <lb/>habeas: Præterea, cur negas impetum e&longs;&longs;e cau&longs;am &longs;ufficientem alterius <lb/>impetus, cum ex eius applicatione ip&longs;o &longs;en&longs;u percipiamus produci alium <lb/>impetum? </s> | <s>igitur illius e&longs;t tollere impedimentum, cuius e&longs;t exigere motum, <lb/>corpus ip&longs;um graue non exigit motum &longs;ur&longs;um, &longs;ed impetus; igitur im­<lb/>petus e&longs;t tollere impedimentum &longs;ui effectus; igitur producere impetum, <lb/>quo vno tolli tantùm pote&longs;t: En tibi rationem à priori, cutum nullam <lb/>habeas: Præterea, cur negas impetum e&longs;&longs;e cau&longs;am &longs;ufficientem alterius <lb/>impetus, cum ex eius applicatione ip&longs;o &longs;en&longs;u percipiamus produci alium <lb/>impetum? </s> |
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| <s>quæ ratio? </s> | <s>quæ ratio? </s> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis primò, hanc primam e&longs;&longs;e difficultatem; cum in hoc im­<lb/>petus maximè differat ab alijs qualitalibus &longs;i quæ &longs;unt, quæ agunt in or­<lb/>bem, vt dicemus &longs;uo loco. </s></p><p type="main"> | <s>Ob&longs;eruabis primò, hanc primam e&longs;&longs;e difficultatem; cum in hoc im­<lb/>petus maximè differat ab alijs qualitatibus &longs;i quæ &longs;unt, quæ agunt in or­<lb/>bem, vt dicemus &longs;uo loco. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis &longs;ecundò, hanc etiam e&longs;&longs;e communem illorum &longs;ententiam, <lb/>qui dicunt imptum ad extrà produci ab ip&longs;o mobili, &longs;ed ita vt ab illis <lb/>vix &longs;olui po&longs;&longs;it; cum tamen à nobis facilè &longs;oluatur. </s></p><p type="main"> | <s>Ob&longs;eruabis &longs;ecundò, hanc etiam e&longs;&longs;e communem illorum &longs;ententiam, <lb/>qui dicunt impetum ad extrà produci ab ip&longs;o mobili, &longs;ed ita vt ab illis <lb/>vix &longs;olui po&longs;&longs;it; cum tamen à nobis facilè &longs;oluatur. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis tertiò, impetum in vtroque muncre cau&longs;æ &longs;ube&longs;&longs;e tantùm <lb/>vni lineæ; &longs;cilicet exigit motum per vnam lineam; cum per plures &longs;i­<lb/>mul motus e&longs;&longs;e non po&longs;&longs;it; ne idem mobile &longs;imul e&longs;&longs;et in pluribus lo­<lb/>cis; & producit impetum per vnam lincam; cum producat tantùm pro­<lb/>pter motum. </s></p><p type="main"> | <s>Ob&longs;eruabis tertiò, impetum in vtroque munere cau&longs;æ &longs;ube&longs;&longs;e tantùm <lb/>vni lineæ; &longs;cilicet exigit motum per vnam lineam; cum per plures &longs;i­<lb/>mul motus e&longs;&longs;e non po&longs;&longs;it; ne idem mobile &longs;imul e&longs;&longs;et in pluribus lo­<lb/>cis; & producit impetum per vnam lineam; cum producat tantùm pro­<lb/>pter motum. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis quartò, alias qualitates, &longs;i quæ &longs;unt, non agere ad extra, <lb/>vt tollant impedimentum &longs;ui effectus ad intra; qui &longs;cilicet ab impedi­<lb/>mento extrin&longs;eco impediri non pote&longs;t; vt accidit in ip&longs;o impetu; etenim <lb/>corpus non pote&longs;t moueri ni&longs;i nouum locum acquirat: neque nouum <lb/>locum acquirere ab alio corpore occupatum, ni&longs;i corpus hoc loco ce­<lb/>dat, neque hoc loco cedere pote&longs;t &longs;ine motu, vel moueri &longs;ine impetu, <lb/>igitur cum impediat motum amoucri debet, accepto dumtaxat impetu <lb/>ab alio mobili. </s></p><p type="main"> | <s>Ob&longs;eruabis quartò, alias qualitates, &longs;i quæ &longs;unt, non agere ad extra, <lb/>vt tollant impedimentum &longs;ui effectus ad intra; qui &longs;cilicet ab impedi­<lb/>mento extrin&longs;eco impediri non pote&longs;t; vt accidit in ip&longs;o impetu; etenim <lb/>corpus non pote&longs;t moueri ni&longs;i nouum locum acquirat: neque nouum <lb/>locum acquirere ab alio corpore occupatum, ni&longs;i corpus hoc loco ce­<lb/>dat, neque hoc loco cedere pote&longs;t &longs;ine motu, vel moueri &longs;ine impetu, <lb/>igitur cum impediat motum amoueri debet, accepto dumtaxat impetu <lb/>ab alio mobili. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis quintò nonnullos e&longs;&longs;e, qui volunt motum vnius corporis <lb/>transferri in aliud corpus; &longs;ed mera e&longs;t metaphora; nihil cnim pror&longs;us <lb/>e&longs;t quod ab vno in aliud tran&longs;eat, &longs;eu transferatur; nec aliud dici po­<lb/>te&longs;t, ni&longs;i quod dictum e&longs;t, impetum &longs;cicilet nouum produci. </s></p><p type="main"> | <s>Ob&longs;eruabis quintò nonnullos e&longs;&longs;e, qui volunt motum vnius corporis <lb/>transferri in aliud corpus; &longs;ed mera e&longs;t metaphora; nihil cnim pror&longs;us <lb/>e&longs;t quod ab vno in aliud tran&longs;eat, &longs;eu transferatur; nec aliud dici po­<lb/>te&longs;t, ni&longs;i quod dictum e&longs;t, impetum &longs;cilicet nouum produci. </s></p><p type="main"> |
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| <s>Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>quæ faciunt lumen, & calorem; quia lumen, & calor &longs;unt veræ qualita­<lb/>tates, non corpu&longs;cula, vt demon&longs;trabimus in 5. tractatu: Adde quod li­<lb/>cet ferrum candens aliud frigidum impellat, etiam veloci&longs;&longs;imè; hoc ip­<lb/>&longs;um æquè frigidum manet; denique in cra&longs;&longs;is tenebris nix &longs;eu glacies <lb/>frigidi&longs;&longs;ima pernici&longs;&longs;imè moueri pote&longs;t: &longs;ed apage i&longs;ta commenta. </s></p><p type="main"> | <s>Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb/>corpus ab alio moueri, quia ab vno in aliud deriuantur corpu&longs;cula illa, <lb/>quæ faciunt lumen, & calorem; quia lumen, & calor &longs;unt veræ qualita­<lb/>tes, non corpu&longs;cula, vt demon&longs;trabimus in 5. tractatu: Adde quod li­<lb/>cet ferrum candens aliud frigidum impellat, etiam veloci&longs;&longs;imè; hoc ip­<lb/>&longs;um æquè frigidum manet; denique in cra&longs;&longs;is tenebris nix &longs;eu glacies <lb/>frigidi&longs;&longs;ima pernici&longs;&longs;imè moueri pote&longs;t: &longs;ed apage i&longs;ta commenta. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Omnes partes impetus mobilis agunt ad extra actione communi.<emph.end type="italics"/></s><s> Probatur <lb/>per Ax. 13. n. </s> | <s><emph type="italics"/>Omnes partes impetus mobilis agunt ad extra actione communi.<emph.end type="italics"/></s><s> Probatur <lb/>per Ax. 13. n. </s> |
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| <s>1. ni&longs;i enim agerent actione communi &longs;ed quælibet &longs;uam <lb/>produceret; cur potius in hac parte &longs;ubiecti, quam in alia, demde ap­<lb/>pìicatur tantùm vna immediatè; Igitur agunt omnes actione commu­<lb/>ni; omnes inquam illæ, quæ impediuntur; cum enim impetus agat <lb/>tantùm ad extrà vt tollat impedimentum &longs;ui motus; ille pro&longs;ectò age­<lb/>re non debet, cuius motus vel effectus non impeditur. </s></p><pb xlink:href="026/01/066.jpg" pagenum="34"/><p type="main"> | <s>1. ni&longs;i enim agerent actione communi &longs;ed quælibet &longs;uam <lb/>produceret; cur potius in hac parte &longs;ubiecti, quam in alia, deinde ap­<lb/>plicatur tantùm vna immediatè; Igitur agunt omnes actione commu­<lb/>ni; omnes inquam illæ, quæ impediuntur; cum enim impetus agat <lb/>tantùm ad extrà vt tollat impedimentum &longs;ui motus; ille pro&longs;ectò age­<lb/>re non debet, cuius motus vel effectus non impeditur. </s></p><pb xlink:href="026/01/066.jpg" pagenum="34"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 49.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Quo minùs impeditur impetus, minùs agit ad extra, & contrà; quo plùs <lb/>impeditur, plùs agit.<emph.end type="italics"/></s><s> Cum enim ideò agat ad extra, vt tollat impedi­<lb/>mentum; certè &longs;i nullum e&longs;t, nihil agit, &longs;i minùs, minùs agit; igitur <lb/>agit pro rata, id e&longs;t, pro diucr&longs;a impedimenti ratione. </s></p><p type="main"> | <s><emph type="italics"/>Quo minùs impeditur impetus, minùs agit ad extra, & contrà; quo plùs <lb/>impeditur, plùs agit.<emph.end type="italics"/></s><s> Cum enim ideò agat ad extra, vt tollat impedi­<lb/>mentum; certè &longs;i nullum e&longs;t, nihil agit, &longs;i minùs, minùs agit; igitur <lb/>agit pro rata, id e&longs;t, pro diuer&longs;a impedimenti ratione. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 50.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 50.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si linea motus, quam directionis appellant, ducatur per centrum vriu&longs;que <lb/>corporis, maximum est impedimentum,<emph.end type="italics"/> vt patet. </s> | <s><emph type="italics"/>Si linea motus, quam directionis appellant, ducatur per centrum vtriu&longs;que <lb/>corporis, maximum est impedimentum,<emph.end type="italics"/> vt patet. </s> |
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| <s>&longs;int enim duo globi, <lb/>A mobilis, & B. occurrens ip&longs;i A, &longs;itque linea directionis DE ducta <lb/>per centrum vtriu&longs;que AB, & punctum contactus &longs;it C; certè glo­<lb/>bus B maximum ponit impedimentum, quod ab eo poni po&longs;&longs;it; Igitur <lb/>impetus globi A agit quantùm pote&longs;t in globum B; vt &longs;cilicet maxi­<lb/>mum impedimentum remoucat. </s></p><p type="main"> | <s>&longs;int enim duo globi, <lb/>A mobilis, & B. occurrens ip&longs;i A, &longs;itque linea directionis DE ducta <lb/>per centrum vtriu&longs;que AB, & punctum contactus &longs;it C; certè glo­<lb/>bus B maximum ponit impedimentum, quod ab eo poni po&longs;&longs;it; Igitur <lb/>impetus globi A agit quantùm pote&longs;t in globum B; vt &longs;cilicet maxi­<lb/>mum impedimentum remoueat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 54.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc eadem cau&longs;a nece&longs;&longs;aria etiam immedia&longs;e applicata diuer&longs;um impe<emph.end type="italics"/><pb xlink:href="026/01/068.jpg" pagenum="36"/><emph type="italics"/>tum producit; vt patet in impetu, non tamen est eodem modo applicata, <lb/>id e&longs;t in eadem linea.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Hinc eadem cau&longs;a nece&longs;&longs;aria etiam immediate applicata diuer&longs;um impe<emph.end type="italics"/><pb xlink:href="026/01/068.jpg" pagenum="36"/><emph type="italics"/>tum producit; vt patet in impetu, non tamen est eodem modo applicata, <lb/>id e&longs;t in eadem linea.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 55.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 55.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc impetus remi&longs;&longs;us potest producere inten&longs;um; & hæc e&longs;t altera diffcul­<lb/>tas; cum &longs;cilicet maior globus in minorem impingitur<emph.end type="italics"/>; cum enim omnes <lb/>partes impetus maioris globi agant actione communi per Th. 46. & <lb/>cum agant quantùm maximè po&longs;&longs;unt; in minore globo, tot partes pro­<lb/>ducunt impetus, quot in maiore, vt patet; igitur in minore globo pau­<lb/>cioribus partibus &longs;ubiecti di&longs;tribuuntur plures partes impetus; crgo in <lb/>qualibet parte &longs;ubiecti &longs;unt plures; &longs;ed hoc e&longs;t e&longs;&longs;e inten&longs;um, vt con&longs;tat, <lb/>igitur impetus remi&longs;&longs;us producit inten&longs;um; quod e&longs;t paradoxon egre­<lb/>gium. </s></p><p type="main"> | <s><emph type="italics"/>Hinc impetus remi&longs;&longs;us potest producere inten&longs;um; & hæc e&longs;t altera difficul­<lb/>tas; cum &longs;cilicet maior globus in minorem impingitur<emph.end type="italics"/>; cum enim omnes <lb/>partes impetus maioris globi agant actione communi per Th. 46. & <lb/>cum agant quantùm maximè po&longs;&longs;unt; in minore globo, tot partes pro­<lb/>ducunt impetus, quot in maiore, vt patet; igitur in minore globo pau­<lb/>cioribus partibus &longs;ubiecti di&longs;tribuuntur plures partes impetus; crgo in <lb/>qualibet parte &longs;ubiecti &longs;unt plures; &longs;ed hoc e&longs;t e&longs;&longs;e inten&longs;um, vt con&longs;tat, <lb/>igitur impetus remi&longs;&longs;us producit inten&longs;um; quod e&longs;t paradoxon egre­<lb/>gium. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis primò, &longs;ingularem impetus proprictatem, quæ alijs qua­<lb/>litatibus minimè competit; nam aliæ qualitates v. <!-- REMOVE S-->g. <!-- REMOVE S-->calor; lumen in <lb/>cadem di&longs;tantia effectum &longs;emper æquè inten&longs;um producunt; &longs;ecus verò <lb/>impetus, qui pro maiori vel minori obice maiorem, vel minorem, hoc <lb/>e&longs;t inten&longs;iorem, vel remi&longs;&longs;iorem impetum in eadem di&longs;tantia producit; <lb/>cuius ratio ex eo capite petitur; quòd impetus agat tantùm ad extra <lb/>propter &longs;uum effectum ad intra, vt &longs;cilicet tollat impedimentum; igi­<lb/>tur in totum, quod impedit, agit; igitur non habet certam, & deter­<lb/>minatam &longs;phæram; cum tantùm agat in obicem, &longs;iue &longs;it maior, &longs;iue <lb/>minor: Quia verò e&longs;t cau&longs;a nece&longs;&longs;aria, æqualem effectum producit, id <lb/>e&longs;t tot partes impetus in maiore, quot in minore, ergo, cum in mino­<lb/>re &longs;int pauciores partes &longs;ubiecti, & plures in maiore; haud dubiè quæli­<lb/>bet pars minoris habebit plures partes effectus, & quælibet pars maio­<lb/>ris pauciores; igitur effectus erit inten&longs;ior in minore, & remi&longs;&longs;ior in <lb/>maiorc. </s> | <s>Ob&longs;eruabis primò, &longs;ingularem impetus proprietatem, quæ alijs qua­<lb/>litatibus minimè competit; nam aliæ qualitates v. <!-- REMOVE S-->g. <!-- REMOVE S-->calor; lumen in <lb/>eadem di&longs;tantia effectum &longs;emper æquè inten&longs;um producunt; &longs;ecus verò <lb/>impetus, qui pro maiori vel minori obice maiorem, vel minorem, hoc <lb/>e&longs;t inten&longs;iorem, vel remi&longs;&longs;iorem impetum in eadem di&longs;tantia producit; <lb/>cuius ratio ex eo capite petitur; quòd impetus agat tantùm ad extra <lb/>propter &longs;uum effectum ad intra, vt &longs;cilicet tollat impedimentum; igi­<lb/>tur in totum, quod impedit, agit; igitur non habet certam, & deter­<lb/>minatam &longs;phæram; cum tantùm agat in obicem, &longs;iue &longs;it maior, &longs;iue <lb/>minor: Quia verò e&longs;t cau&longs;a nece&longs;&longs;aria, æqualem effectum producit, id <lb/>e&longs;t tot partes impetus in maiore, quot in minore, ergo, cum in mino­<lb/>re &longs;int pauciores partes &longs;ubiecti, & plures in maiore; haud dubiè quæli­<lb/>bet pars minoris habebit plures partes effectus, & quælibet pars maio­<lb/>ris pauciores; igitur effectus erit inten&longs;ior in minore, & remi&longs;&longs;ior in <lb/>maiore. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Prætereà, cum dixi omnes partcs mobilis actione communi agere ad <lb/>extra; ita primò intelligi debet, vt omnes illæ partes moueantur: &longs;ecun­<lb/>dò, vt linea motus, &longs;eu directionis per centra grauitatis vtriu&longs;que glo­<lb/>bi v, g. <!-- REMOVE S-->ducatur; alioquin, vel omnes actione communi non agunt, vel <lb/>minus agunt, de quo infrà; &longs;ufficit verò iuxta præ&longs;ens in&longs;titutum, vt <lb/>globus ita impellat alium vel æqualem, vel inæqualem, vt linea dire­<lb/>ctionis ducatur per centrum grauitatis alterius; vide figuram. </s> | <s>Prætereà, cum dixi omnes partes mobilis actione communi agere ad <lb/>extra; ita primò intelligi debet, vt omnes illæ partes moueantur: &longs;ecun­<lb/>dò, vt linea motus, &longs;eu directionis per centra grauitatis vtriu&longs;que glo­<lb/>bi v, g. <!-- REMOVE S-->ducatur; alioquin, vel omnes actione communi non agunt, vel <lb/>minus agunt, de quo infrà; &longs;ufficit verò iuxta præ&longs;ens in&longs;titutum, vt <lb/>globus ita impellat alium vel æqualem, vel inæqualem, vt linea dire­<lb/>ctionis ducatur per centrum grauitatis alterius; vide figuram. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea­<lb/>directionis ducta per centra grauitatis vtriu&longs;que producit in eo æqualem<emph.end type="italics"/>; Pro­<lb/>batur, quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria, quæ tunc agit quantum pote&longs;t <lb/>per Th. 57. &longs;ed æqualis pote&longs;t producere æqualemi. </s> | <s><emph type="italics"/>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea <lb/>directionis ducta per centra grauitatis vtriu&longs;que producit in eo æqualem<emph.end type="italics"/>; Pro­<lb/>batur, quia impetus e&longs;t cau&longs;a nece&longs;&longs;aria, quæ tunc agit quantum pote&longs;t <lb/>per Th. 57. &longs;ed æqualis pote&longs;t producere æqualem: </s> |
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| <s>Probatur primò, <lb/>exemplo aliarum qualitatum; &longs;ecundò, quia ideo agit vt tollat impedi­<lb/>mentum, hoc e&longs;t vt corpus illud amoueat loco; igitur æquali motu per <lb/>&longs;e; alioquin ni&longs;i æquali motu amoueret, non tolleret impedimentum, <lb/>vt pater; tertiò &longs;int 30. partes impetus, certèvel producent plures vel <lb/>pauciores, vel totidem, non plures; cur enim potius 31. quam 32. <lb/>nec etiam pauciores; cur enim potius 20. quam 18, &c. </s> | <s>Probatur primò, <lb/>exemplo aliarum qualitatum; &longs;ecundò, quia ideo agit vt tollat impedi­<lb/>mentum, hoc e&longs;t vt corpus illud amoueat loco; igitur æquali motu per <lb/>&longs;e; alioquin ni&longs;i æquali motu amoueret, non tolleret impedimentum, <lb/>vt pater; tertiò &longs;int 30. partes impetus, certèvel producent plures vel <lb/>pauciores, vel totidem, non plures; cur enim potius 31. quam 32. <lb/>nec etiam pauciores; cur enim potius 20. quam 18, &c. </s> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc reijcics illos, qui volunt à globo æquali produci in æquali &longs;ub­<lb/>duplum impetum; in &longs;ubduplo &longs;ubtriplum; in &longs;ubquadruplo &longs;ubquin­<lb/>tuplum; ratio illorum e&longs;t; quia duo globi æquales in&longs;tanti contactus <lb/>perinde &longs;e habent, atque &longs;i conflarent vnum corpus; &longs;ed &longs;i conflarent <lb/>vnum corpus quilibet &longs;ubduplum impetum haberet; &longs;i verò globus cum <lb/>alio &longs;ubduplo faceret vnum mobilc; haud dubiè minor, id e&longs;t, &longs;ubduplus <lb/>haberet tantùm &longs;ubtriplum impetum; atque ita deinceps; hoc totum <lb/>fal&longs;i&longs;&longs;imum e&longs;t; nam primò &longs;i globus æqualis acciperet tantùm &longs;ubdu­<lb/>plum impetum ab alio, &longs;ubduplo tantùm motu ferretur; igitur &longs;ubdu­<lb/>plum &longs;patium decurreret, quod e&longs;t contra experientiam, & Th. 47. Se­<lb/>cundò, ratio propo&longs;ita nulla e&longs;t; quia quando globus impactus impellit <lb/>alium, e&longs;t veluti potentiâ, quæ cum tota&longs;ua vi, & cum impetu agit, <lb/>cuius nulla pars transfertur in alium globum; nec enim migrat de <lb/>de &longs;ubiecto in &longs;ubiectum, &longs;ed producit &longs;ibi æqualem: equidem &longs;i duo <lb/>globi æquales e&longs;&longs;ent vel coniuncti, vel contigui in linea directionis, <lb/>quilibet pro rata acciperet impetus producti partem à potentia applica­<lb/>ta; &longs;i e&longs;&longs;ent æquales, qui&longs;que &longs;ubduplum: &longs;i alter &longs;ubduplus &longs;ubtri­<lb/>plum, &c. </s> | <s>Hinc reijcis illos, qui volunt à globo æquali produci in æquali &longs;ub­<lb/>duplum impetum; in &longs;ubduplo &longs;ubtriplum; in &longs;ubquadruplo &longs;ubquin­<lb/>tuplum; ratio illorum e&longs;t; quia duo globi æquales in&longs;tanti contactus <lb/>perinde &longs;e habent, atque &longs;i conflarent vnum corpus; &longs;ed &longs;i conflarent <lb/>vnum corpus quilibet &longs;ubduplum impetum haberet; &longs;i verò globus cum <lb/>alio &longs;ubduplo faceret vnum mobile; haud dubiè minor, id e&longs;t, &longs;ubduplus <lb/>haberet tantùm &longs;ubtriplum impetum; atque ita deinceps; hoc totum <lb/>fal&longs;i&longs;&longs;imum e&longs;t; nam primò &longs;i globus æqualis acciperet tantùm &longs;ubdu­<lb/>plum impetum ab alio, &longs;ubduplo tantùm motu ferretur; igitur &longs;ubdu­<lb/>plum &longs;patium decurreret, quod e&longs;t contra experientiam, & Th. 47. Se­<lb/>cundò, ratio propo&longs;ita nulla e&longs;t; quia quando globus impactus impellit <lb/>alium, e&longs;t veluti potentiâ, quæ cum tota&longs;ua vi, & cum impetu agit, <lb/>cuius nulla pars transfertur in alium globum; nec enim migrat de <lb/>de &longs;ubiecto in &longs;ubiectum, &longs;ed producit &longs;ibi æqualem: equidem &longs;i duo <lb/>globi æquales e&longs;&longs;ent vel coniuncti, vel contigui in linea directionis, <lb/>quilibet pro rata acciperet impetus producti partem à potentia applica­<lb/>ta; &longs;i e&longs;&longs;ent æquales, qui&longs;que &longs;ubduplum: &longs;i alter &longs;ubduplus &longs;ubtri­<lb/>plum, &c. </s> |
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| <s>&longs;ed hæc &longs;unt &longs;atis facilia. </s></p><p type="main"> | <s>&longs;ed hæc &longs;unt &longs;atis facilia. </s></p><p type="main"> |
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| <s>Obijci fortè po&longs;&longs;et ab aliquo primò experientia; videmus enim &longs;æpè <lb/>globum impul&longs;um in ludo Tudiculario moueri tardiùs globo impellen­<lb/>te; re&longs;pondeo id &longs;æpè accidere; tùm quia linea directionis non connec­<lb/>tit centra vtriu&longs;que globi; igitur minor e&longs;t ictus per Th 52. tùm quia <lb/>globus impellens, vel impul&longs;us deficiunt à perfecta &longs;phæra; tùm quia <lb/>non e&longs;t perfecta æqualitas globorum; adde quod quò accuratiùs prædi­<lb/>ctæ leges ob&longs;eruantur, ip&longs;i motus ad æqualitatem propiùs accedunt, vt <lb/>con&longs;tat experientia. </s></p><p type="main"> | <s>Obijci fortè po&longs;&longs;et ab aliquo primò experientia; videmus enim &longs;æpè <lb/>globum impul&longs;um in ludo Tudiculario moueri tardiùs globo impellen­<lb/>te; re&longs;pondeo id &longs;æpè accidere; tùm quia linea directionis non connec­<lb/>tit centra vtriu&longs;que globi; igitur minor e&longs;t ictus per Th 52. tùm quia <lb/>globus impellens, vel impul&longs;us deficiunt à perfecta &longs;phæra; tùm quia <lb/>non e&longs;t perfecta æqualitas globorum; adde quod quò accuratiùs prædi­<lb/>ctæ leges ob&longs;eruantur, ip&longs;i motus ad æqualitatem propiùs accedunt, vt <lb/>con&longs;tat experientia. </s></p><p type="main"> |
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| <s>Obiici po&longs;&longs;et &longs;ecundò de&longs;trui aliquid impetus globi impellentis ab ip&longs;o <lb/>ictu, vt con&longs;tat experientia; igitur illa pars impetus, quæ de&longs;truitur, non <lb/>producit nouum impetum in globo impul&longs;o; Re&longs;pondco de&longs;truiquidem <lb/>aliquid impetus in globo impacto, vt videbimus infrà; cum tamen de­<lb/>&longs;truatur tantùm &longs;equenti po&longs;t ictum in&longs;tanti; certè cum exi&longs;tat adhuc <lb/>ip&longs;o in&longs;tanti contactus, nece&longs;&longs;ariò agit, quippe aliquid vltimo in&longs;tanti <lb/>pote&longs;t agere; adde quod illud ip&longs;um repugnat manife&longs;tæ experientiæ; <lb/>licèt enim aliquando de&longs;truatur totus impetus in globo impacto, quod <lb/>&longs;æpè accidit in ludo Tudiculario, nam illicò &longs;i&longs;tit pila eburnea; alius <lb/>tamen globus velociter mouetur, cuius effectus rationem infrà addu­<lb/>cemus. </s></p><p type="main"> | <s>Obiici po&longs;&longs;et &longs;ecundò de&longs;trui aliquid impetus globi impellentis ab ip&longs;o <lb/>ictu, vt con&longs;tat experientia; igitur illa pars impetus, quæ de&longs;truitur, non <lb/>producit nouum impetum in globo impul&longs;o; </s><s>Re&longs;pondeo de&longs;truiquidem <lb/>aliquid impetus in globo impacto, vt videbimus infrà; cum tamen de­<lb/>&longs;truatur tantùm &longs;equenti po&longs;t ictum in&longs;tanti; certè cum exi&longs;tat adhuc <lb/>ip&longs;o in&longs;tanti contactus, nece&longs;&longs;ariò agit, quippe aliquid vltimo in&longs;tanti <lb/>pote&longs;t agere; adde quod illud ip&longs;um repugnat manife&longs;tæ experientiæ; <lb/>licèt enim aliquando de&longs;truatur totus impetus in globo impacto, quod <lb/>&longs;æpè accidit in ludo Tudiculario, nam illicò &longs;i&longs;tit pila eburnea; alius <lb/>tamen globus velociter mouetur, cuius effectus rationem infrà addu­<lb/>cemus. </s></p><p type="main"> |
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| <s>Obijci po&longs;&longs;et tertiò inde &longs;equi progre&longs;&longs;um in infinitum, nam globus <lb/>A impactus in globum B impellet cum æquali motu, & B in C etiam <lb/>æquali, C in D, atque ita deinceps; modò illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rectà ducatur; Re&longs;pondco, vel il-<pb xlink:href="026/01/071.jpg" pagenum="39"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan­<lb/>gant; vel aliquod &longs;patium inter &longs;ingulos intercipi; &longs;i primum, produci­<lb/>tur impetus à potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; non verò <lb/>vnus globus in alio, vt con&longs;tat; &longs;icut duo pondera &longs;imul attollo, quorum <lb/>vnum alteri incumbit: &longs;i verò non &longs;e tangant, dico antequam A im­<lb/>pingatur in B, dum &longs;patium illud interiectum percurrit, amittere aliquid <lb/>impetus: idem dico de B, & C, vnde &longs;i nihil impetus in eo primo motu <lb/>periret & linea directionis omnium centra perfectè connecteret; ita vt <lb/>omnium ictus illi omnino &longs;ine vlla deflexione re&longs;ponderent; haud du­<lb/>biè non po&longs;&longs;ent e&longs;&longs;e tot globi, quin po&longs;&longs;et alius addi, qui ab vltimo <lb/>pelleretur; &longs;ed vix illa omnia de quibus &longs;uprà po&longs;&longs;unt ob&longs;eruari; Hinc <lb/>tamen facilè vna pars aëris aliam pellit, quod di&longs;tinctè videmus in <lb/>aqua; &longs;ed de his aliàs, &longs;ufficiat modò propo&longs;itam obiectionem inde <lb/>manere &longs;olutam. </s></p><p type="main"> | <s>Obijci po&longs;&longs;et tertiò inde &longs;equi progre&longs;&longs;um in infinitum, nam globus <lb/>A impactus in globum B impellet cum æquali motu, & B in C etiam <lb/>æquali, C in D, atque ita deinceps; modò illi globi ita &longs;tatuantur, vt <lb/>linea directionis per omnium centra rectà ducatur; Re&longs;pondco, vel il-<pb xlink:href="026/01/071.jpg" pagenum="39"/>los omnes globos ita e&longs;&longs;e contiguos, vt mutuo contactu &longs;e inuicem tan­<lb/>gant; vel aliquod &longs;patium inter &longs;ingulos intercipi; &longs;i primum, produci­<lb/>tur impetus à potentia motrice in omnibus, &longs;i &longs;ufficiens e&longs;t; non verò <lb/>vnus globus in alio, vt con&longs;tat; &longs;icut duo pondera &longs;imul attollo, quorum <lb/>vnum alteri incumbit: &longs;i verò non &longs;e tangant, dico antequam A im­<lb/>pingatur in B, dum &longs;patium illud interiectum percurrit, amittere aliquid <lb/>impetus: idem dico de B, & C, vnde &longs;i nihil impetus in eo primo motu <lb/>periret & linea directionis omnium centra perfectè connecteret; ita vt <lb/>omnium ictus illi omnino &longs;ine vlla deflexione re&longs;ponderent; haud du­<lb/>biè non po&longs;&longs;ent e&longs;&longs;e tot globi, quin po&longs;&longs;et alius addi, qui ab vltimo <lb/>pelleretur; &longs;ed vix illa omnia de quibus &longs;uprà po&longs;&longs;unt ob&longs;eruari; Hinc <lb/>tamen facilè vna pars aëris aliam pellit, quod di&longs;tinctè videmus in <lb/>aqua; &longs;ed de his aliàs, &longs;ufficiat modò propo&longs;itam obiectionem inde <lb/>manere &longs;olutam. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Globus maior impactus in minorem imprimit illi inten&longs;iorem impetum, & <lb/>velociorem motum per Th.<emph.end type="italics"/> 48. <emph type="italics"/>&<emph.end type="italics"/> 47. Nec e&longs;t quod aliqui opponant Prin­<lb/>cipium illud mechanicum; id e&longs;t, nullum corpus po&longs;le maiorem veloci­<lb/>tatis gradum alteri corpori imprimere; eo &longs;cilicet gradu, quem ip&longs;um <lb/>habet; nec enim inuenio Principium illud apud eos Mechanicos, qui <lb/>mechanica momenta &longs;uarum demon&longs;trationum momentis confirmant; <lb/>quî porro fieri pote&longs;t, vt principium illud admittatur, quod manife&longs;tæ <lb/>experientiæ repugnat? </s> | <s><emph type="italics"/>Globus maior impactus in minorem imprimit illi inten&longs;iorem impetum, & <lb/>velociorem motum per Th.<emph.end type="italics"/> 48. <emph type="italics"/>&<emph.end type="italics"/> 47. Nec e&longs;t quod aliqui opponant Prin­<lb/>cipium illud mechanicum; id e&longs;t, nullum corpus po&longs;&longs;e maiorem veloci­<lb/>tatis gradum alteri corpori imprimere; eo &longs;cilicet gradu, quem ip&longs;um <lb/>habet; nec enim inuenio Principium illud apud eos Mechanicos, qui <lb/>mechanica momenta &longs;uarum demon&longs;trationum momentis confirmant; <lb/>quî porro fieri pote&longs;t, vt principium illud admittatur, quod manife&longs;tæ <lb/>experientiæ repugnat? </s> |
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| <s>Quis enim non vidit vel maius &longs;axum in aliud <lb/>etiam tardo motu impactum maiorem motum, & impetum imprimere? </s> | <s>Quis enim non vidit vel maius &longs;axum in aliud <lb/>etiam tardo motu impactum maiorem motum, & impetum imprimere? </s> |
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| <s><lb/>quis non vidit maiores illas onerarias naues etiam pigro, & tardo motu <lb/>labentes maximum impetum minori occurrenti cymbæ ctiam impri­<lb/>mere? </s> | <s><lb/>quis non vidit maiores illas onerarias naues etiam pigro, & tardo motu <lb/>labentes maximum impetum minori occurrenti cymbæ etiam impri­<lb/>mere? </s> |
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| <s>Rationem habes in Th. 47. &longs;ed dices; igitur aliquis velocitatis <lb/>gradus nullam habet cau&longs;am; igitur e&longs;t à nihilo, quod dici non pote&longs;t. </s> | <s>Rationem habes in Th. 47. &longs;ed dices; igitur aliquis velocitatis <lb/>gradus nullam habet cau&longs;am; igitur e&longs;t à nihilo, quod dici non pote&longs;t. </s> |
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| <s><lb/>Re&longs;pondeo, plures partes impetus non produci in minore globo, quàm <lb/>&longs;int in maiore; igitur nulla pars e&longs;t impetus minoris globi, quæ &longs;ui <lb/>cau&longs;am &longs;ufficientem non habeat; &longs;ed cum partes impetus maioris globi <lb/>di&longs;tribuantur pluribus partibus &longs;ubiecti, faciunt remi&longs;&longs;um impetum, igi­<lb/>tur & tardum; cum &longs;cilicct impetus vnius partis non iuuet motum alte­<lb/>rius per Th. 37. at verò cum partes impetus producti in minore globo <lb/>di&longs;tribuantur paucioribus partibus &longs;ubiecti, faciunt inten&longs;iorem im­<lb/>petum; igitur velociorem motum, quippe omnes producuntur ab <lb/>omnibus illis actione communi per Ax. 17. num. </s> | <s><lb/>Re&longs;pondeo, plures partes impetus non produci in minore globo, quàm <lb/>&longs;int in maiore; igitur nulla pars e&longs;t impetus minoris globi, quæ &longs;ui <lb/>cau&longs;am &longs;ufficientem non habeat; &longs;ed cum partes impetus maioris globi <lb/>di&longs;tribuantur pluribus partibus &longs;ubiecti, faciunt remi&longs;&longs;um impetum, igi­<lb/>tur & tardum; cum &longs;cilicet impetus vnius partis non iuuet motum alte­<lb/>rius per Th. 37. at verò cum partes impetus producti in minore globo <lb/>di&longs;tribuantur paucioribus partibus &longs;ubiecti, faciunt inten&longs;iorem im­<lb/>petum; igitur velociorem motum, quippe omnes producuntur ab <lb/>omnibus illis actione communi per Ax. 17. num. </s> |
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| <s>1. quid clarius. </s></p><p type="main"> | <s>1. quid clarius. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis primò, vtrumque globum e&longs;&longs;e eiu&longs;dem materiæ; &longs;i enim <lb/>&longs;int diuer&longs;æ materiæ, &longs;ecùs accidit, quàm diximus; &longs;i v. <!-- REMOVE S-->g. <!-- REMOVE S-->æncus mi­<lb/>nor pellatur ab cburneo maiore, maiorem motum hic illi non impri­<lb/>met; licèt enim &longs;it maior exten&longs;io eburnci; e&longs;t tamen minus pondus; <lb/>igitur pauciores partes. </s> | <s>Ob&longs;eruabis primò, vtrumque globum e&longs;&longs;e eiu&longs;dem materiæ; &longs;i enim <lb/>&longs;int diuer&longs;æ materiæ, &longs;ecùs accidit, quàm diximus; &longs;i v. <!-- REMOVE S-->g. <!-- REMOVE S-->æneus mi­<lb/>nor pellatur ab eburneo maiore, maiorem motum hic illi non impri­<lb/>met; licèt enim &longs;it maior exten&longs;io eburnei; e&longs;t tamen minus pondus; <lb/>igitur pauciores partes. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Secundò, cos globos accipiendos e&longs;&longs;e, quorum partes, vel non auo­<lb/>lent ab ictu, vel non comprimantur; comprimuntur in plumbeis, <lb/>æncis, & auolant in vitreis; cum enim &longs;it compre&longs;&longs;io, vel partium di­<lb/>ui&longs;io, de&longs;truitur multùm impetus. </s></p><p type="main"> | <s>Secundò, eos globos accipiendos e&longs;&longs;e, quorum partes, vel non auo­<lb/>lent ab ictu, vel non comprimantur; comprimuntur in plumbeis, <lb/>æneis, & auolant in vitreis; cum enim &longs;it compre&longs;&longs;io, vel partium di­<lb/>ui&longs;io, de&longs;truitur multùm impetus. </s></p><p type="main"> |
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| <s>Tcrtiò reiice commentum illorum, qui dicunt corpus illud e&longs;&longs;e ma­<lb/>joris vclocitatis capax, quod plures habet partes materiæ &longs;ub eadem <lb/>quantitate; nam &longs;uppo&longs;ita eadem re&longs;i&longs;tentiæ ratione, omne corpus e&longs;t <lb/>capax illius vclocitatis, cuius alind e&longs;t capax; cum nullus &longs;it motus, quo <lb/>non po&longs;&longs;it dari velocior, & tardior, vt dicemus infrà; immò &longs;it glo­<lb/>bus plumbeus 12. librarum, &longs;it eburncus eiu&longs;dem diametri 2. librarum, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->haud dubiè eadem potentia producet inten&longs;iorem impetum in <lb/>cburnco, vt patet experientia, & ratio con&longs;tat ex dictis; qua&longs;i verò &longs;it <lb/>aliqua materiæ inertia, quæ motum re&longs;puat; licèt fortè maior &longs;it pro­<lb/>portio re&longs;i&longs;tentiæ medij comparatz cum globo cburneo, quàm compa­<lb/>ratæ cum plumbeo; &longs;ed de re&longs;i&longs;tentia de percu&longs;&longs;ionc, & de &longs;patio age­<lb/>mus infra. </s> | <s>Tertiò reiice commentum illorum, qui dicunt corpus illud e&longs;&longs;e ma­<lb/>joris velocitatis capax, quod plures habet partes materiæ &longs;ub eadem <lb/>quantitate; nam &longs;uppo&longs;ita eadem re&longs;i&longs;tentiæ ratione, omne corpus e&longs;t <lb/>capax illius velocitatis, cuius aliud e&longs;t capax; cum nullus &longs;it motus, quo <lb/>non po&longs;&longs;it dari velocior, & tardior, vt dicemus infrà; immò &longs;it glo­<lb/>bus plumbeus 12. librarum, &longs;it eburneus eiu&longs;dem diametri 2. librarum, <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->haud dubiè eadem potentia producet inten&longs;iorem impetum in <lb/>eburneo, vt patet experientia, & ratio con&longs;tat ex dictis; qua&longs;i verò &longs;it <lb/>aliqua materiæ inertia, quæ motum re&longs;puat; licèt fortè maior &longs;it pro­<lb/>portio re&longs;i&longs;tentiæ medij comparatæ cum globo eburneo, quàm compa­<lb/>ratæ cum plumbeo; &longs;ed de re&longs;i&longs;tentia de percu&longs;&longs;ione, & de &longs;patio age­<lb/>mus infra. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 63.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 63.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Omnis globus, qui in alium, qui mouetur impingitur, dum hie mouetur, vt­<lb/>lociùs mouetur eo &c. </s> | <s><emph type="italics"/>Omnis globus, qui in alium, qui mouetur impingitur, dum hic mouetur, ve­<lb/>lociùs mouetur eo &c. </s> |
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| <s>in quem impingitur <emph.end type="italics"/> patet; alioquin numquam a&longs;&longs;equi <lb/>po&longs;&longs;et, quod ex ip&longs;is terminis con&longs;tat. </s></p><p type="main"> | <s>in quem impingitur <emph.end type="italics"/> patet; alioquin numquam a&longs;&longs;equi <lb/>po&longs;&longs;et, quod ex ip&longs;is terminis con&longs;tat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hie impetus neuus preductus miner e&longs;t eo qus preduceretur in codem glob­<lb/>immobili<emph.end type="italics"/>: ratio c&longs;t; quia &longs;i &longs;i&longs;tcret, maius e&longs;&longs;et impedimentum, quia <lb/>totum motum impediret, cuius tantùm partem impedit, dum mouctur, <lb/>licèt paulò tardius; igitur minus agit ad cxtra per Th. 49. </s></p><p type="main"> | <s><emph type="italics"/>Hic impetus nouus productus minor e&longs;t eo qui produceretur in eodem globo <lb/>immobili<emph.end type="italics"/>: ratio e&longs;t; quia &longs;i &longs;i&longs;teret, maius e&longs;&longs;et impedimentum, quia <lb/>totum motum impediret, cuius tantùm partem impedit, dum mouetur , <lb/>licèt paulò tardius; igitur minus agit ad extra per Th. 49. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc paradoxon egregium &longs;i quod aliud; globus percu&longs;&longs;us ab alio eadem <lb/>&longs;emper velocitate mouetur, &longs;iue moueretur in&longs;tanti percu&longs;&longs;ionis, &longs;iue &longs;i­<lb/>&longs;teret.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it globus A quie&longs;cens, cui unprimantur ab alio B 40. gra­<lb/>dus velocitatis: id e&longs;t æqualis impetus impetui percutientis, iam verò <lb/>moueatur A, cum 20. grad. <!-- REMOVE S-->vclocitatis, & B, qui mouetur cum 40. <lb/>impingatur, certè cum impediatur tantùm &longs;ubduplum motus, produce­<lb/>tur tantùm &longs;ubduplum impetus, id c&longs;t 20. qui &longs;i addantur 20. grad. <!-- REMOVE S-->erunt <lb/>40. quæ omnia con&longs;tant per Th.49.48.&c. </s> | <s><emph type="italics"/>Hinc paradoxon egregium &longs;i quod aliud; globus percu&longs;&longs;us ab alio eadem <lb/>&longs;emper velocitate mouetur, &longs;iue moueretur in&longs;tanti percu&longs;&longs;ionis, &longs;iue &longs;i­<lb/>&longs;teret.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it globus A quie&longs;cens, cui imprimantur ab alio B 40. gra­<lb/>dus velocitatis: id e&longs;t æqualis impetus impetui percutientis, iam verò <lb/>moueatur A, cum 20. grad. <!-- REMOVE S-->velocitatis, & B, qui mouetur cum 40. <lb/>impingatur, certè cum impediatur tantùm &longs;ubduplum motus, produce­<lb/>tur tantùm &longs;ubduplum impetus, id e&longs;t 20. qui &longs;i addantur 20. grad. <!-- REMOVE S-->erunt <lb/>40. quæ omnia con&longs;tant per Th.49.48.&c. </s> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc &longs;i &longs;ecundò percutiatur idem globus, &longs;patium totum, quod per­<lb/>currit tùm à primò, tùm à &longs;ecundo ictu e&longs;t maius co, quod à primo ictu <lb/>confeci&longs;&longs;et, &longs;i non fui&longs;&longs;et &longs;ecundò percu&longs;&longs;us; maius inquam &longs;egmento &longs;pa­<lb/>tij interiecto inter primum & &longs;ecundum ictum. </s></p><p type="main"> | <s>Hinc &longs;i &longs;ecundò percutiatur idem globus, &longs;patium totum, quod per­<lb/>currit tùm à primò, tùm à &longs;ecundo ictu e&longs;t maius eo, quod à primo ictu <lb/>confeci&longs;&longs;et, &longs;i non fui&longs;&longs;et &longs;ecundò percu&longs;&longs;us; maius inquam &longs;egmento &longs;pa­<lb/>tij interiecto inter primum & &longs;ecundum ictum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc reiicies aliquos, quorum &longs;ententiam habes apud Doctum Mer­<lb/>&longs;emium, <emph type="italics"/>in prop.<emph.end type="italics"/> 20. <emph type="italics"/>phæn. </s> | <s>Hinc reiicies aliquos, quorum &longs;ententiam habes apud Doctum Mer­<lb/>&longs;emium, <emph type="italics"/>in prop.<emph.end type="italics"/> 20. <emph type="italics"/>phæn. mech. quorum &longs;unt hæc verba; &longs;i malleus pilam <lb/>currentem eodem, ac anteà modo percutiat, nonam &longs;ui motus partem; &longs;i verò <lb/>currentem tertia vice percutiat, vnam vige&longs;imam &longs;eptimam &longs;ui motus par­<lb/>tem ei tribuet, atque ita deinceps.<emph.end type="italics"/></s><s> Supponit primò hæc &longs;ententia mal­<lb/>leum e&longs;&longs;e duplum pilæ percu&longs;&longs;æ. </s> |
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| <s>mech. </s> | |
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| <s>quorum &longs;unt hæc verba; &longs;i malleus pilam <lb/>currentem eodem, ac anteà modo percutiat, nonam &longs;ui motus partem; &longs;i verò <lb/>currentem tertia vice percutiat, vnam vige&longs;imam &longs;eptimam &longs;ui motus par­<lb/>tem ei tribuet, atque ita deinceps.<emph.end type="italics"/></s><s> Supponit primò hæc &longs;ententia mal­<lb/>leum e&longs;&longs;e duplum pilæ percu&longs;&longs;æ. </s> | <s>Secundò, malleum imprimere pilæ &longs;ub­<lb/>duplæ &longs;ubtriplum motum; quod fal&longs;um e&longs;t, vt con&longs;tat ex Th 6. & Co­<lb/>roll. </s> |
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| <s>Secundò, mallcum imprimere pilæ &longs;ub­<lb/>duplæ &longs;ubtriplum motum; quod fal&longs;um e&longs;t, vt con&longs;tat ex Th 6. & Co­<lb/>roll. </s> | <s>1. Præterea, licètin primà percu&longs;&longs;ione imprimeret tantùm prædi­<lb/>ctæ pilæ &longs;ubtriplum impetum, in &longs;ecunda percu&longs;&longs;ione maiorem impri­<lb/>meret po&longs;t longiorem motum, vbi iam ad quietem propiùs accedit; mi­<lb/>norem verò paulò po&longs;t initium motus, vt con&longs;tat ex dictis, & ex ip&longs;a ex­<lb/>perientia; pote&longs;t quidem in aliquo puncto &longs;ui motus &longs;ecunda vice per­<lb/>cuti, in quo &longs;ubtriplum tantùm motum imprimet; hoc e&longs;t eo in&longs;tanti­<lb/>quo tantùm ami&longs;it tertiam fui impetus partem; tum deinde in tertia <lb/>percu&longs;&longs;ione pote&longs;t tantùm (1/27) motus partem illi tribuere; eo &longs;cilicet in­<lb/>&longs;tanti, quo tantùm ami&longs;it (1/27) &longs;ui impetus partem; &longs;ed in alijs temporis <lb/>punctis longè alia erit impetus producti ratio; Igitur tota hæc progre&longs;­<lb/>&longs;io gratis omninò fuit excogitata. </s></p><p type="main"> |
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| <s>1. Præterea, licètin primà percu&longs;&longs;ione imprimeret tantùm prædi­<lb/>ctæ pilæ &longs;ubtriplum impetum, in &longs;ecunda percu&longs;&longs;ione maiorem impri­<lb/>meret po&longs;t longiorem motum, vbi iam ad quictem propiùs accedit; mi­<lb/>norem verò paulò po&longs;t initium motus, vt con&longs;tat ex dictis, & exip&longs;a ex­<lb/>perientia; potc&longs;t quidem in aliquo puncto &longs;ui motus &longs;ecunda vice per­<lb/>cuti, in quo &longs;ubtriplum tantùm motum imprimet; hoc e&longs;t eo in&longs;tanti­<lb/>quo tantùm ami&longs;it tertiam fui impetus partem; tum deindc in tertia <lb/>percu&longs;&longs;ione pote&longs;t tantùm (1/27) motus partem illi tribuere; eo &longs;cilicet in­<lb/>&longs;tanti, quo tantùm ami&longs;it (1/27) &longs;ui impetus partem; &longs;ed in alijs cemporis <lb/>punctis longè alia crit impetus producti ratio; Igitur tota hæc progre&longs;­<lb/>&longs;io gratis omninò fuit excogitata. </s></p><p type="main"> | |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc ctiam po&longs;t &longs;ecundam percu&longs;&longs;ioncm æquale &longs;patium conficier al­<lb/>teri, quod iam confecit po&longs;t primam æqualibus temporibus; igitur æqua­<lb/>lis e&longs;t velocitas vtriu&longs;que motus; quia &longs;cilicet, &longs;i e&longs;t æqualis impetus, e&longs;t <lb/>qualis motus: Ex his maximam carum dubitationum partem &longs;oluere po­<lb/>teris quæ in eadem Mer&longs;enni propo&longs;itione courinentur reliquas vero ex <lb/>dicendis infrà. </s></p><pb xlink:href="026/01/074.jpg" pagenum="42"/><p type="main"> | <s>Hinc etiam po&longs;t &longs;ecundam percu&longs;&longs;ionem æquale &longs;patium conficiet al­<lb/>teri, quod iam confecit po&longs;t primam æqualibus temporibus; igitur æqua­<lb/>lis e&longs;t velocitas vtriu&longs;que motus; quia &longs;cilicet, &longs;i e&longs;t æqualis impetus, e&longs;t <lb/>qualis motus: Ex his maximam carum dubitationum partem &longs;oluere po­<lb/>teris quæ in eadem Mer&longs;enni propo&longs;itione courinentur reliquas vero ex <lb/>dicendis infrà. </s></p><pb xlink:href="026/01/074.jpg" pagenum="42"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ex dictis ctiam colliges diuer&longs;as percu&longs;&longs;ionum rationes &longs;uppo&longs;ita di­<lb/>uer&longs;a ratione ponderum globi percutientis, & percu&longs;&longs;i; cum enim impe­<lb/>tus productus &longs;it æqualis per &longs;e impetui producenti, per Th.60. modò <lb/>debita fiat applicatio, de qua in Th.50. &longs;i percutiens &longs;it duplus percu&longs;&longs;i, <lb/>&longs;uppo&longs;ita eadem materia, motus percu&longs;&longs;i erit duplò velocior; quia im­<lb/>petus erit duplò inten&longs;ior, vt con&longs;tat ex Th. 61. &longs;i verò &longs;it quadruplus, <lb/>quadruplo, &c. </s> | <s>Ex dictis etiam colliges diuer&longs;as percu&longs;&longs;ionum rationes &longs;uppo&longs;ita di­<lb/>uer&longs;a ratione ponderum globi percutientis, & percu&longs;&longs;i; cum enim impe­<lb/>tus productus &longs;it æqualis per &longs;e impetui producenti, per Th.60. modò <lb/>debita fiat applicatio, de qua in Th.50. &longs;i percutiens &longs;it duplus percu&longs;&longs;i, <lb/>&longs;uppo&longs;ita eadem materia, motus percu&longs;&longs;i erit duplò velocior; quia im­<lb/>petus erit duplò inten&longs;ior, vt con&longs;tat ex Th. 61. &longs;i verò &longs;it quadruplus, <lb/>quadruplo, &c. </s> |
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| <s>Igitur velocitates motuum &longs;unt in ratiòne ponderum <lb/>permutando. </s></p><p type="main"> | <s>Igitur velocitates motuum &longs;unt in ratiòne ponderum <lb/>permutando. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si corpus percu&longs;&longs;um &longs;it oblongum, & percu&longs;&longs;io fiat in centro grauitatis eiu&longs;­<lb/>dem corpois; producitur impetus in percu&longs;&longs;io æqualis impetui percutientis<emph.end type="italics"/>; &longs;ed <lb/>opus e&longs;t aliqua figura: Sit corpus AD, parallelipedum; diuidatur æqua­<lb/>liter in E ita vt E &longs;it centrum grauitatis; &longs;i percu&longs;&longs;io &longs;iat in E per lineam <lb/>perpendicularem HE, producetur impetus in corpore AD æqualis im­<lb/>petui corporis percutientis; quia &longs;cilicet à corpore AD non pote&longs;t maius <lb/>e&longs;&longs;e impedimentum; igitur agit quantùm pote&longs;t impetus corporis per­<lb/>cutientis per Th.50. igitur producit æqualem per Th.69. </s></p><p type="main"> | <s><emph type="italics"/>Si corpus percu&longs;&longs;um &longs;it oblongum, & percu&longs;&longs;io fiat in centro grauitatis eiu&longs;­<lb/>dem corporis; producitur impetus in percu&longs;&longs;io æqualis impetui percutientis<emph.end type="italics"/>; &longs;ed <lb/>opus e&longs;t aliqua figura: Sit corpus AD, parallelipedum; diuidatur æqua­<lb/>liter in E ita vt E &longs;it centrum grauitatis; &longs;i percu&longs;&longs;io fiatin E per lineam <lb/>perpendicularem HE, producetur impetus in corpore AD æqualis im­<lb/>petui corporis percutientis; quia &longs;cilicet à corpore AD non pote&longs;t maius <lb/>e&longs;&longs;e impedimentum; igitur agit quantùm pote&longs;t impetus corporis per­<lb/>cutientis per Th.50. igitur producit æqualem per Th.69. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si percu&longs;&longs;io fiat in<emph.end type="italics"/> F <emph type="italics"/>per lineam perpendicularem<emph.end type="italics"/> IF, <emph type="italics"/>minus erit impedi­<lb/>mentum, quàm per<emph.end type="italics"/> HE, Quia &longs;i per HE, moueri tantùm pote&longs;t motu <lb/>recto, &longs;i per IF, etiam motu circulari circa aliquod centrum; &longs;ed hic <lb/>motus e&longs;t facilior quam ille; igitur minus e&longs;t impedimentum; (&longs;uppono <lb/>autem cylindrum BC vtroque modo moueri po&longs;&longs;e ab applicata potentia) <lb/>igitur minùs impetus producitur, &longs;i percu&longs;&longs;io fiat per IF, quàm &longs;i fiat <lb/>per LK: In qua verò proportione &longs;it minus impedimentum, & minori <lb/>opus impetu, po&longs;ito eodem potentiæ ni&longs;u, determinabimus facilè aliàs; <lb/>vt etiam demon&longs;trabimus circa quod centrum hic circularis motus ficri <lb/>debeat. </s></p><p type="main"> | <s><emph type="italics"/>Si percu&longs;&longs;io fiat in<emph.end type="italics"/> F <emph type="italics"/>per lineam perpendicularem<emph.end type="italics"/> IF, <emph type="italics"/>minus erit impedi­<lb/>mentum, quàm per<emph.end type="italics"/> HE, Quia &longs;i per HE, moueri tantùm pote&longs;t motu <lb/>recto, &longs;i per IF, etiam motu circulari circa aliquod centrum; &longs;ed hic <lb/>motus e&longs;t facilior quam ille; igitur minus e&longs;t impedimentum; (&longs;uppono <lb/>autem cylindrum BC vtroque modo moueri po&longs;&longs;e ab applicata potentia) <lb/>igitur minùs impetus producitur, &longs;i percu&longs;&longs;io fiat per IF, quàm &longs;i fiat <lb/>per LK: In qua verò proportione &longs;it minus impedimentum, & minori <lb/>opus impetu, po&longs;ito eodem potentiæ ni&longs;u, determinabimus facilè aliàs; <lb/>vt etiam demon&longs;trabimus circa quod centrum hic circularis motus fieri <lb/>debeat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ex duobus capitibus minus e&longs;&longs;e pote&longs;t impedimentum; primum e&longs;t, <lb/>quod petitur à puncto contactus, &longs;ecundum à linea incidentiæ; v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>accipiatur punctum E, in quo e&longs;t centrum grauitatis corporis AD, & in <lb/>eo &longs;iat percu&longs;&longs;io; maximum e&longs;t impedimentum ratione puncti conta­<lb/>ctus, in quo fit percu&longs;&longs;io; &longs;i verò percu&longs;&longs;io fiat per lincam perpendicu­<lb/>larem HE, maximum e&longs;t impedimentum, ratione lineæ; &longs;i autem ex <lb/>vtroque capite &longs;imul accidat impedimentum, maximum e&longs;t omnium; <lb/>iam verò &longs;i accipiatur punctum E, & linea percu&longs;sionis ME; minor e&longs;t <lb/>percu&longs;sio ratione lineæ non puncti; accipiatur punctum N, & linea <lb/>percu&longs;sionis MN, minor e&longs;t percu&longs;sio ratione puncti non lineæ, acci­<lb/>piatur punctum N, & linea IN, minor e&longs;t percu&longs;sio ratione vtriu&longs;que; <lb/>&longs;i demum accipiatur punctum E, & linea ME, minor e&longs;t percu&longs;sio ra-<pb xlink:href="026/01/075.jpg" pagenum="43"/>tione lineæ non puncti; accipiatur punctum N linea percu&longs;&longs;ionis MN, <lb/>minor e&longs;t percu&longs;&longs;io ratione puncti non lineæ; &longs;i accipiatur punctum N, <lb/>& linea IN, minor e&longs;t percu&longs;&longs;io ratione vtriu&longs;que: &longs;i demum accipia­<lb/>tur punctum E & linea HE, maior e&longs;t percu&longs;&longs;io ratione vtriu&longs;que; igi­<lb/>tur &longs;unt quatuor coniugationes; &longs;eu quatuor cla&longs;&longs;es diucr&longs;arum percu&longs;­<lb/>&longs;ionum. </s> | <s>Ex duobus capitibus minus e&longs;&longs;e pote&longs;t impedimentum; primum e&longs;t, <lb/>quod petitur à puncto contactus, &longs;ecundum à linea incidentiæ; v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>accipiatur punctum E, in quo e&longs;t centrum grauitatis corporis AD, & in <lb/>eo fiat percu&longs;&longs;io; maximum e&longs;t impedimentum ratione puncti conta­<lb/>ctus, in quo fit percu&longs;&longs;io; &longs;i verò percu&longs;&longs;io fiat per lineam perpendicu­<lb/>larem HE, maximum e&longs;t impedimentum, ratione lineæ; &longs;i autem ex <lb/>vtroque capite &longs;imul accidat impedimentum, maximum e&longs;t omnium; <lb/>iam verò &longs;i accipiatur punctum E, & linea percu&longs;sionis ME; minor e&longs;t <lb/>percu&longs;sio ratione lineæ non puncti; accipiatur punctum N, & linea <lb/>percu&longs;sionis MN, minor e&longs;t percu&longs;sio ratione puncti non lineæ, acci­<lb/>piatur punctum N, & linea IN, minor e&longs;t percu&longs;sio ratione vtriu&longs;que; <lb/>&longs;i demum accipiatur punctum E, & linea ME, minor e&longs;t percu&longs;sio ra­<pb xlink:href="026/01/075.jpg" pagenum="43"/>tione lineæ non puncti; accipiatur punctum N linea percu&longs;&longs;ionis MN, <lb/>minor e&longs;t percu&longs;&longs;io ratione puncti non lineæ; &longs;i accipiatur punctum N, <lb/>& linea IN, minor e&longs;t percu&longs;&longs;io ratione vtriu&longs;que: &longs;i demum accipia­<lb/>tur punctum E & linea HE, maior e&longs;t percu&longs;&longs;io ratione vtriu&longs;que; igi­<lb/>tur &longs;unt quatuor coniugationes; &longs;eu quatuor cla&longs;&longs;es diuer&longs;arum percu&longs;­<lb/>&longs;ionum. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Corpus oblongum parallelipedum percutiens aliud corpus, putà globu&mtail;, <lb/>motu recto per lineam directionis, quæ producta à puncto contactus ducitur per <lb/>centrum globi, dum fiat contactus in centro grauitatis parallelipedi, maximum <lb/>ictum infligit, &longs;eu agit quæntùm pote&longs;t.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it parallelipedum EB; quod <lb/>moueatur motu recto parallclo, lineis CD, HG, &c. </s> | <s><emph type="italics"/>Corpus oblongum parallelipedum percutiens aliud corpus, putà globu&mtail;, <lb/>motu recto per lineam directionis, quæ producta à puncto contactus ducitur per <lb/>centrum globi, dum fiat contactus in centro grauitatis parallelipedi, maximum <lb/>ictum infligit, &longs;eu agit quantùm pote&longs;t.<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;it parallelipedum EB; quod <lb/>moueatur motu recto parallelo, lineis CD, HG, &c. </s> |
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| | <s>&longs;itque globus in <lb/>D; haud dubiè agit quantùm pote&longs;t, quia &longs;cilicet e&longs;t maximum impedi­<lb/>mentum per Th.68. Tam enim globus in D impedit motum paralleli­<lb/>pedi, quàm parallelipedum motum globi impacti per lineam ID; impedit <lb/>inquam ratione oppo&longs;itionis; quia centra grauitatis vtriu&longs;que con­<lb/>currunt in eadem linea; igitur &longs;i maximum e&longs;t impedimentum, agit <lb/>quantùm pote&longs;t Th. 50. hinc producitur impetus æqualis per Th.60. </s></p><p type="main"> |
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| <s>&longs;itque globus in <lb/>D; haud dubiè agit quantùm pote&longs;t, quia &longs;cilicet e&longs;t maximum impedi­<lb/>mentum per Th.68. Tam enim globus in D impedit motum parallcli­<lb/>pedi, quàm parallclip edum motum globi impacti per lineam ID; impedit <lb/>inquam ratione oppo&longs;itionis; quia centra grauitatis vtriu&longs;que con­<lb/>currunt in eadem linea; igitur &longs;i maximum e&longs;t impedimentum, agit <lb/>quantùm pote&longs;t Th. 50. hinc producitur impetus æqualis per Th.60. </s></p><p type="main"> | |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si percu&longs;&longs;io fiat in G, id e&longs;t &longs;i globus e&longs;&longs;et in G, producetur minor impetus, <lb/>& in<emph.end type="italics"/> M <emph type="italics"/>adhuc minor<emph.end type="italics"/>; vt con&longs;tat ex dictis in &longs;uperioribus Theorematis; <lb/>in qua vero proportionc determinabimus aliàs. </s></p><p type="main"> | <s><emph type="italics"/>Si percu&longs;&longs;io fiat in G, id e&longs;t &longs;i globus e&longs;&longs;et in G, producetur minor impetus, <lb/>& in<emph.end type="italics"/> M <emph type="italics"/>adhuc minor<emph.end type="italics"/>; vt con&longs;tat ex dictis in &longs;uperioribus Theorematis; <lb/>in qua vero proportione determinabimus aliàs. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si corpus percutiens non &longs;it par allelipedum, &longs;ed alterius &longs;iguræ v.g.<emph.end type="italics"/> <emph type="italics"/>trigo­<lb/>non,<emph.end type="italics"/> ADE, &longs;itque maioris facilitatis gratia Orthonium; eiu&longs;que motus <lb/>&longs;it parallelus lineis ED, BC: &longs;it autem DA dupla DE; &longs;itque diui&longs;a to­<lb/>ta DA æqualiter in C, in C non erit maximus ictus; quia in C non <pb xlink:href="026/01/076.jpg" pagenum="44"/>e&longs;t centrum grauitatis, vt patet; vt autem habeatur centrum impre&longs;&longs;io­<lb/>nis; a&longs;&longs;umatur AN media proportionalis inter totam AD, & &longs;ubdu­<lb/>plum AC; certè cum triangulum ANO &longs;it &longs;ubduplum totius ADE, <lb/>vt con&longs;tat ex Geometria, & æquale trapezo ND EO; erit impetus in <lb/>vtroque æqualis; igitur in N erit centrum impre&longs;&longs;ionis, vel impetus; vt <lb/>autem habeatur centrum percu&longs;&longs;ionis; in quo &longs;cilicet maximus ictus in­<lb/>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb/>DE, centrum percu&longs;&longs;ionis erit in I; quippe in I totus impeditur impetus <lb/>grauitatis vtrimque, cum &longs;it in æquilibrio; quomodo verò inueniatur <lb/>punctum H facilè habetur ex Archimede, ductis &longs;cilicet AF, DB, quæ <lb/>diuidant bifariam æqualiter DE, EA; vel a&longs;&longs;umpta AI dupla ID, quod <lb/>demon&longs;trabimus in Mechan. <!-- KEEP S--></s></p><p type="main"> | <s><emph type="italics"/>Si corpus percutiens non &longs;it parallelipedum, &longs;ed alterius figuræ v.g.<emph.end type="italics"/> <emph type="italics"/>trigo­<lb/>non,<emph.end type="italics"/> ADE, &longs;itque maioris facilitatis gratia Orthonium; eiu&longs;que motus <lb/>&longs;it parallelus lineis ED, BC: &longs;it autem DA dupla DE; &longs;itque diui&longs;a to­<lb/>ta DA æqualiter in C, in C non erit maximus ictus; quia in C non <pb xlink:href="026/01/076.jpg" pagenum="44"/>e&longs;t centrum grauitatis, vt patet; vt autem habeatur centrum impre&longs;&longs;io­<lb/>nis; a&longs;&longs;umatur AN media proportionalis inter totam AD, & &longs;ubdu­<lb/>plum AC; certè cum triangulum ANO &longs;it &longs;ubduplum totius ADE, <lb/>vt con&longs;tat ex Geometria, & æquale trapezo ND EO; erit impetus in <lb/>vtroque æqualis; igitur in N erit centrum impre&longs;&longs;ionis, vel impetus; vt <lb/>autem habeatur centrum percu&longs;&longs;ionis; in quo &longs;cilicet maximus ictus in­<lb/>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb/>DE, centrum percu&longs;&longs;ionis erit in I; quippe in I totus impeditur impetus <lb/>grauitatis vtrimque, cum &longs;it in æquilibrio; quomodo verò inueniatur <lb/>punctum H facilè habetur ex Archimede, ductis &longs;cilicet AF, DB, quæ <lb/>diuidant bifariam æqualiter DE, EA; vel a&longs;&longs;umpta AI dupla ID, quod <lb/>demon&longs;trabimus in Mechan. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"/> CA, <emph type="italics"/>diuer&longs;a e&longs;t <lb/>ratio percu&longs;&longs;ionum ab ea, quàm &longs;uprà propo&longs;uimus<emph.end type="italics"/>; moucatur enim circa <lb/>centrum C, fitque CA diui&longs;a bifariam in B, haud dubiè punctum A <lb/>faciet arcum AE eo tempore, quò punctum B faciet BD &longs;ubduplum <lb/>AE; igitur punctum A duplò velociùs mouetur quàm B, vt con&longs;tat; igi­<lb/>tur habet duplò maiorem impetum; cum effectum habeat duplò maio­<lb/>rem per Ax. 13. n. </s> | <s><emph type="italics"/>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"/> CA, <emph type="italics"/>diuer&longs;a e&longs;t <lb/>ratio percu&longs;&longs;ionum ab ea, quàm &longs;uprà propo&longs;uimus<emph.end type="italics"/>; moueatur enim circa <lb/>centrum C, fitque CA diui&longs;a bifariam in B, haud dubiè punctum A <lb/>faciet arcum AE eo tempore, quò punctum B faciet BD &longs;ubduplum <lb/>AE; igitur punctum A duplò velociùs mouetur quàm B, vt con&longs;tat; igi­<lb/>tur habet duplò maiorem impetum; cum effectum habeat duplò maio­<lb/>rem per Ax. 13. n. </s> |
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| <s>4. igitur cum totus motus &longs;egmenti AB &longs;it ad to­<lb/>tum motum &longs;egmenti BC, vt &longs;patia acqui&longs;ita; certè &longs;patia acqui&longs;ita <lb/>&longs;unt vt arcus; igitur & trapezus BAED, continet 3/4 totius CAE, vt <lb/>con&longs;tat; &longs;unt enim &longs;ectores &longs;imilis in ratione duplicata radiorum; igi­<lb/>tur totus motus &longs;egmenti BC &longs;ubquadruplus motus totius CA;, gitur <lb/>& impetus; vt autem habeatur centrum impre&longs;&longs;ionis, vel impetus; &longs;it &longs;e­<lb/>ctor CHI, &longs;ubduplus totius CAE quod quomodo fiat, patet ex Geo­<lb/>metria; accipiatur tantùm &longs;ubdupla diagonalis quadrati lateris CA, igi­<lb/>tur in puncto H e&longs;t centrum impre&longs;&longs;ionis, &longs;eu media proportionalis in­<lb/>ter totam CA, & &longs;ubduplam CB: vt autem habeatur percu&longs;&longs;ionis, a&longs;­<lb/>&longs;umatur CY dupla YA; Dico punctum Y e&longs;&longs;c centrum percu&longs;&longs;ionis; <lb/>quia perinde &longs;e habet, atque &longs;i e&longs;&longs;et trianguli cadentis ictus, vt demon­<lb/>&longs;trabimus aliàs nunc tantùm indica&longs;&longs;e &longs;ufficiat. </s></p><p type="main"> | <s>4. igitur cum totus motus &longs;egmenti AB &longs;it ad to­<lb/>tum motum &longs;egmenti BC, vt &longs;patia acqui&longs;ita; certè &longs;patia acqui&longs;ita <lb/>&longs;unt vt arcus; igitur & trapezus BAED, continet 3/4 totius CAE, vt <lb/>con&longs;tat; &longs;unt enim &longs;ectores &longs;imilis in ratione duplicata radiorum; igi­<lb/>tur totus motus &longs;egmenti BC &longs;ubquadruplus motus totius CA; igitur <lb/>& impetus; vt autem habeatur centrum impre&longs;&longs;ionis, vel impetus; &longs;it &longs;e­<lb/>ctor CHI, &longs;ubduplus totius CAE quod quomodo fiat, patet ex Geo­<lb/>metria; accipiatur tantùm &longs;ubdupla diagonalis quadrati lateris CA, igi­<lb/>tur in puncto H e&longs;t centrum impre&longs;&longs;ionis, &longs;eu media proportionalis in­<lb/>ter totam CA, & &longs;ubduplam CB: vt autem habeatur percu&longs;&longs;ionis, a&longs;­<lb/>&longs;umatur CY dupla YA; </s> |
| | <s>Dico punctum Y e&longs;&longs;e centrum percu&longs;&longs;ionis; <lb/>quia perinde &longs;e habet, atque &longs;i e&longs;&longs;et trianguli cadentis ictus, vt demon­<lb/>&longs;trabimus aliàs nunc tantùm indica&longs;&longs;e &longs;ufficiat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc etiam&longs;oluctur, quod proponunt aliqui; &longs;eu potiùs quærunt; <lb/>in quà &longs;cilicet parte maiorem ictum infligat en&longs;is; &longs;i enim &longs;it ciu&longs;dem <lb/>cra&longs;&longs;itici in omnibus &longs;uis partibus, idem dicendum e&longs;t quod de cylin­<lb/>dro CA; &longs;i verò in mucronem de&longs;inat, inueniemus etiam centrum <lb/>percu&longs;&longs;ionis. </s></p><p type="main"> | <s>Hinc etiam &longs;oluetur, quod proponunt aliqui; &longs;eu potiùs quærunt; <lb/>in quà &longs;cilicet parte maiorem ictum infligat en&longs;is; &longs;i enim &longs;it eiu&longs;dem <lb/>cra&longs;&longs;itiei in omnibus &longs;uis partibus, idem dicendum e&longs;t quod de cylin­<lb/>dro CA; &longs;i verò in mucronem de&longs;inat, inueniemus etiam centrum <lb/>percu&longs;&longs;ionis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hîc ob&longs;erua nouum di&longs;crimen, quod intercedit inter impetum, & <lb/>alias qualitates; quæ fortè non po&longs;&longs;unt intendi in infinitum, ratio di&longs;­<lb/>criminis e&longs;t, quia totus calor exten&longs;us in maiore &longs;ubiecto non pote&longs;t <lb/>produci in minore, in quo eadem cau&longs;a cumdem &longs;emper effectum pro­<lb/>ducit; quia &longs;cilicet agit vniformiter difformiter; at verò impetus exten­<lb/>&longs;us in magno <expan abbr="den&longs;o&qacute;ue">den&longs;oque</expan> malleo pote&longs;t producere æqualem in maximâ <lb/>ferè pilâ. </s></p><p type="main"> | <s>Hîc ob&longs;erua nouum di&longs;crimen, quod intercedit inter impetum, & <lb/>alias qualitates; quæ fortè non po&longs;&longs;unt intendi in infinitum, ratio di&longs;­<lb/>criminis e&longs;t, quia totus calor exten&longs;us in maiore &longs;ubiecto non pote&longs;t <lb/>produci in minore, in quo eadem cau&longs;a eumdem &longs;emper effectum pro­<lb/>ducit; quia &longs;cilicet agit vniformiter difformiter; at verò impetus exten­<lb/>&longs;us in magno <expan abbr="den&longs;o&qacute;ue">den&longs;oque</expan> malleo pote&longs;t producere æqualem in maximâ <lb/>ferè pilâ. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus &longs;imilis, id e&longs;t, ad eamdem lineam determinatus, & æqualis in in­<lb/>ten&longs;ione, non pote&longs;t intendere alium &longs;imilem<emph.end type="italics"/>; Probatur, quia agit tantùm ad <lb/>extra, vt tollat impedimentum per Th. 44. &longs;ed eorum mobilium, quæ <lb/>ver&longs;us eamdem partem pari velocitate mouentur, neutrum impedit al­<lb/>terius motum, vt con&longs;tat; igitur impetus &longs;imilis, &c. </s></p><p type="main"> | <s><emph type="italics"/>Impetus &longs;imilis, id e&longs;t, ad <expan abbr="eãdem">eandem</expan> lineam determinatus, & æqualis in in­<lb/>ten&longs;ione, non pote&longs;t intendere alium &longs;imilem<emph.end type="italics"/>; Probatur, quia agit tantùm ad <lb/>extra, vt tollat impedimentum per Th. 44. &longs;ed eorum mobilium, quæ <lb/>ver&longs;us <expan abbr="eãdem">eandem</expan> partem pari velocitate mouentur, neutrum impedit al­<lb/>terius motum, vt con&longs;tat; igitur impetus &longs;imilis, &c. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;erua de impetu &longs;imili id tantùm dici; &longs;imili inquam id e&longs;t non <lb/>modò eiu&longs;dem inten&longs;ionis; &longs;ed etiam eiu&longs;dem lineæ: &longs;i enim alterum <lb/>de&longs;it, haud dubiè &longs;imilis impetus non e&longs;t; &longs;ic impetus quatuor grad. <!-- REMOVE S-->in­<lb/>tendere pote&longs;t impetum duorum graduum; licèt vterque ad eamdem li­<lb/>neam &longs;it determinatus; &longs;i verò ad diuer&longs;as lineas determinentur; etiam <lb/>impetus vt duo pote&longs;t intendere impetum vt quatuor. </s> | <s>Ob&longs;erua de impetu &longs;imili id tantùm dici; &longs;imili inquam id e&longs;t non <lb/>modò eiu&longs;dem inten&longs;ionis; &longs;ed etiam eiu&longs;dem lineæ: &longs;i enim alterum <lb/>de&longs;it, haud dubiè &longs;imilis impetus non e&longs;t; &longs;ic impetus quatuor grad. <!-- REMOVE S-->in­<lb/>tendere pote&longs;t impetum duorum graduum; licèt vterque ad <expan abbr="eãdem">eandem</expan> li­<lb/>neam &longs;it determinatus; &longs;i verò ad diuer&longs;as lineas determinentur; etiam <lb/>impetus vt duo pote&longs;t intendere impetum vt quatuor. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Exten&longs;io impetus respondet extentioni &longs;ui &longs;nbiecti, &longs;cilicet mobilis<emph.end type="italics"/>; cum <lb/>enim extra &longs;ubjectum e&longs;&longs;e non po&longs;&longs;it, cum &longs;it qualitas; certè ibi e&longs;t, vbi <lb/>&longs;ubjectum e&longs;t; nam penetratur accidens cum ip&longs;o &longs;ujecto. </s></p><p type="main"> | <s><emph type="italics"/>Exten&longs;io impetus respondet extentioni &longs;ui &longs;ubiecti, &longs;cilicet mobilis<emph.end type="italics"/>; cum <lb/>enim extra &longs;ubjectum e&longs;&longs;e non po&longs;&longs;it, cum &longs;it qualitas; certè ibi e&longs;t, vbi <lb/>&longs;ubjectum e&longs;t; nam penetratur accidens cum ip&longs;o <expan abbr="&longs;ujecto">&longs;ubjecto</expan>. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scolium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 77.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 77.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Datur impetus altero impetu perfectior &longs;ecundum entitatem<emph.end type="italics"/>; dixi &longs;ecun­<lb/>dum entitatem; quia iam dictum e&longs;t &longs;uprà dari perfectiorem &longs;ecundum <lb/>inten&longs;ionem; huius Theorematis veritas mihi maximè demon&longs;tranda <lb/>e&longs;t, ex quo tàm multa infrà deducemus; &longs;ic autem probamus; Quotie&longs;­<lb/>cunque mouetur corpus, producuntur &longs;altem tot partes impetus quot <lb/>&longs;unt partes mobilis per Th. 33. Quotie&longs;cunque producuntur in mobili <lb/>tot partes impetus quot &longs;unt in mobili partes &longs;ubjecti, mouetur mobile, <lb/>modó non impediatur; quia po&longs;ita cau&longs;a nece&longs;&longs;aria, & non impedita per <lb/>Ax. 11. ponitur effectus, quod de omni cau&longs;a, &longs;ed de fotmali poti&longs;&longs;imum <lb/>dicidebet; præterea-datur aliquod pondus, quod data potentia &longs;ine me­<lb/>chanico organo moucre non pote&longs;t, licèt cum organo facilè moueat; hæc <lb/>hypothe&longs;is certa e&longs;t; igitur cum mouet, producit tot partes impetus quot <lb/>&longs;unt nece&longs;&longs;ariæ, vt omnibus partibus mobilis di&longs;tribuantur per idem Th. <!-- REMOVE S--><lb/>33. cum verò non mouet, non producit tot partes impetus vt con&longs;tat ex <lb/>dictis; igitur producit plures cnm organo in mobili, quàm &longs;ine organo; <lb/>igitur imperfectiores, quod demon&longs;tro: &longs;it enim vectis BF, cuius cen­<lb/>trum &longs;eu fulcrum &longs;it in A, potentia in B, pondus G, quod attollitur in F; <lb/>plures partes impetus produci po&longs;&longs;unt in F, vel in E, quàm in B, &longs;cilicet <lb/>in ip&longs;o pondere; quia pondus quod non pote&longs;t attolli in B, attollitur in <lb/>E, vel in F, vt patet ex dictis; præterea punctum F mouetur tardius, quàm <lb/>B; quia motus &longs;unt vt arcus, atcus vt &longs;emidiametri, hæ demum vt AF, <lb/>ad AB; igitur motus puncti F, e&longs;t tardior, vel imperfectior; igitur im­<lb/>petus puncti F, e&longs;t imperfectior impetu puncti B, per Ax. 13 num.4. atqui <lb/>non e&longs;t imperfectior ratione numeri partium, igitur ratione entiratis, <lb/>quæ imperfectior e&longs;t; igitur datur impetus altero impetu imperfectior. </s> | <s><emph type="italics"/>Datur impetus altero impetu perfectior &longs;ecundum entitatem<emph.end type="italics"/>; dixi &longs;ecun­<lb/>dum entitatem; quia iam dictum e&longs;t &longs;uprà dari perfectiorem &longs;ecundum <lb/>inten&longs;ionem; huius Theorematis veritas mihi maximè demon&longs;tranda <lb/>e&longs;t, ex quo tàm multa infrà deducemus; &longs;ic autem probamus; Quotie&longs;­<lb/>cunque mouetur corpus, producuntur &longs;altem tot partes impetus quot <lb/>&longs;unt partes mobilis per Th. 33. Quotie&longs;cunque producuntur in mobili <lb/>tot partes impetus quot &longs;unt in mobili partes &longs;ubjecti, mouetur mobile, <lb/>modó non impediatur; quia po&longs;ita cau&longs;a nece&longs;&longs;aria, & non impedita per <lb/>Ax. 11. ponitur effectus, quod de omni cau&longs;a, &longs;ed de formali poti&longs;&longs;imum <lb/>dici debet; præterea datur aliquod pondus, quod data potentia &longs;ine me­<lb/>chanico organo mouere non pote&longs;t, licèt cum organo facilè moueat; hæc <lb/>hypothe&longs;is certa e&longs;t; igitur cum mouet, producit tot partes impetus quot <lb/>&longs;unt nece&longs;&longs;ariæ, vt omnibus partibus mobilis di&longs;tribuantur per idem Th. <!-- REMOVE S--><lb/>33. cum verò non mouet, non producit tot partes impetus vt con&longs;tat ex <lb/>dictis; igitur producit plures cum organo in mobili, quàm &longs;ine organo; <lb/>igitur imperfectiores, quod demon&longs;tro: &longs;it enim vectis BF, cuius cen­<lb/>trum &longs;eu fulcrum &longs;it in A, potentia in B, pondus G, quod attollitur in F; <lb/>plures partes impetus produci po&longs;&longs;unt in F, vel in E, quàm in B, &longs;cilicet <lb/>in ip&longs;o pondere; quia pondus quod non pote&longs;t attolli in B, attollitur in <lb/>E, vel in F, vt patet ex dictis; præterea punctum F mouetur tardius, quàm <lb/>B; quia motus &longs;unt vt arcus, arcus vt &longs;emidiametri, hæ demum vt AF, <lb/>ad AB; igitur motus puncti F, e&longs;t tardior, vel imperfectior; igitur im­<lb/>petus puncti F, e&longs;t imperfectior impetu puncti B, per Ax. 13 num.4. atqui <lb/>non e&longs;t imperfectior ratione numeri partium, igitur ratione entitatis, <lb/>quæ imperfectior e&longs;t; igitur datur impetus altero impetu imperfectior. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Tertiò, &longs;i dato quocunque motu pote&longs;t dari tardior: igitur dato quo­<lb/>cunque impetu pote&longs;t dari imperfectior. </s></p><p type="main"> | <s>Tertiò, &longs;i dato quocunque motu pote&longs;t dari tardior: igitur dato quo­<lb/>cunque impetu pote&longs;t dari imperfectior. </s></p><p type="main"> |
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| <s>Quartò, &longs;i daretur punctum impetus in inten&longs;ione: non po&longs;&longs;et dari <lb/>motus tatdior in infinitum &longs;ine diuer&longs;is gradibus perfectionis. </s></p><p type="main"> | <s>Quartò, &longs;i daretur punctum impetus in inten&longs;ione: non po&longs;&longs;et dari <lb/>motus tardior in infinitum &longs;ine diuer&longs;is gradibus perfectionis. </s></p><p type="main"> |
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| <s>Quintò, &longs;ine hac diuer&longs;a impetus perfectione nonp o&longs;&longs;et explicari <lb/>productio continua impetus, quæ &longs;it temporibus inæqualibus, neque de­<lb/>&longs;tructio ciu&longs;dem impetus; nec motus in diuer&longs;is planis inclinatis, vel in­<lb/>diuer&longs;is lineis citra perpendicularem, &longs;ed de his omnibus &longs;uo loco. </s></p><p type="main"> | <s>Quintò, &longs;ine hac diuer&longs;a impetus perfectione non po&longs;&longs;et explicari <lb/>productio continua impetus, quæ &longs;it temporibus inæqualibus, neque de­<lb/>&longs;tructio eiu&longs;dem impetus; nec motus in diuer&longs;is planis inclinatis, vel in­<lb/>diuer&longs;is lineis citra perpendicularem, &longs;ed de his omnibus &longs;uo loco. </s></p><p type="main"> |
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| <s>Sextò, Denique ratio propo&longs;ita rem i&longs;tam euincit; cum enim in motu <lb/>vectis plures partes producantur ver&longs;us centrum, &longs;cilicet, in maiori pon­<lb/>dere, quod attollitur; & cum hæ habeant motum tardiorem, &longs;equitur ne­<lb/>ce&longs;&longs;ariò e&longs;&longs;e imperfectiores. </s></p><p type="main"> | <s>Sextò, Denique ratio propo&longs;ita rem i&longs;tam euincit; cum enim in motu <lb/>vectis plures partes producantur ver&longs;us centrum, &longs;cilicet, in maiori pon­<lb/>dere, quod attollitur; & cum hæ habeant motum tardiorem, &longs;equitur ne­<lb/>ce&longs;&longs;ariò e&longs;&longs;e imperfectiores. </s></p><p type="main"> |
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| <s><emph type="italics"/>Non pote&longs;t explicari tarditas motus &longs;ine diuer&longs;a perfectione impetus, per <lb/>pauciores &longs;cilicet eiu&longs;dem impetus partes.<emph.end type="italics"/></s><s> Primò, quia cum retardari po&longs;&longs;it <lb/>hic motus, & de&longs;trui &longs;ucce&longs;&longs;inè hic impetus; cumque in&longs;tantia motus <lb/>velocioris &longs;int breuiora; certè initio motus, breuiori &longs;cilicet tempore <lb/>imperfectior impetus de&longs;trui tantùm pote&longs;t; cum enim æqualis æquali­<lb/>bus temporibus; certè inæqualis inæqualibus. </s> | <s><emph type="italics"/>Non pote&longs;t explicari tarditas motus &longs;ine diuer&longs;a perfectione impetus, per <lb/>pauciores &longs;cilicet eiu&longs;dem impetus partes.<emph.end type="italics"/></s><s> Primò, quia cum retardari po&longs;&longs;it <lb/>hic motus, & de&longs;trui &longs;ucce&longs;&longs;inè hic impetus; cumque in&longs;tantia motus <lb/>velocioris &longs;int breuiora; certè initio motus, breuiori &longs;cilicet tempore <lb/>imperfectior impetus de&longs;trui tantùm pote&longs;t; cum enim æqualis æquali­<lb/>bus temporibus; certè inæqualis inæqualibus. </s> |
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| <s>Secundò quia vix explica­<lb/>ri pore&longs;t quomodo duæ formæ homogeneæ in eodem &longs;ubiecti puncto <lb/>exi&longs;tere po&longs;&longs;int, quod ctiam in commune e&longs;t calori, lumini, &c. </s></p><p type="main"> | <s>Secundò quia vix explica­<lb/>ri pore&longs;t quomodo duæ formæ homogeneæ in eodem &longs;ubiecti puncto <lb/>exi&longs;tere po&longs;&longs;int, quod etiam in commune e&longs;t calori, lumini, &c. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc difficiliùs attollitur pertica CA ex puncto C motu circulari, <lb/>quàm ex puncto B motu recto; quia &longs;cilicet, cum motu recto ex puncto B <lb/>attollitur, omnes partes mouentur motu æquali; igitur impetus æqualiter <lb/>omnibus di&longs;tribuitur; igitur modò producantur tot partes impetus, quot <lb/>&longs;unt partes in mobili; haud dubiè attolletur: at verò, cum motu circulari <lb/>ex puncto C attollitur, omnes partcs inæquali motu attolluntur; igitur <lb/>plures &longs;unt nece&longs;&longs;ariæ, vt attollatur motu circulari; igitur difficiliùs iuxta <lb/>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb/>maius momentum habet, de quo aùàs. </s></p><p type="main"> | <s>Hinc difficiliùs attollitur pertica CA ex puncto C motu circulari, <lb/>quàm ex puncto B motu recto; quia &longs;cilicet, cum motu recto ex puncto B <lb/>attollitur, omnes partes mouentur motu æquali; igitur impetus æqualiter <lb/>omnibus di&longs;tribuitur; igitur modò producantur tot partes impetus, quot <lb/>&longs;unt partes in mobili; haud dubiè attolletur: at verò, cum motu circulari <lb/>ex puncto C attollitur, omnes partes inæquali motu attolluntur; igitur <lb/>plures &longs;unt nece&longs;&longs;ariæ, vt attollatur motu circulari; igitur difficiliùs iuxta <lb/>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb/>maius momentum habet, de quo aùàs. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc ratio cuidens illius experimenti, quo manife&longs;tè con&longs;tat perti-<pb xlink:href="026/01/080.jpg" pagenum="48"/>cam CA, ex A, facilius attolli motu recto, quàm circulari; cum &longs;ci­<lb/>licct cuiu&longs;dam qua&longs;i reflexionis opera eodem tempore vtraque extremi­<lb/>tas æquali motu attollitur. </s></p><p type="main"> | <s>Hinc ratio euidens illius experimenti, quo manife&longs;tè con&longs;tat perti-<pb xlink:href="026/01/080.jpg" pagenum="48"/>cam CA, ex A, facilius attolli motu recto, quàm circulari; cum &longs;ci­<lb/>licet cuiu&longs;dam qua&longs;i reflexionis opera eodem tempore vtraque extremi­<lb/>tas æquali motu attollitur. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main"> |
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| <s><margin.target id="note1"/><emph type="italics"/>Fig.<emph.end type="italics"/>7. <lb/><emph type="italics"/>Tab.<emph.end type="italics"/>1.<!-- KEEP S--></s></p><p type="main"> | <s><margin.target id="note1"/><emph type="italics"/>Fig.<emph.end type="italics"/>7. <lb/><emph type="italics"/>Tab.<emph.end type="italics"/>1.<!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Si verò applicetur potentia extra centrum vectis v. <!-- REMOVE S-->g. <!-- REMOVE S-->in<emph.end type="italics"/> F, <emph type="italics"/>po&longs;ito centro in<emph.end type="italics"/><lb/>A, <emph type="italics"/>producitur impetus minor ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; <emph type="italics"/>ab verò ver&longs;us<emph.end type="italics"/> E, <emph type="italics"/>producitur <lb/>eiu&longs;dem perfectionis proportionaliter, cuius e&longs;t ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; denique ab E, <lb/>ver&longs;us B, producitur quidem vnum punctum, vel vnus gradus impetus <lb/>eiu&longs;dem perfectionis cum eo, qui productus e&longs;t in F, & in E (&longs;upponi­<lb/>turenim ex. </s> | <s><emph type="italics"/>Si verò applicetur potentia extra centrum vectis v. <!-- REMOVE S-->g. <!-- REMOVE S-->in<emph.end type="italics"/> F, <emph type="italics"/>po&longs;ito centro in<emph.end type="italics"/><lb/>A, <emph type="italics"/>producitur impetus minor ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; <emph type="italics"/>ab verò ver&longs;us<emph.end type="italics"/> E, <emph type="italics"/>producitur <lb/>eiu&longs;dem perfectionis proportionaliter, cuius e&longs;t ab<emph.end type="italics"/> F, <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A; denique ab E, <lb/>ver&longs;us B, producitur quidem vnum punctum, vel vnus gradus impetus <lb/>eiu&longs;dem perfectionis cum eo, qui productus e&longs;t in F, & in E (&longs;upponi­<lb/>tur enim ex. gr. <!-- REMOVE S-->vnus tantùm gradus in F, & in E, productus) at verò <lb/>producuntur alij imperfectiones. </s> |
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| <s>gr. <!-- REMOVE S-->vnus tantùm gradus in F, & in E, productus) at verò <lb/>producuntur alij imperfectiones. </s> | |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus perfectus producere pote&longs;t imperfectum<emph.end type="italics"/>; patet in vecte; nam po­<lb/>tentia, &longs;en pondus extremitati appen&longs;um producit in &longs;e impetum, à quo <lb/>deinde impetus in toto vecte producitur per Th.42. &longs;ed impetus pon­<lb/>deris appen&longs;i e&longs;t ciu&longs;dem perfectionis cum impetu producto in ip&longs;a ve­<lb/>ctis extremitate, ex qua pendet; cum &longs;it vrriu&longs;que æqualis motus; &longs;ed <lb/>ver&longs;us centrum ciu&longs;dem vectis producitur impetus imperfectior per <lb/>Th.82. igitur imperfectus à perfecto producitur. </s></p><p type="main"> | <s><emph type="italics"/>Impetus perfectus producere pote&longs;t imperfectum<emph.end type="italics"/>; patet in vecte; nam po­<lb/>tentia, &longs;en pondus extremitati appen&longs;um producit in &longs;e impetum, à quo <lb/>deinde impetus in toto vecte producitur per Th.42. &longs;ed impetus pon­<lb/>deris appen&longs;i e&longs;t eiu&longs;dem perfectionis cum impetu producto in ip&longs;a ve­<lb/>ctis extremitate, ex qua pendet; cum &longs;it vtriu&longs;que æqualis motus; &longs;ed <lb/>ver&longs;us centrum eiu&longs;dem vectis producitur impetus imperfectior per <lb/>Th.82. igitur imperfectus à perfecto producitur. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 85.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"/> 3. <emph type="italics"/>num.<emph.end type="italics"/> 2. <lb/>adde quod nunquam effectus perfectio &longs;uperat perfectionem cau&longs;æ; dixi <lb/>perfectum ab imperfecto; &longs;cilicet &longs;i con&longs;ideretur perfectio ratione en-<pb xlink:href="026/01/081.jpg" pagenum="49"/>titatis; cum reuerâ, vt dictum e&longs;t &longs;uprà, remi&longs;&longs;us producat inten&longs;um, <lb/>quod in vecte clari&longs;&longs;unum e&longs;t; quippe momentum applicatum in F, quod <lb/>tardiùs mouetur deor&longs;um, quàm B, &longs;ur&longs;um, vt patet, habet impetum re­<lb/>mi&longs;&longs;iorem, qui tamen producit in B, inten&longs;iorem: Pro quo, ob&longs;eruabis <lb/>impetum imperfectum cum alio perfecto actione communi agentem <lb/>po&longs;&longs;e concurrere ad producendum perfectum, vt patet; non tamen in <lb/>ratione cau&longs;æ totalis: &longs;imiliter plures imperfecti &longs;imul concurrentes <lb/>po&longs;&longs;unt producere perfectum; quia plures imperfecti conjunctim adæ­<lb/>quant perfectionem alterius perfectioris &longs;inguli &longs;eor&longs;im. </s></p><p type="main"> | <s><emph type="italics"/>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"/> 3. <emph type="italics"/>num.<emph.end type="italics"/> 2. <lb/>adde quod nunquam effectus perfectio &longs;uperat perfectionem cau&longs;æ; dixi <lb/>perfectum ab imperfecto; &longs;cilicet &longs;i con&longs;ideretur perfectio ratione en-<pb xlink:href="026/01/081.jpg" pagenum="49"/>titatis; cum reuerâ, vt dictum e&longs;t &longs;uprà, remi&longs;&longs;us producat inten&longs;um, <lb/>quod in vecte clari&longs;&longs;imum e&longs;t; quippe momentum applicatum in F, quod <lb/>tardiùs mouetur deor&longs;um, quàm B, &longs;ur&longs;um, vt patet, habet impetum re­<lb/>mi&longs;&longs;iorem, qui tamen producit in B, inten&longs;iorem: Pro quo, ob&longs;eruabis <lb/>impetum imperfectum cum alio perfecto actione communi agentem <lb/>po&longs;&longs;e concurrere ad producendum perfectum, vt patet; non tamen in <lb/>ratione cau&longs;æ totalis: &longs;imiliter plures imperfecti &longs;imul concurrentes <lb/>po&longs;&longs;unt producere perfectum; quia plures imperfecti conjunctim adæ­<lb/>quant perfectionem alterius perfectioris &longs;inguli &longs;eor&longs;im. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis &longs;ecundò præclarum naturæ in&longs;titutum, quo factum e&longs;t; <lb/>vt cum vires hominum maiora pondera leuare non po&longs;&longs;int, &longs;i &longs;eor&longs;un <lb/>con&longs;iderentur; cum organis tamen mechanicis conjunctæ nullum pon­<lb/>dus quantumuis immane leuare non po&longs;&longs;int; quod certè nullo modo ac­<lb/>cideret, ni&longs;i plures partes impetus producerent neque plures producere <lb/>po&longs;&longs;ent, ni&longs;i minoris perfectionis e&longs;&longs;ent; quia faciliùs producitur effe­<lb/>ctus imperfectus, quam perfectus per Ax. 13.num.4. </s></p><p type="main"> | <s>Ob&longs;eruabis &longs;ecundò præclarum naturæ in&longs;titutum, quo factum e&longs;t; <lb/>vt cum vires hominum maiora pondera leuare non po&longs;&longs;int, &longs;i &longs;eor&longs;un <lb/>con&longs;iderentur; cum organis tamen mechanicis conjunctæ nullum pon­<lb/>dus quantumuis immane leuare non po&longs;&longs;int; quod certè nullo modo ac­<lb/>cideret, ni&longs;i plures partes impetus producerent neque plures producere <lb/>po&longs;&longs;ent, ni&longs;i minoris perfectionis e&longs;&longs;ent; quia faciliùs producitur effe­<lb/>ctus imperfectus, quam perfectus per Ax. 13.num.4. </s></p><p type="main"> |
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| <s>Quartò, hinc quoque benè explicatur diuer&longs;itas impetus, quæ oritur <lb/>tum à diuer&longs;o medio, tùm à plano inclinato, tùm ab aliis impedimentis, <lb/>tùm à diuer&longs;o ni&longs;u eiu&longs;dem potentiæ, tùm maximè à diuer&longs;o applicatio­<lb/>nis modo; de quibus aliàs. </s></p><p type="main"> | <s>Quartò, hinc quoque benè explicatur diuer&longs;itas impetus, quæ oritur <lb/>tum à diuer&longs;o medio, tùm à plano inclinato, tùm ab aliis impedimentis, <lb/>tùm à diuer&longs;o ni&longs;u eiu&longs;dem potentiæ, tùm maximè à diuer&longs;o applicatio­<lb/>nis modo; de quibus aliàs. </s></p><p type="main"> |
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| <s>Quintò, &longs;i potentia applicata mobili immediatè illud moueat motu <lb/>recto, vel in &longs;ingulis punctis mobilis producitur vnum punctum impe­<lb/>tus, vel plura; &longs;i primum, erit primus tantùm gradus maximæ perfectio­<lb/>nis; ita vt perfectiorem producere non po&longs;&longs;it, ad quem e&longs;t determinata <lb/>potentia; imperfectiorem tamen impetu innato, de quo infrà; &longs;i verò <lb/>&longs;ecundum, producet in &longs;ingulis paitibus eumdem gradum perfecti&longs;&longs;i­<lb/>mum cum aliis pluribus, vel paucioribus heterogeneis, & imperfectio­<lb/>ribus. </s></p><p type="main"> | <s>Quintò, &longs;i potentia applicata mobili immediatè illud moueat motu <lb/>recto, vel in &longs;ingulis punctis mobilis producitur vnum punctum impe­<lb/>tus, vel plura; &longs;i primum, erit primus tantùm gradus maximæ perfectio­<lb/>nis; ita vt perfectiorem producere non po&longs;&longs;it, ad quem e&longs;t determinata <lb/>potentia; imperfectiorem tamen impetu innato, de quo infrà; &longs;i verò <lb/>&longs;ecundum, producet in &longs;ingulis partibus <expan abbr="eũdem">eundem</expan> gradum perfecti&longs;&longs;i­<lb/>mum cum aliis pluribus, vel paucioribus heterogeneis, & imperfectio­<lb/>ribus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 86.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Illa progatio non fit per motum localem, ita vt pars impetus producta in <lb/>prima parte &longs;ubiecti tran&longs;eat ad &longs;ecundam,<emph.end type="italics"/> patet; quia cum impetus &longs;it ac­<lb/>cidens per Th. 8. de &longs;ubiecto in &longs;ubiectum tran&longs;ire non pote&longs;t per deff. </s> | <s><emph type="italics"/>Illa progatio non fit per motum localem, ita vt pars impetus producta in <lb/>prima parte &longs;ubiecti tran&longs;eat ad &longs;ecundam,<emph.end type="italics"/> patet; quia cum impetus &longs;it ac­<lb/>cidens per Th. 8. de &longs;ubiecto in &longs;ubiectum tran&longs;ire non pote&longs;t per deff. </s> |
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| <s><lb/>accidentis; de qua in Metaphy&longs;icâ; nec e&longs;t quod aliqui dicant &longs;e <expan abbr="nõ">non</expan> po&longs;&longs;e <lb/>concipere, quomodo id fiat &longs;ine motu locali; cum ip&longs;is etiam oculis <lb/>qua&longs;i ocrnatur; cum enim percutis corpus oblongum AE, & cadit ictus <lb/>in extremitatem A, corpus ip&longs;um totum &longs;unul moues; igitur pars impe­<lb/>tus, quæ recipitur in A, non migrat in E, &longs;ed hæc producitur in A, & <lb/>alia in B, alia in C, atque ita deinceps. </s></p><p type="main"> | <s><lb/>accidentis; de qua in Metaphy&longs;icâ; nec e&longs;t quod aliqui dicant &longs;e <expan abbr="nõ">non</expan> po&longs;&longs;e <lb/>concipere, quomodo id fiat &longs;ine motu locali; cum ip&longs;is etiam oculis <lb/>qua&longs;i cernatur; cum enim percutis corpus oblongum AE, & cadit ictus <lb/>in extremitatem A, corpus ip&longs;um totum &longs;imul moues; igitur pars impe­<lb/>tus, quæ recipitur in A, non migrat in E, &longs;ed hæc producitur in A, & <lb/>alia in B, alia in C, atque ita deinceps. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 96.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 96.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Cum duo corpora &longs;e&longs;e mutuò tangunt, impetus in vtroque propagatur<emph.end type="italics"/> &longs;int <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->globi A & B, æquales &longs;ibi inuicem contigui in C, &longs;it applicata po­<lb/>tentia in D, non modò producet impetum in globo A, &longs;ed etiam in B: <lb/>probatur primò, quia &longs;e habent per modum vnius, vt patet ex re&longs;i&longs;ten­<lb/>&longs;tia, nec enim A moueri pote&longs;t &longs;ine B per lineam DE, quod certè cla­<lb/>ri&longs;&longs;imum e&longs;t; probatur &longs;ecundò quia &longs;i A produceret impetum in B, duo <lb/>globi, vel 3. vel 5. vel infiniti tantùm re&longs;i&longs;terent, quantùm vnicus glo­<lb/>bus, quod fal&longs;um & ab&longs;urdum e&longs;t. </s> | <s><emph type="italics"/>Cum duo corpora &longs;e&longs;e mutuò tangunt, impetus in vtroque propagatur<emph.end type="italics"/> &longs;int <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->globi A & B, æquales &longs;ibi inuicem contigui in C, &longs;it applicata po­<lb/>tentia in D, non modò producet impetum in globo A, &longs;ed etiam in B: <lb/>probatur primò, quia &longs;e habent per modum vnius, vt patet ex re&longs;i&longs;ten­<lb/>tia, nec enim A moueri pote&longs;t &longs;ine B per lineam DE, quod certè cla­<lb/>ri&longs;&longs;imum e&longs;t; probatur &longs;ecundò quia &longs;i A produceret impetum in B, duo <lb/>globi, vel 3. vel 5. vel infiniti tantùm re&longs;i&longs;terent, quantùm vnicus glo­<lb/>bus, quod fal&longs;um & ab&longs;urdum e&longs;t. </s> |
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| <s>Tertiò, Ratio à priori e&longs;t; quia idco <lb/>producitur, & propagatur impetus in toto A; quia vna pars non pote&longs;t <lb/>moueri &longs;ine alia per Th. 33. &longs;ed non pote&longs;t A moueri ni&longs;i moucatur B; <lb/>igitur in vtroque &longs;imul, & æqualiter propagatur impetus. </s></p><p type="main"> | <s>Tertiò, Ratio à priori e&longs;t; quia ideo <lb/>producitur, & propagatur impetus in toto A; quia vna pars non pote&longs;t <lb/>moueri &longs;ine alia per Th. 33. &longs;ed non pote&longs;t A moueri ni&longs;i moueatur B; <lb/>igitur in vtroque &longs;imul, & æqualiter propagatur impetus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc percu&longs;&longs;io vel ictus globi B, cui alter A à tergo immediatè in­<lb/>&longs;t&longs;tit maior e&longs;t. </s></p><p type="main"> | <s>Hinc percu&longs;&longs;io vel ictus globi B, cui alter A à tergo immediatè in­<lb/>&longs;i&longs;tit maior e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 98.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 98.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Inten&longs;io impetus propagati iuxta hunc modum &longs;e habet, vt distantia à cen­<lb/>tro motus<emph.end type="italics"/>; &longs;int enim punctum B, & pnnctum A: ita &longs;e habet inten&longs;io <lb/>impetus puncti A ad inten&longs;ionem impetus puncti B, vt di&longs;tantia AC <lb/>ad BC. Probatur, quia cum impetus &longs;int vt motus, motus vt &longs;patia, &longs;patia <lb/>verò &longs;int arcus AE. BD; arcus &longs;unt, vt &longs;emidiametri AC, BC; igitur vt <lb/>di&longs;tantiæ quòd erat demon&longs;trandum. </s></p><p type="main"> | <s><emph type="italics"/>Inten&longs;io impetus propagati iuxta hunc modum &longs;e habet, vt distantia à cen­<lb/>tro motus<emph.end type="italics"/>; &longs;int enim punctum B, & punctum A: ita &longs;e habet inten&longs;io <lb/>impetus puncti A ad inten&longs;ionem impetus puncti B, vt di&longs;tantia AC <lb/>ad BC. Probatur, quia cum impetus &longs;int vt motus, motus vt &longs;patia, &longs;patia <lb/>verò &longs;int arcus AE. BD; arcus &longs;unt, vt &longs;emidiametri AC, BC; igitur vt <lb/>di&longs;tantiæ quòd erat demon&longs;trandum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus, qui producitur ver&longs;us centrum vectis in pondere, licèt cre&longs;cat nu­<lb/>mero, decre&longs;cit tamen in perfectione.<emph.end type="italics"/></s><s> Probatur per Th.81. ex motu imper­<lb/>ctiore, cui re&longs;pondet impetus imperfectior per Ax. 17.num.4. non ratio­<lb/>ne numeri, qui maior e&longs;t per Th.99. igitur ratione entitatis, &longs;eu perfe­<lb/>ctionis entitatiuæ. </s></p><p type="main"> | <s><emph type="italics"/>Impetus, qui producitur ver&longs;us centrum vectis in pondere, licèt cre&longs;cat nu­<lb/>mero, decre&longs;cit tamen in perfectione.<emph.end type="italics"/></s><s> Probatur per Th.81. ex motu imper­<lb/>fectiore, cui re&longs;pondet impetus imperfectior per Ax. 17.num.4. non ratio­<lb/>ne numeri, qui maior e&longs;t per Th.99. igitur ratione entitatis, &longs;eu perfe­<lb/>ctionis entitatiuæ. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Non producuntur plures partes impetus in vecte ver&longs;us centrum, id est, non <lb/>&longs;unt plures in punclo vectis propiùs ad centrum accedente, quàm in co; quod <lb/>longiùs distat:<emph.end type="italics"/> Probatur primò, quia fru&longs;trà e&longs;&longs;ent plures. </s> | <s><emph type="italics"/>Non producuntur plures partes impetus in vecte ver&longs;us centrum, id est, non <lb/>&longs;unt plures in puncto vectis propiùs ad centrum accedente, quàm in co; quod <lb/>longiùs distat:<emph.end type="italics"/> Probatur primò, quia fru&longs;trà e&longs;&longs;ent plures. </s> |
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| <s>Secundò, cur <lb/>potiùs in vna proportione, quàm in alia? </s></p><p type="main"> | <s>Secundò, cur <lb/>potiùs in vna proportione, quàm in alia? </s></p><p type="main"> |
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| <s><emph type="italics"/>Iam facilè explicatur ex dictis, quomodo, & cuius rationis pondera attol­<lb/>lantur ex diuer&longs;is punctis vectis<emph.end type="italics"/>; &longs;it enim idem vectis AC, & producan­<lb/>tur.v.g. </s> | <s><emph type="italics"/>Iam facilè explicatur ex dictis, quomodo, & cuius rationis pondera attol­<lb/>lantur ex diuer&longs;is punctis vectis<emph.end type="italics"/>; &longs;it enim idem vectis AC, & producan­<lb/>tur.v.g. </s> |
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| <s>in &longs;ingulis punctis vectis &longs;ingula puncta impetus, &longs;ed diuer&longs;æ <lb/>perfectionis; haud dubiè plures partes impetus imperfecti po&longs;&longs;unt face­<lb/>re impetum æqualem in perfectione alteri, qui con&longs;tat paucioribus, &longs;ed <lb/>perfectioribus; igitur cum impetus B &longs;it imperfectior duplò quàm im­<lb/>petus in A, duplò plures partes impetus producentur in B, quàm in A, er­<lb/>go duplò maius pondus moucbitur; atque ita deinceps; eum enim ap­<lb/>ponitur pondus in B, producuntur in eo partes impetus omnes eiu&longs;dem <lb/>perfectionis; quæ &longs;cilicet re&longs;pondet B, id e&longs;t, quæ e&longs;t &longs;ubdupla perfectio­<lb/>nis impetus A; igitur plures partes producuntur, quàm &longs;i e&longs;&longs;ent perfe­<lb/>ctionis A; &longs;ed pauciores quàm &longs;i e&longs;&longs;ent perfectionis O, quæ minor e&longs;t; <lb/>quippe eadem potentia, &longs;eu cau&longs;a, quæ agit quantum pote&longs;t (quod &longs;up­<lb/>pono modò) producit æqualem effectum in perfectione, per Ax. 13. n. </s> | <s>in &longs;ingulis punctis vectis &longs;ingula puncta impetus, &longs;ed diuer&longs;æ <lb/>perfectionis; haud dubiè plures partes impetus imperfecti po&longs;&longs;unt face­<lb/>re impetum æqualem in perfectione alteri, qui con&longs;tat paucioribus, &longs;ed <lb/>perfectioribus; igitur cum impetus B &longs;it imperfectior duplò quàm im­<lb/>petus in A, duplò plures partes impetus producentur in B, quàm in A, er­<lb/>go duplò maius pondus mouebitur; atque ita deinceps; eum enim ap­<lb/>ponitur pondus in B, producuntur in eo partes impetus omnes eiu&longs;dem <lb/>perfectionis; quæ &longs;cilicet re&longs;pondet B, id e&longs;t, quæ e&longs;t &longs;ubdupla perfectio­<lb/>nis impetus A; igitur plures partes producuntur, quàm &longs;i e&longs;&longs;ent perfe­<lb/>ctionis A; &longs;ed pauciores quàm &longs;i e&longs;&longs;ent perfectionis O, quæ minor e&longs;t; <lb/>quippe eadem potentia, &longs;eu cau&longs;a, quæ agit quantum pote&longs;t (quod &longs;up­<lb/>pono modò) producit æqualem effectum in perfectione, per Ax. 13. n. </s> |
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| <s><lb/>4. &longs;ed æqualis perfectio pote&longs;t con&longs;tare pluribus, vel paucioribus parti­<lb/>bus perfectionis, nam 4. pattes perfectionis vt 4. faciunt æqualem effe­<lb/>ctum alteri qui con&longs;tat 8. partibus perfectionis vt 2. quod certum e&longs;t; &longs;ed <lb/>de his plura aliàs. </s></p><p type="main"> | <s><lb/>4. &longs;ed æqualis perfectio pote&longs;t con&longs;tare pluribus, vel paucioribus parti­<lb/>bus perfectionis, nam 4. pattes perfectionis vt 4. faciunt æqualem effe­<lb/>ctum alteri qui con&longs;tat 8. partibus perfectionis vt 2. quod certum e&longs;t; &longs;ed <lb/>de his plura aliàs. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 109.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 109.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Perfectio decre&longs;cit ver&longs;us centrum iuxta diuer&longs;am rationem longitudinum <lb/>vectis, &longs;eu distantiarum.<emph.end type="italics"/> v.g.&longs;it idem vectis AC, ita decre&longs;cit ab A ver&longs;us <lb/>centrum C; vt impetus puncti B &longs;it &longs;ubduplus in perfectione, puncti R <lb/>fubtriplus: iam verò &longs;it vectis &longs;ubduplus prioris BC, &longs;ectus bifariam in <lb/>Z; &longs;i impetus productus in B, qu&ecedil; e&longs;t extremitas minoris vectis B &longs;it æqua­<lb/>lis perfectionis cum impetu producto in A (& reuera &longs;unt æquales) &longs;i <lb/>æquali æmpore percurrant arcus æquales, &longs;cilicet AV, & BD) certè im-<pb xlink:href="026/01/091.jpg" pagenum="59"/>pertus productus in Z e&longs;t æqualis producto in B, cum B pertinet ad ma­<lb/>iorem vectem; quia vt AC totus maior vectis e&longs;t ad BC ita BC ad <lb/>ZC: igitur decre&longs;cit perfectio versùs centrum iuxta rationem longi­<lb/>tudinum. </s></p><p type="main"> | <s><emph type="italics"/>Perfectio decre&longs;cit ver&longs;us centrum iuxta diuer&longs;am rationem longitudinum <lb/>vectis, &longs;eu distantiarum.<emph.end type="italics"/> v.g.&longs;it idem vectis AC, ita decre&longs;cit ab A ver&longs;us <lb/>centrum C; vt impetus puncti B &longs;it &longs;ubduplus in perfectione, puncti R <lb/>&longs;ubtriplus: iam verò &longs;it vectis &longs;ubduplus prioris BC, &longs;ectus bifariam in <lb/>Z; &longs;i impetus productus in B, qu&ecedil; e&longs;t extremitas minoris vectis B &longs;it æqua­<lb/>lis perfectionis cum impetu producto in A (& reuera &longs;unt æquales) &longs;i <lb/>æquali tempore percurrant arcus æquales, &longs;cilicet AV, & BD) certè im-<pb xlink:href="026/01/091.jpg" pagenum="59"/>petus productus in Z e&longs;t æqualis producto in B, cum B pertinet ad ma­<lb/>iorem vectem; quia vt AC totus maior vectis e&longs;t ad BC ita BC ad <lb/>ZC: igitur decre&longs;cit perfectio versùs centrum iuxta rationem longi­<lb/>tudinum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 110.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 110.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Ob&longs;erua tamen quacumque data potentia po&longs;&longs;e dari minorem; quia <lb/>quocumque dato motu, etiam recto, pote&longs;t dari tardior; igitur quocum­<lb/>que impetu imperfectior; igitur quando appellaui potentiam minimam; <lb/>intellige illam quæ comparatur cum vnico puncto impetus talis perfe­<lb/>ctionis; hæc enim reuera minima e&longs;t illarum omnium, quæ po&longs;&longs;unt pro­<lb/>ducere impetum talis perfectionis, &longs;i verò comparetur cum impetu im­<lb/>perfectiore, haud dubiè minima non e&longs;t. </s></p><p type="main"> | <s>Ob&longs;erua tamen quacumque data potentia po&longs;&longs;e dari minorem; quia <lb/>quocumque dato motu, etiam recto, pote&longs;t dari tardior; igitur quocum­<lb/>que impetu imperfectior; igitur quando appellaui potentiam minimam; <lb/>intellige illam quæ comparatur cum vnico puncto impetus talis perfe­<lb/>ctionis; hæc enim reuera minima e&longs;t illarum omnium, quæ po&longs;&longs;unt pro­<lb/>ducere impetum talis perfectionis, &longs;i verò comparetur cum impetu im­<lb/>perfectiore, haud dubiè minima non e&longs;t. </s></p><p type="main"> |
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| <s>Ob&longs;erua præterea &longs;uppo&longs;itum e&longs;&longs;e hactenus in extremitate vectis &longs;iue <lb/>maioris, &longs;iue minoris, produci impetum ciu&longs;dem perfectionis, ciu&longs;que <lb/>vnicum punctum, &longs;eu partem, vnde potentia quæ applicatur maiori vecti <lb/>conuenit quidem cum ea, quæ applicatur minori in eo, quòd vtraque in <lb/>extremitate &longs;ui vectis producat vnum punctum impetus eiu&longs;dem perfe­<lb/>ctionis; differt tamen in eo, quòd illa, quæ applicatur maiori vecti, &longs;it <lb/>maior iuxta rationes prædictas in Theoremate. <!-- KEEP S--></s> | <s>Ob&longs;erua præterea &longs;uppo&longs;itum e&longs;&longs;e hactenus in extremitate vectis &longs;iue <lb/>maioris, &longs;iue minoris, produci impetum eiu&longs;dem perfectionis, eiu&longs;que <lb/>vnicum punctum, &longs;eu partem, vnde potentia quæ applicatur maiori vecti <lb/>conuenit quidem cum ea, quæ applicatur minori in eo, quòd vtraque in <lb/>extremitate &longs;ui vectis producat vnum punctum impetus eiu&longs;dem perfe­<lb/>ctionis; differt tamen in eo, quòd illa, quæ applicatur maiori vecti, &longs;it <lb/>maior iuxta rationes prædictas in Theoremate. <!-- KEEP S--></s> |
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| <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->illa, quæ applicatur <lb/>vecti. </s> | <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->illa, quæ applicatur <lb/>vecti. </s> |
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| <s>2. punctorum e&longs;t ad eam, quæ applicatur vecti trium punctorum, <lb/>&longs;cu partium, vt 1. 1/2 ad 2. & &longs;i vectis &longs;it 4. punctorum ad 2. 1/2; &longs;i 5. ad 3. <lb/>&longs;i 6. ad 3. 1/2; &longs;i 7. ad 4. &longs;i 8. ad 4. 1/2. Vides egregiam progre&longs;&longs;ionem; &longs;it <lb/>enim vectis 2. punctorum AB, in puncto A, quod e&longs;t extremitas, produ­<lb/>catur punctum impetus datæ perfectionis, in B producetur aliud, cuius <lb/>perfectio e&longs;t &longs;ubdupla prioris per Th. 109. igitur caracter, &longs;eu momen­<lb/>tum totius impetus e&longs;t 1. 1/2. &longs;it porrò vectis 4. punctorum CDEF, in <lb/>C, quod e&longs;t extremitas; producatur vnum punctum impetus ciu&longs;dem <lb/>perfectionis cum eo, quod productum e&longs;t in A; certè in D producetur <lb/>aliud cuius perfectio erit ad priorem vt 3.ad 4. per idem Th. &longs;ic autem <lb/>notetur 1/4, in E 2/4, in F 3/4, in C vero 4/4; perfectiones enim &longs;unt vt lon-<pb xlink:href="026/01/092.jpg" pagenum="60"/>gitudines; quæ &longs;i colligantur, habebis characterem totius impetus, 2 1/2: <lb/>igitur totus impetus productus in minore vecte, qui con&longs;tat 2. punctis, <lb/>e&longs;t ad impetum, qui producitur in maiore con&longs;tante 4.punctis, vt 1. 1/2 ad <lb/>2. 1/2; igitur vectis maior maiorem potentiam ad mouendum ip&longs;um ve­<lb/>ctem requirit; non certè in de&longs;cen&longs;u; quippe &longs;uo pondere de&longs;cendit, &longs;ed <lb/>in plano horizontali; ni&longs;i enim potentia po&longs;&longs;it mouere vectem; haud <lb/>dubiè nullum pondus vecte mouebit. </s></p><p type="main"> | <s>2. punctorum e&longs;t ad eam, quæ applicatur vecti trium punctorum, <lb/>&longs;cu partium, vt 1. 1/2 ad 2. & &longs;i vectis &longs;it 4. punctorum ad 2. 1/2; &longs;i 5. ad 3. <lb/>&longs;i 6. ad 3. 1/2; &longs;i 7. ad 4. &longs;i 8. ad 4. 1/2. Vides egregiam progre&longs;&longs;ionem; &longs;it <lb/>enim vectis 2. punctorum AB, in puncto A, quod e&longs;t extremitas, produ­<lb/>catur punctum impetus datæ perfectionis, in B producetur aliud, cuius <lb/>perfectio e&longs;t &longs;ubdupla prioris per Th. 109. igitur caracter, &longs;eu momen­<lb/>tum totius impetus e&longs;t 1. 1/2. &longs;it porrò vectis 4. punctorum CDEF, in <lb/>C, quod e&longs;t extremitas; producatur vnum punctum impetus eiu&longs;dem <lb/>perfectionis cum eo, quod productum e&longs;t in A; certè in D producetur <lb/>aliud cuius perfectio erit ad priorem vt 3.ad 4. per idem Th. &longs;ic autem <lb/>notetur 1/4, in E 2/4, in F 3/4, in C vero 4/4; perfectiones enim &longs;unt vt lon-<pb xlink:href="026/01/092.jpg" pagenum="60"/>gitudines; quæ &longs;i colligantur, habebis characterem totius impetus, 2 1/2: <lb/>igitur totus impetus productus in minore vecte, qui con&longs;tat 2. punctis, <lb/>e&longs;t ad impetum, qui producitur in maiore con&longs;tante 4.punctis, vt 1. 1/2 ad <lb/>2. 1/2; igitur vectis maior maiorem potentiam ad mouendum ip&longs;um ve­<lb/>ctem requirit; non certè in de&longs;cen&longs;u; quippe &longs;uo pondere de&longs;cendit, &longs;ed <lb/>in plano horizontali; ni&longs;i enim potentia po&longs;&longs;it mouere vectem; haud <lb/>dubiè nullum pondus vecte mouebit. </s></p><p type="main"> |
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| <s>At verò &longs;i potentia &longs;it tantùm dupla minimæ, quæ datum vectem mo­<lb/>uere po&longs;&longs;it; haud dubiè dato illo vecte datum ferè quodcumque pondus <lb/>mouere poterit; cum ip&longs;e vectis con&longs;tet ferè infinitis punctis in longi­<lb/>tudine, vt patet ex dictis, & con&longs;ideranti patebit. </s></p><p type="main"> | <s>At verò &longs;i potentia &longs;it tantùm dupla minimæ, quæ datum vectem mo­<lb/>uere po&longs;&longs;it; haud dubiè dato illo vecte datum ferè quodcumque pondus <lb/>mouere poterit; cum ip&longs;e vectis con&longs;tet ferè infinitis punctis in longi­<lb/>tudine, vt patet ex dictis, & con&longs;ideranti patebit. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis demum in mechanicis nullam ferè haberi rationem pon­<lb/>deris ip&longs;ius vectis; parum enim pro nihilo computatur: Ex his tamen <lb/>erui po&longs;&longs;unt veri&longs;&longs;imæ rationes Phy&longs;icæ proportionum vectis AH; &longs;ia­<lb/>que A extremitas, H centrum; &longs;itque BH 1/2. CH 1/4, DH 1/2, EH (1/16), <lb/>FH (1/32), GH (1/64) pondus I applicetur in A, & moueatur; certè in B moue­<lb/>bitur pondus K duplum I; quia, cum impetus productus in B, &longs;it &longs;ubdu­<lb/>plus in perfectione illius, qui producitur in A; vt æqualis producatur in <lb/>B, & in A, debent produci in B duplò plures partes impetus; igitur du­<lb/>plò maius pondus mouebit; at verò in C mouebitur pondus L quadru­<lb/>plum I, in D octuplum, atque ita deinceps; donec tandem in G mot ea­<lb/>tur pondus, quod &longs;it ad I vt 64. ad 1. & cum adhuc po&longs;&longs;int accipi inter <lb/>GH, partes aliquotæ minores, & minores ferè in infinitum, non mirum <lb/>e&longs;t &longs;i pondus maius po&longs;&longs;it adhuc moueri. </s></p><p type="main"> | <s>Ob&longs;eruabis demum in mechanicis nullam ferè haberi rationem pon­<lb/>deris ip&longs;ius vectis; parum enim pro nihilo computatur: Ex his tamen <lb/>erui po&longs;&longs;unt veri&longs;&longs;imæ rationes Phy&longs;icæ proportionum vectis AH; &longs;ia­<lb/>que A extremitas, H centrum; &longs;itque BH 1/2. CH 1/4, DH 1/2, EH (1/16), <lb/>FH (1/32), GH (1/64) pondus I applicetur in A, & moueatur; certè in B moue­<lb/>bitur pondus K duplum I; quia, cum impetus productus in B, &longs;it &longs;ubdu­<lb/>plus in perfectione illius, qui producitur in A; vt æqualis producatur in <lb/>B, & in A, debent produci in B duplò plures partes impetus; igitur du­<lb/>plò maius pondus mouebit; at verò in C mouebitur pondus L quadru­<lb/>plum I, in D octuplum, atque ita deinceps; donec tandem in G mouea­<lb/>tur pondus, quod &longs;it ad I vt 64. ad 1. & cum adhuc po&longs;&longs;int accipi inter <lb/>GH, partes aliquotæ minores, & minores ferè in infinitum, non mirum <lb/>e&longs;t &longs;i pondus maius po&longs;&longs;it adhuc moueri. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis etiam in omni vecte ab&longs;trahendo ab eius pondere, & ap­<lb/>plicata eadem potentia, hoc e&longs;&longs;e commune; vt po&longs;&longs;it quodcumque pon­<lb/>dus attolli, licèt difficiliùs in minore; quia hic non pote&longs;t in tam mul­<lb/>tas partes aliquotas &longs;en&longs;ibiliter diuidi, in medio tamen vecte duplum <lb/>femper pondus mouetur; &longs;iue ip&longs;e vectis &longs;it maior, &longs;iue minor. </s></p><p type="main"> | <s>Ob&longs;eruabis etiam in omni vecte ab&longs;trahendo ab eius pondere, & ap­<lb/>plicata eadem potentia, hoc e&longs;&longs;e commune; vt po&longs;&longs;it quodcumque pon­<lb/>dus attolli, licèt difficiliùs in minore; quia hic non pote&longs;t in tam mul­<lb/>tas partes aliquotas &longs;en&longs;ibiliter diuidi, in medio tamen vecte duplum <lb/>&longs;emper pondus mouetur; &longs;iue ip&longs;e vectis &longs;it maior, &longs;iue minor. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis deinde, &longs;i centrum vectis non &longs;it in altera extremitate, <lb/>&longs;ed. </s> | <s>Ob&longs;eruabis deinde, &longs;i centrum vectis non &longs;it in altera extremitate, <lb/>&longs;ed. </s> |
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| <s><emph type="italics"/>Potentia verò motrix determinatur vel à &longs;uo fine intrin&longs;eco, vel potius ab <lb/>ip&longs;a &longs;ua natura<emph.end type="italics"/>; &longs;ic grauitas &longs;eu potentia motrix grauium determinata <lb/>e&longs;t ad motum deor&longs;um perpendicularem, dum in medio libero corpus <lb/>graue mouetur; vel à plano inclinato; pro cuius diuer&longs;a inclinatione <lb/>diuer&longs;a e&longs;t linea motus deor&longs;um; vel ab ip&longs;a via, &longs;eu exitu patefacto; <lb/>&longs;ic potentia motrix compre&longs;&longs;orum &longs;uas vires exerit, & mobile ip&longs;um <lb/>agit, quâ patet viâ, &longs;ur&longs;um, deor&longs;um &c. </s> | <s><emph type="italics"/>Potentia verò motrix determinatur vel à &longs;uo fine intrin&longs;eco, vel potius ab <lb/>ip&longs;a &longs;ua natura<emph.end type="italics"/>; &longs;ic grauitas &longs;eu potentia motrix grauium determinata <lb/>e&longs;t ad motum deor&longs;um perpendicularem, dum in medio libero corpus <lb/>graue mouetur; vel à plano inclinato; pro cuius diuer&longs;a inclinatione <lb/>diuer&longs;a e&longs;t linea motus deor&longs;um; vel ab ip&longs;a via, &longs;eu exitu patefacto; <lb/>&longs;ic potentia motrix compre&longs;&longs;orum &longs;uas vires exerit, & mobile ip&longs;um <lb/>agit, quâ patet viâ, &longs;ur&longs;um, deor&longs;um &c. </s> |
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| <s>vel ab appetitu &longs;eu libero, &longs;eu <lb/>&longs;en&longs;itiuo; &longs;ic potentia progre&longs;&longs;iua animantium cò corpus agit, quò iu­<lb/>bet appetitus, vel ab aliqua affectione intrin&longs;eca intrin&longs;ecùs vel extrin­<lb/>&longs;ecùs adueniente; &longs;ic dilatatur pupilla, vel contrahitur pro diuer&longs;a lu­<lb/>minis appul&longs;i vi, vel obiecti di&longs;tantia: Huc reuoca motus illos natura­<lb/>les, qui animalibus competunt v. <!-- REMOVE S-->g. <!-- REMOVE S-->tu&longs;&longs;is, &longs;ingultus, &longs;ternuationis, &c. </s> | <s>vel ab appetitu &longs;eu libero, &longs;eu <lb/>&longs;en&longs;itiuo; &longs;ic potentia progre&longs;&longs;iua animantium cò corpus agit, quò iu­<lb/>bet appetitus, vel ab aliqua affectione intrin&longs;eca intrin&longs;ecùs vel extrin­<lb/>&longs;ecùs adueniente; &longs;ic dilatatur pupilla, vel contrahitur pro diuer&longs;a lu­<lb/>minis appul&longs;i vi, vel obiecti di&longs;tantia: Huc reuoca motus illos natura­<lb/>les, qui animalibus competunt v. <!-- REMOVE S-->g. <!-- REMOVE S-->tu&longs;&longs;is, &longs;ingultus, &longs;ternutationis, &c. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 120.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 120.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Corpus proiectum in aliud ita illud impellit, vt determinet lineam motus <lb/>ratione puncti contactus<emph.end type="italics"/>; Sit enim, ne mnltiplicemus figuras, globus, <lb/>cuius linea directionis &longs;it DC, punctum contactus C, ita globus A im­<lb/>pellet globum B, vt linea motus, ad quam determinatur, &longs;it CB, id e&longs;t <lb/>ducta à puncto contactus ad centrum globi impul&longs;i; &longs;it etiam globus <lb/>P impactus in globum A punctum contactus &longs;it D, linea motus, ad <lb/>quam determinatur, e&longs;t DA, quæ &longs;cilicet à puncto contactus ducitur <lb/>per centrum grauitatis corporis impul&longs;i: experientia huius rei certa <lb/>e&longs;t, nec ignorant qui in ludo minoris tudiculæ ver&longs;ati &longs;unt; ratio au­<lb/>tem inde tantùm duci pote&longs;t, quod &longs;cilicet ab ip&longs;o puncto contactus ita <lb/>diffunditur impetus, vt hinc inde æqualiter in vtroque hemi&longs;phærio <lb/>diffundatur; coniungitur autem vtrumque hemi&longs;phærium circulo A, <lb/>vel B, in priore figura, e&longs;tque vtriu&longs;que communis &longs;ectio; cum autem <lb/>vtrimque &longs;it æqualis impetus, nulla e&longs;t ratio, cur linea directionis in­<lb/>clinet potiùs in vnum hemi&longs;phærium, quàm in aliud: præterea cum <lb/>motus orbis globi determinetur à motu centri; cum &longs;cilicet globus in <lb/>globum impingitur; haud dubiè non pote&longs;t e&longs;&longs;e alius motus centri, ni&longs;i <lb/>qui determinatur à puncto contactus, à quo vnica tantùm linea ad cen­<lb/>trum duci pote&longs;t, vt con&longs;tat; & hæc ratio veri&longs;&longs;ima e&longs;t, & totam rem <lb/>ip&longs;am cuincit. </s></p><p type="main"> | <s><emph type="italics"/>Corpus proiectum in aliud ita illud impellit, vt determinet lineam motus <lb/>ratione puncti contactus<emph.end type="italics"/>; Sit enim, ne multiplicemus figuras, globus, <lb/>cuius linea directionis &longs;it DC, punctum contactus C, ita globus A im­<lb/>pellet globum B, vt linea motus, ad quam determinatur, &longs;it CB, id e&longs;t <lb/>ducta à puncto contactus ad centrum globi impul&longs;i; &longs;it etiam globus <lb/>P impactus in globum A punctum contactus &longs;it D, linea motus, ad <lb/>quam determinatur, e&longs;t DA, quæ &longs;cilicet à puncto contactus ducitur <lb/>per centrum grauitatis corporis impul&longs;i: experientia huius rei certa <lb/>e&longs;t, nec ignorant qui in ludo minoris tudiculæ ver&longs;ati &longs;unt; ratio au­<lb/>tem inde tantùm duci pote&longs;t, quod &longs;cilicet ab ip&longs;o puncto contactus ita <lb/>diffunditur impetus, vt hinc inde æqualiter in vtroque hemi&longs;phærio <lb/>diffundatur; coniungitur autem vtrumque hemi&longs;phærium circulo A, <lb/>vel B, in priore figura, e&longs;tque vtriu&longs;que communis &longs;ectio; cum autem <lb/>vtrimque &longs;it æqualis impetus, nulla e&longs;t ratio, cur linea directionis in­<lb/>clinet potiùs in vnum hemi&longs;phærium, quàm in aliud: præterea cum <lb/>motus orbis globi determinetur à motu centri; cum &longs;cilicet globus in <lb/>globum impingitur; haud dubiè non pote&longs;t e&longs;&longs;e alius motus centri, ni&longs;i <lb/>qui determinatur à puncto contactus, à quo vnica tantùm linea ad cen­<lb/>trum duci pote&longs;t, vt con&longs;tat; & hæc ratio veri&longs;&longs;ima e&longs;t, & totam rem <lb/>ip&longs;am euincit. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 121.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 121.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc licèt diuer&longs;æ &longs;int linea motus globi impellentis, &longs;i tamen &longs;it idem pun­<lb/>ctum contactus ad eamdem lineam globus impul&longs;us determinabitur,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->li­<lb/>cet globus P. ciu&longs;dem figuræ tangat globum A in D per lineam PD &longs;iue <lb/>per lineam HD &longs;iue per quamlibet aliam, globus A mouebitur &longs;emper <lb/>per lineam directionis DA propter rationem propo&longs;itam, quod etiam <lb/>mille experimentis conuincitur. </s> | <s><emph type="italics"/>Hinc licèt diuer&longs;æ &longs;int linea motus globi impellentis, &longs;i tamen &longs;it idem pun­<lb/>ctum contactus ad <expan abbr="eãdem">eandem</expan> lineam globus impul&longs;us determinabitur,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->li­<lb/>cet globus P. eiu&longs;dem figuræ tangat globum A in D per lineam PD &longs;iue <lb/>per lineam HD &longs;iue per quamlibet aliam, globus A mouebitur &longs;emper <lb/>per lineam directionis DA propter rationem propo&longs;itam, quod etiam <lb/>mille experimentis conuincitur. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 132.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si globus major in minorem impingatur per lineam directionis, quæ conne­<lb/>ctat centra, &longs;eruat eamdem lineam<emph.end type="italics"/>; patet etiam experientiâ, cuius ratio e&longs;t <lb/>minor re&longs;i&longs;tentia minoris globi; &longs;i verò &longs;it alia linea directionis, omni­<lb/>nò reflectitur &longs;uo modo; id e&longs;t mutat lineam; &longs;ed de his omnibus fusè <lb/>aliàs; hîc tantùm &longs;ufficiat indica&longs;&longs;e; (&longs;uppo&longs;ita linea directionis cen­<lb/>trali &longs;eu connectente centra, &longs;ic enim deinceps eam appellabimus, in <lb/>quo ca&longs;u duplex determinatio tertiam mediam conflare non pote&longs;t) in­<lb/>dica&longs;&longs;e inquam &longs;ufficiat nouam determinationem, vel e&longs;&longs;e æqualem prio­<lb/>ri, vel maiorem, vel minorem; &longs;i æqualis e&longs;t, globus impactus &longs;i&longs;tit; &longs;i <lb/>maior, reflectitur; &longs;i minor, eamdem lineam, &longs;ed lentiùs pro rata pro­<lb/>&longs;equitur. </s></p><p type="main"> | <s><emph type="italics"/>Si globus major in minorem impingatur per lineam directionis, quæ conne­<lb/>ctat centra, &longs;eruat <expan abbr="eãdem">eandem</expan> lineam<emph.end type="italics"/>; patet etiam experientiâ, cuius ratio e&longs;t <lb/>minor re&longs;i&longs;tentia minoris globi; &longs;i verò &longs;it alia linea directionis, omni­<lb/>nò reflectitur &longs;uo modo; id e&longs;t mutat lineam; &longs;ed de his omnibus fusè <lb/>aliàs; hîc tantùm &longs;ufficiat indica&longs;&longs;e; (&longs;uppo&longs;ita linea directionis cen­<lb/>trali &longs;eu connectente centra, &longs;ic enim deinceps eam appellabimus, in <lb/>quo ca&longs;u duplex determinatio tertiam mediam conflare non pote&longs;t) in­<lb/>dica&longs;&longs;e inquam &longs;ufficiat nouam determinationem, vel e&longs;&longs;e æqualem prio­<lb/>ri, vel maiorem, vel minorem; &longs;i æqualis e&longs;t, globus impactus &longs;i&longs;tit; &longs;i <lb/>maior, reflectitur; &longs;i minor, <expan abbr="eãdem">eandem</expan> lineam, &longs;ed lentiùs pro rata pro­<lb/>&longs;equitur. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 133.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 133.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 135.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 135.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Siduo globi projecti &longs;ibi inuicem occurrant in lineæ directionis connectente <lb/>centra, reflectitur vterque æquali motu, quo antè.<emph.end type="italics"/></s><s> Probatur; &longs;unt enim globi <pb xlink:href="026/01/098.jpg" pagenum="66"/>A & B, & A feratur per lineam DE, & B per lineam ED, punctum con­<lb/>tactus &longs;it C, haud dubiè globus A impactus in B amittit totum &longs;uum im­<lb/>petum per Th.127. & 128. B, item impactus in A amittit totum &longs;uum per <lb/>camdem rationem; globus A producit impetum in B æqualem &longs;uo per <lb/>Th.60. item B producit in A æqualem per idem Th. igitur tantùm perit <lb/>impetus quantùm accedit; igitur in vtroque globo remanet æqualis im­<lb/>petus priori; igitur æquali motu vterque mouetur, quod erat dem. </s> | <s><emph type="italics"/>Si duo globi projecti &longs;ibi inuicem occurrant in lineæ directionis connectente <lb/>centra, reflectitur vterque æquali motu, quo antè.<emph.end type="italics"/></s><s> Probatur; &longs;unt enim globi <pb xlink:href="026/01/098.jpg" pagenum="66"/>A & B, & A feratur per lineam DE, & B per lineam ED, punctum con­<lb/>tactus &longs;it C, haud dubiè globus A impactus in B amittit totum &longs;uum im­<lb/>petum per Th.127. & 128. B, item impactus in A amittit totum &longs;uum per <lb/>eandem rationem; globus A producit impetum in B æqualem &longs;uo per <lb/>Th.60. item B producit in A æqualem per idem Th. igitur tantùm perit <lb/>impetus quantùm accedit; igitur in vtroque globo remanet æqualis im­<lb/>petus priori; igitur æquali motu vterque mouetur, quod erat dem. </s> |
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| <s>& hæc <lb/>e&longs;t ratio veri&longs;&longs;ima toties probatæ experientiæ. </s></p><p type="main"> | <s>& hæc <lb/>e&longs;t ratio veri&longs;&longs;ima toties probatæ experientiæ. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 138.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 138.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si &longs;it duplex impetus in eodem mobili ad eamdem lineam determinatus, non <lb/>mutabitur linea; &longs;ed cre&longs;cet motus & &longs;patium<emph.end type="italics"/> Imprimatur impetus in A, <lb/>per AB, quo dato tempore percurratur &longs;patium AB; deinde produca­<lb/>tur &longs;imul alius impetus æqualis priori in eodem mobili per lineam AB; <lb/>Dico quod eodem tempore percurretur tota AE, dupla &longs;cilicet AB; <lb/>quia &longs;cilicet dupla cau&longs;a non impedita duplum effectum habet per Ax. <!-- REMOVE S--><lb/>13. num.1. duplus impetus duplum motum; igitur duplum &longs;patium; &longs;i <lb/>verò &longs;it triplus impetus, triplum erit &longs;patium, &c. </s> | <s><emph type="italics"/>Si &longs;it duplex impetus in eodem mobili ad <expan abbr="eãdem">eandem</expan> lineam determinatus, non <lb/>mutabitur linea; &longs;ed cre&longs;cet motus & &longs;patium<emph.end type="italics"/> Imprimatur impetus in A, <lb/>per AB, quo dato tempore percurratur &longs;patium AB; deinde produca­<lb/>tur &longs;imul alius impetus æqualis priori in eodem mobili per lineam AB; <lb/>Dico quod eodem tempore percurretur tota AE, dupla &longs;cilicet AB; <lb/>quia &longs;cilicet dupla cau&longs;a non impedita duplum effectum habet per Ax. <!-- REMOVE S--><lb/>13. num.1. duplus impetus duplum motum; igitur duplum &longs;patium; &longs;i <lb/>verò &longs;it triplus impetus, triplum erit &longs;patium, &c. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 139.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 139.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si lineæ duplicis impetus, faciunt angulum acutiorem, longius erit &longs;patium<emph.end type="italics"/><pb xlink:href="026/01/099.jpg" pagenum="67"/><emph type="italics"/>acqui&longs;itum<emph.end type="italics"/>: &longs;int duæ lineæ IK IL, mobili &longs;eilicet &longs;tatuto in I; <lb/>haud dubiè noua linea erit IM; & quo angulus KIL, erit acutior (&longs;up­<lb/>po&longs;itis æqualibus &longs;emper lateribus IK IL) Diagonalis IM, erit ma­<lb/>ior; donec tandem IL & IK coeant in eandem lineam; tunc enim li­<lb/>nea erit dupla IK per Th. &longs;uperius: quandiu verò e&longs;t aliquis angulus in <lb/>I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen <lb/>propiùs &longs;emper accedit; quæ omnia con&longs;tant ex elementis. </s></p><p type="main"> | <s><emph type="italics"/>Si lineæ duplicis impetus, faciunt angulum acutiorem, longius erit &longs;patium<emph.end type="italics"/><pb xlink:href="026/01/099.jpg" pagenum="67"/><emph type="italics"/>acqui&longs;itum<emph.end type="italics"/>: &longs;int duæ lineæ IK IL, mobili &longs;cilicet &longs;tatuto in I; <lb/>haud dubiè noua linea erit IM; & quo angulus KIL, erit acutior (&longs;up­<lb/>po&longs;itis æqualibus &longs;emper lateribus IK IL) Diagonalis IM, erit ma­<lb/>ior; donec tandem IL & IK coeant in eandem lineam; tunc enim li­<lb/>nea erit dupla IK per Th. &longs;uperius: quandiu verò e&longs;t aliquis angulus in <lb/>I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen <lb/>propiùs &longs;emper accedit; quæ omnia con&longs;tant ex elementis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 140.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 140.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 141.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 141.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Ex his nece&longs;&longs;aria ducitur ratio, cur impetus duplus ad diuer&longs;as lineas de­<lb/>terminatus non habeat motum duplum, & con&longs;equenter &longs;patium duplum<emph.end type="italics"/>; nec <lb/>enim AE e&longs;t dupla AB, vt con&longs;tat; nam &longs;i lineæ &longs;int oppo&longs;itæ ex <lb/>diametro vt BA BE totus de&longs;truitur impetus, per Th.133. &longs;i verò vna <lb/>in eamdem lineam coëat cum aliâ, nihil impetus de&longs;truitur, nec impedi­<lb/>tur per Th.138. igitur quà proportione propiùs accedet ad oppo&longs;itas; <lb/>plùs de&longs;truetur, & minus erit &longs;patium; & quâ proportione accedent <lb/>propiùs ad coëuntes, minùs de&longs;truetur, & maius erit &longs;patium, vt con&longs;tat <lb/>ex dictis. </s></p><p type="main"> | <s><emph type="italics"/>Ex his nece&longs;&longs;aria ducitur ratio, cur impetus duplus ad diuer&longs;as lineas de­<lb/>terminatus non habeat motum duplum, & con&longs;equenter &longs;patium duplum<emph.end type="italics"/>; nec <lb/>enim AE e&longs;t dupla AB, vt con&longs;tat; nam &longs;i lineæ &longs;int oppo&longs;itæ ex <lb/>diametro vt BA BE totus de&longs;truitur impetus, per Th.133. &longs;i verò vna <lb/>in <expan abbr="eãdem">eandem</expan> lineam coëat cum aliâ, nihil impetus de&longs;truitur, nec impedi­<lb/>tur per Th.138. igitur quà proportione propiùs accedet ad oppo&longs;itas; <lb/>plùs de&longs;truetur, & minus erit &longs;patium; & quâ proportione accedent <lb/>propiùs ad coëuntes, minùs de&longs;truetur, & maius erit &longs;patium, vt con&longs;tat <lb/>ex dictis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 142.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 142.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 149.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 149.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>In lineis oppo&longs;itis impetus de&longs;truitur ab impetu &longs;uo modo<emph.end type="italics"/>; &longs;it enim globus <lb/>proiectus ver&longs;us au&longs;trum; cui deinde imprimatur nouus impetus ver­<lb/>&longs;us Boream; de&longs;truitur prior vt con&longs;tat, igitur ad exigentiam alicuius, <lb/>&longs;ed nihil e&longs;t quod po&longs;&longs;it exigere, ni&longs;i nouus impetus, &longs;cilicet mediatè; <lb/>nihil enim aliud e&longs;t applicatum, igitar nihil aliud exigit per Ax. 10. <lb/>hæc porrò exigentia non e&longs;t immediata, &longs;ed mediata, vt dixi. </s></p><p type="main"> | <s><emph type="italics"/>In lineis oppo&longs;itis impetus de&longs;truitur ab impetu &longs;uo modo<emph.end type="italics"/>; &longs;it enim globus <lb/>proiectus ver&longs;us au&longs;trum; cui deinde imprimatur nouus impetus ver­<lb/>&longs;us Boream; de&longs;truitur prior vt con&longs;tat, igitur ad exigentiam alicuius, <lb/>&longs;ed nihil e&longs;t quod po&longs;&longs;it exigere, ni&longs;i nouus impetus, &longs;cilicet mediatè; <lb/>nihil enim aliud e&longs;t applicatum, igitur nihil aliud exigit per Ax. 10. <lb/>hæc porrò exigentia non e&longs;t immediata, &longs;ed mediata, vt dixi. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 150.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 150.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Sextò, Impetus naturalis innatus nunquam de&longs;truitur; quia nunquam <lb/>e&longs;t fru&longs;trà; quippe &longs;emper habet alterum &longs;uorum effectuum formalium, <lb/>id e&longs;t vel motum deor&longs;um, vel grauitationem, adde quod fru&longs;trà de­<lb/>&longs;trueretur, cum &longs;it &longs;emper applicata potentia, id e&longs;t ip&longs;a grauitas, &longs;ed de <lb/>his infrâ fusè. </s></p><pb xlink:href="026/01/103.jpg" pagenum="71"/><p type="main"> | <s>Sextò, Impetus naturalis innatus nunquam de&longs;truitur; quia nunquam <lb/>e&longs;t fru&longs;trà; quippe &longs;emper habet alterum &longs;uorum effectuum formalium, <lb/>id e&longs;t vel motum deor&longs;um, vel grauitationem, adde quod fru&longs;trà de­<lb/>&longs;trueretur, cum &longs;it &longs;emper applicata potentia, id e&longs;t ip&longs;a grauitas, &longs;ed de <lb/>his infrâ fusè. </s></p><pb xlink:href="026/01/103.jpg" pagenum="71"/><p type="main"> |
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| <s>Septimò, Impetus &longs;ur&longs;um de&longs;truitur etiam, quia e&longs;t fru&longs;trà; quippe <lb/>naturalis detrahit aliquid &longs;patij pro rata; igitur ne aliquid impetus &longs;it <lb/>fru&longs;trà, de&longs;truitur; idem dico de impetu per inclinatam &longs;ur&longs;um, licèt <lb/>minùs de&longs;truatur quàm in perpendiculari &longs;ur&longs;um; idem de impetu per <lb/>inclinatam deor&longs;um, &longs;ed minùs adhuc, &longs;ed hæc acuratiori medita ioni <lb/>&longs;unt relinquenda; quod reuerâ præ&longs;tabimus in lib.4. de motu mixto; <lb/>quidquid &longs;it, con&longs;tat ex dictis per idem Principium probari po&longs;&longs;e de­<lb/>&longs;tructionem impetus, &longs;cilicet ne &longs;it fru&longs;trà; &longs;ed de his aliàs fusè. </s></p><p type="main"> | <s>Septimò, Impetus &longs;ur&longs;um de&longs;truitur etiam, quia e&longs;t fru&longs;trà; quippe <lb/>naturalis detrahit aliquid &longs;patij pro rata; igitur ne aliquid impetus &longs;it <lb/>fru&longs;trà, de&longs;truitur; idem dico de impetu per inclinatam &longs;ur&longs;um, licèt <lb/>minùs de&longs;truatur quàm in perpendiculari &longs;ur&longs;um; idem de impetu per <lb/>inclinatam deor&longs;um, &longs;ed minùs adhuc, &longs;ed hæc acuratiori meditationi <lb/>&longs;unt relinquenda; quod reuerâ præ&longs;tabimus in lib.4. de motu mixto; <lb/>quidquid &longs;it, con&longs;tat ex dictis per idem Principium probari po&longs;&longs;e de­<lb/>&longs;tructionem impetus, &longs;cilicet ne &longs;it fru&longs;trà; &longs;ed de his aliàs fusè. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 153.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 153.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus productus ab extrin&longs;eco e&longs;t tantùm contrarius ratione diuer&longs;æ de­<lb/>terminationis, &longs;eu diuer&longs;æ lineæ<emph.end type="italics"/>; Probatur primò, quia vterque ad omnem <lb/>lineam e&longs;t indifferens per Th.113. igitur vnus non c&longs;t alteri contrarius <lb/>ratione entitatis; cùm vterque &longs;imilem motum, immò eumdem habere <lb/>po&longs;&longs;it, vt patet ex dictis: Igitur ratione tanuùn lineæ vnus alteri e&longs;t <lb/>contrarius; hinc minùs e&longs;t contrarietatis, quo minùs e&longs;t oppo&longs;itionis <lb/>inter lineas & contrà. </s></p><p type="main"> | <s><emph type="italics"/>Impetus productus ab extrin&longs;eco e&longs;t tantùm contrarius ratione diuer&longs;æ de­<lb/>terminationis, &longs;eu diuer&longs;æ lineæ<emph.end type="italics"/>; Probatur primò, quia vterque ad omnem <lb/>lineam e&longs;t indifferens per Th.113. igitur vnus non e&longs;t alteri contrarius <lb/>ratione entitatis; cùm vterque &longs;imilem motum, immò <expan abbr="eũdem">eundem</expan> habere <lb/>po&longs;&longs;it, vt patet ex dictis: </s> |
| | <s>Igitur ratione tantùm lineæ vnus alteri e&longs;t <lb/>contrarius; hinc minùs e&longs;t contrarietatis, quo minùs e&longs;t oppo&longs;itionis <lb/>inter lineas & contrà. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 154.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 154.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 157.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 157.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus ex non contrario eidem fit contrarius<emph.end type="italics"/>; vt patet in eodem ca&longs;u; <lb/>nam impetus naturalis innatus, qui in de&longs;cen&longs;u non erat contrarius <lb/>ac qui&longs;ito, in inotu &longs;ur&longs;um reflexo fit contrarius. </s></p><p type="main"> | <s><emph type="italics"/>Impetus ex non contrario eidem fit contrarius<emph.end type="italics"/>; vt patet in eodem ca&longs;u; <lb/>nam impetus naturalis innatus, qui in de&longs;cen&longs;u non erat contrarius <lb/>acqui&longs;ito, in motu &longs;ur&longs;um reflexo fit contrarius. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 158.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 158.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 161.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 161.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Idem impetus pote&longs;t eumdem alium aliquando plùs, aliquando minùs <lb/>intendere. </s> | <s>Idem impetus pote&longs;t <expan abbr="eũdem">eundem</expan> alium aliquando plùs, aliquando minùs <lb/>intendere. </s> |
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| <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->4. gradus impetus additi aliis 4. per eamdem lineam <lb/>iidem ei&longs;dem, minùs intendunt, vt iam &longs;uprà &longs;atis fusè dictum e&longs;t. </s> | <s>v. <!-- REMOVE S-->g. <!-- REMOVE S-->4. gradus impetus additi aliis 4. per <expan abbr="eãdem">eandem</expan> lineam <lb/>iidem ei&longs;dem, minùs intendunt, vt iam &longs;uprà &longs;atis fusè dictum e&longs;t. </s> |
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| <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus additus alteri, & determinatus ad eamdem lineam, facit maiorem <lb/>& inten&longs;iorom impetum<emph.end type="italics"/>; patet, & vici&longs;&longs;im, & detractus alteri minorem <lb/>facit, & vici&longs;&longs;im. </s></p><p type="main"> | <s><emph type="italics"/>Impetus additus alteri, & determinatus ad <expan abbr="eãdem">eandem</expan> lineam, facit maiorem <lb/>& inten&longs;iorem impetum<emph.end type="italics"/>; patet, & vici&longs;&longs;im, & detractus alteri minorem <lb/>facit, & vici&longs;&longs;im. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>hic motus e&longs;t ab intrin&longs;eco, <lb/>quod probatur; non e&longs;t ab vllâ causâ extrin&longs;ecâ; igitur e&longs;t ab intrin&longs;eca <lb/>per Ax.4. antecedens probatur inductione factâ omnium extrin&longs;ecorum. </s> | <s>hic motus e&longs;t ab intrin&longs;eco, <lb/>quod probatur; non e&longs;t ab vllâ causâ extrin&longs;ecâ; igitur e&longs;t ab intrin&longs;eca <lb/>per Ax.4. antecedens probatur inductione factâ omnium extrin&longs;ecorum. </s> |
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| <s><lb/>Primò non e&longs;t à cau&longs;a prima, vt aliquis fortè minùs prudenter, & magis <lb/>piè, quàm par &longs;it, diceret; quia ille effectus tribui tantùm debet cau&longs;æ <lb/>primæ, qui nullam habere pote&longs;t cau&longs;am &longs;ecundam applicatam, vt patet; <lb/>&longs;ed hic effectus pote&longs;t habere cau&longs;am &longs;ecundam applicatam, quam a&longs;&longs;i­<lb/>gnabimus infrà; deinde cau&longs;a prima agit tantùm naturaliter iuxta exi­<lb/>gentiam cau&longs;arum &longs;ecundarum; igitur ideo moueret corpus graue deor­<lb/>&longs;um; quia tunc motum corpus graue exigeret; &longs;ed lioc milri &longs;u&longs;ficit, vt <lb/>dicatur hic motus e&longs;&longs;e ab intrin&longs;eco; præterea, &longs;i dicatur Deus mouere <lb/>corpus graue deor&longs;um iuxta illius exigentiam, dicetur etiam tùm cale­<lb/>facere, tùm illuminare, ad exigentiam ignis; quippe tàm mihi &longs;en&longs;ibile <lb/>e&longs;t corpus graue de&longs;cendere &longs;ine vi impre&longs;&longs;a ab extrin&longs;eco, quàm ignem <lb/>calefacere, & &longs;olem lucere &longs;ine vi extrin&longs;eca; adde quod illud &longs;olenne <lb/>e&longs;t naturæ in&longs;titutum, vt id, quod exigit res aliqua ad finem &longs;uum con&longs;e­<lb/>quendum, per virtutem intrin&longs;ecam po&longs;&longs;it ponere, &longs;i dumtaxat excipias <lb/>concur&longs;um diuinum, & ip&longs;am con&longs;oruationem; &longs;ic animal exigit vide­<lb/>re, audire, &longs;entire, moueri; igitur habet virtutem intrin&longs;ecam, per quam <lb/>videat, audiat, & moueatur; &longs;ic ignis exigit calefacere, lucere; aër, vel aqua <lb/>frigefacere, quidquid tandem &longs;int i&longs;tæ qualitates, de quibus alibi; &longs;ic <lb/>demum corpus graue exigit moueri deor&longs;um; quis enim neget corpori <lb/>graui tàm natiuum e&longs;&longs;e tendere deor&longs;um, cum &longs;cilicer corpus leuius &longs;ub­<lb/>e&longs;t, quàm &longs;it animali progredi, vrere igni, lucere, &c. </s></p><p type="main"> | <s><lb/>Primò non e&longs;t à cau&longs;a prima, vt aliquis fortè minùs prudenter, & magis <lb/>piè, quàm par &longs;it, diceret; quia ille effectus tribui tantùm debet cau&longs;æ <lb/>primæ, qui nullam habere pote&longs;t cau&longs;am &longs;ecundam applicatam, vt patet; <lb/>&longs;ed hic effectus pote&longs;t habere cau&longs;am &longs;ecundam applicatam, quam a&longs;&longs;i­<lb/>gnabimus infrà; deinde cau&longs;a prima agit tantùm naturaliter iuxta exi­<lb/>gentiam cau&longs;arum &longs;ecundarum; igitur ideo moueret corpus graue deor­<lb/>&longs;um; quia tunc motum corpus graue exigeret; &longs;ed hoc mihi &longs;ufficit, vt <lb/>dicatur hic motus e&longs;&longs;e ab intrin&longs;eco; præterea, &longs;i dicatur Deus mouere <lb/>corpus graue deor&longs;um iuxta illius exigentiam, dicetur etiam tùm cale­<lb/>facere, tùm illuminare, ad exigentiam ignis; quippe tàm mihi &longs;en&longs;ibile <lb/>e&longs;t corpus graue de&longs;cendere &longs;ine vi impre&longs;&longs;a ab extrin&longs;eco, quàm ignem <lb/>calefacere, & &longs;olem lucere &longs;ine vi extrin&longs;eca; adde quod illud &longs;olenne <lb/>e&longs;t naturæ in&longs;titutum, vt id, quod exigit res aliqua ad finem &longs;uum con&longs;e­<lb/>quendum, per virtutem intrin&longs;ecam po&longs;&longs;it ponere, &longs;i dumtaxat excipias <lb/>concur&longs;um diuinum, & ip&longs;am con&longs;eruationem; &longs;ic animal exigit vide­<lb/>re, audire, &longs;entire, moueri; igitur habet virtutem intrin&longs;ecam, per quam <lb/>videat, audiat, & moueatur; &longs;ic ignis exigit calefacere, lucere; aër, vel aqua <lb/>frigefacere, quidquid tandem &longs;int i&longs;tæ qualitates, de quibus alibi; &longs;ic <lb/>demum corpus graue exigit moueri deor&longs;um; quis enim neget corpori <lb/>graui tàm natiuum e&longs;&longs;e tendere deor&longs;um, cum &longs;cilicet corpus leuius &longs;ub­<lb/>e&longs;t, quàm &longs;it animali progredi, vrere igni, lucere, &c. </s></p><p type="main"> |
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| <s>Denique &longs;atis e&longs;t mihi, vt dicatur aliquid cau&longs;a, Phy&longs;icè loquendo, &longs;i <lb/>ex illius applicatione &longs;emper &longs;equatur effectus; nam non nego po&longs;&longs;e fie­<lb/>ri effectus omnes, qui no&longs;tris &longs;en&longs;ibus &longs;ubiiciuntur, &longs;altem extrin&longs;ecos, <lb/>e&longs;&longs;e à cau&longs;a prima, quippe &longs;i &longs;emper ex ignis applicatione Deus diffun­<lb/>deret lucem, & calorem, quem &longs;olus ip&longs;e produceret, igne ip&longs;o inerte re­<lb/>licto, nullam pror&longs;us mutationem perciperemus; & nemo e&longs;&longs;et, qui non <lb/>exi&longs;timaret lucom hanc & calorem ltunc e&longs;&longs;e ab igne; igitur Phy&longs;icè lo­<lb/>quendo cau&longs;am appellamus id, ex cuius applicatione &longs;emper &longs;equitur <lb/>effectus, vt iam diximus in Ax. 11.l.1. n.1. Igitur cum ex corpore graui <lb/>po&longs;ito in aëre libero &longs;equatur motus deor&longs;um; dicendum e&longs;t, Phy&longs;icè lo­<lb/>quendò, e&longs;&longs;e huius motus cau&longs;am, id e&longs;t in ordine ad Phy&longs;icam, perinde <lb/>omninò &longs;e habere, atque &longs;i e&longs;&longs;et cau&longs;a, licèt cau&longs;a non e&longs;&longs;et. </s></p><pb xlink:href="026/01/109.jpg" pagenum="77"/><p type="main"> | <s>Denique &longs;atis e&longs;t mihi, vt dicatur aliquid cau&longs;a, Phy&longs;icè loquendo, &longs;i <lb/>ex illius applicatione &longs;emper &longs;equatur effectus; nam non nego po&longs;&longs;e fie­<lb/>ri effectus omnes, qui no&longs;tris &longs;en&longs;ibus &longs;ubiiciuntur, &longs;altem extrin&longs;ecos, <lb/>e&longs;&longs;e à cau&longs;a prima, quippe &longs;i &longs;emper ex ignis applicatione Deus diffun­<lb/>deret lucem, & calorem, quem &longs;olus ip&longs;e produceret, igne ip&longs;o inerte re­<lb/>licto, nullam pror&longs;us mutationem perciperemus; & nemo e&longs;&longs;et, qui non <lb/>exi&longs;timaret lucem hanc & calorem hunc e&longs;&longs;e ab igne; igitur Phy&longs;icè lo­<lb/>quendo cau&longs;am appellamus id, ex cuius applicatione &longs;emper &longs;equitur <lb/>effectus, vt iam diximus in Ax. 11.l.1. n.1. Igitur cum ex corpore graui <lb/>po&longs;ito in aëre libero &longs;equatur motus deor&longs;um; dicendum e&longs;t, Phy&longs;icè lo­<lb/>quendò, e&longs;&longs;e huius motus cau&longs;am, id e&longs;t in ordine ad Phy&longs;icam, perinde <lb/>omninò &longs;e habere, atque &longs;i e&longs;&longs;et cau&longs;a, licèt cau&longs;a non e&longs;&longs;et. </s></p><pb xlink:href="026/01/109.jpg" pagenum="77"/><p type="main"> |
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| <s>Secundò hic motus non e&longs;t ab aëre ambiente; probatur, ruderet aër <lb/>deor&longs;um corpus graue, quia leuior e&longs;t, id e&longs;t ne &longs;uprà &longs;e corpus grauins <lb/>haberet; &longs;ed eâdem ratione corpus graue debet remouere &longs;ur&longs;um aëra, <lb/>id e&longs;t corpus leue, ne infrà &longs;e habeat corpus leuius; e&longs;t enim par omni­<lb/>nò ratio: Præterea &longs;i aër trudit deor&longs;inn corpus graue, quia ip&longs;i loco <lb/>cedit; certè ip&longs;e aër mouetur, igitur ab intrin&longs;eco; &longs;i enim vna pars aë­<lb/>ris pellit aliam, & hæc aliam, tandem ad aliquam peruenitur, quæ &longs;e ip­<lb/>&longs;am mouet; igitur motus illius e&longs;t ab intrin&longs;eco; igitur motus natura­<lb/>lis; deinde non modò lapis de&longs;cendit per aëra, &longs;ed per mediam aquam; <lb/>igitur &longs;i ab aëre truditur deor&longs;um, idem dicendum e&longs;t de aquâ, a qui <lb/>haud dubiè maiore vi truderetur; nam corpus den&longs;um maiore vi pellit, <lb/>quàm rarum, vt con&longs;tat exprientiâ; cum tamen corpus graue per me­<lb/>dium den&longs;ius difficiliùs de cendat; igitur medium ip&longs;um re&longs;i&longs;tit motui, <lb/>quis hoc neget? </s> | <s>Secundò hic motus non e&longs;t ab aëre ambiente; probatur, ruderet aër <lb/>deor&longs;um corpus graue, quia leuior e&longs;t, id e&longs;t ne &longs;uprà &longs;e corpus grauius <lb/>haberet; &longs;ed eâdem ratione corpus graue debet remouere &longs;ur&longs;um aëra, <lb/>id e&longs;t corpus leue, ne infrà &longs;e habeat corpus leuius; e&longs;t enim par omni­<lb/>nò ratio: Præterea &longs;i aër trudit deor&longs;inn corpus graue, quia ip&longs;i loco <lb/>cedit; certè ip&longs;e aër mouetur, igitur ab intrin&longs;eco; &longs;i enim vna pars aë­<lb/>ris pellit aliam, & hæc aliam, tandem ad aliquam peruenitur, quæ &longs;e ip­<lb/>&longs;am mouet; igitur motus illius e&longs;t ab intrin&longs;eco; igitur motus natura­<lb/>lis; deinde non modò lapis de&longs;cendit per aëra, &longs;ed per mediam aquam; <lb/>igitur &longs;i ab aëre truditur deor&longs;um, idem dicendum e&longs;t de aquâ, a qui <lb/>haud dubiè maiore vi truderetur; nam corpus den&longs;um maiore vi pellit, <lb/>quàm rarum, vt con&longs;tat exprientiâ; cum tamen corpus graue per me­<lb/>dium den&longs;ius difficiliùs decendat; igitur medium ip&longs;um re&longs;i&longs;tit motui, <lb/>quis hoc neget? </s> |
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| <s>igitur non e&longs;t cau&longs;a motus, quem impedit. </s></p><p type="main"> | <s>igitur non e&longs;t cau&longs;a motus, quem impedit. </s></p><p type="main"> |
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| <s>Denique &longs;i corpus graue non tendit, fertur que deor&longs;um &longs;uá &longs;ponte, <lb/>&longs;ed ab aëre extru&longs;um; igitur dum vix &longs;u&longs;tineo manu; o. </s> | <s>Denique &longs;i corpus graue non tendit, fertur que deor&longs;um &longs;uá &longs;ponte, <lb/>&longs;ed ab aëre extru&longs;um; igitur dum vix &longs;u&longs;tineo manu; o. </s> |
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| <s>libras ferri, &longs;eu <lb/>plumbi; hæc vis illata manui, quam probè &longs;entio, e&longs;t ab aëre impel­<lb/>lente plumbum, quod e&longs;t ridiculum, cnm eadem quantitas aëris incu­<lb/>ber, & &longs;ub&longs;it manui, &longs;iue &longs;u&longs;tineat plumbum, &longs;iue &longs;it vacua; ex hoc, ni <lb/>fallor, euincitur pondus ip&longs;um &longs;ui &longs;ponte deor&longs;unr tendere. </s></p><p type="main"> | <s>libras ferri, &longs;eu <lb/>plumbi; hæc vis illata manui, quam probè &longs;entio, e&longs;t ab aëre impel­<lb/>lente plumbum, quod e&longs;t ridiculum, cum eadem quantitas aëris incu­<lb/>ber, & &longs;ub&longs;it manui, &longs;iue &longs;u&longs;tineat plumbum, &longs;iue &longs;it vacua; ex hoc, ni <lb/>fallor, euincitur pondus ip&longs;um &longs;ui &longs;ponte deor&longs;um tendere. </s></p><p type="main"> |
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| <s>Tertiò non de&longs;unt, qui dicant corpus graue trahi ab ip&longs;a vi quadam <lb/>magneticâ, quod triplici modo fieri pote&longs;t; Primò per qualitatem <lb/>quamdam diffu&longs;am, quod dici non pote&longs;t; quia capillus traheretur faci­<lb/>liùs, quàm ingens &longs;axum, quàm ma&longs;&longs;a, &longs;eu lamina; & faciliùs eadem po­<lb/>tentia motrix minus pondus moueret quàm maius, cæteris paribus; præ­<lb/>terea manum meam æqualiter traheret, &longs;iue &longs;it cum aliquo pondere con­<lb/>iuncta, &longs;iuc &longs;it nuda &longs;ine pondere; deinde illa virtus tractrix ita diffun­<lb/>ditur, vt in maiori di&longs;tantia &longs;it infirmior, fortior in minori; alioqui <lb/>diffunderetur in infinitum, quod dici non pote&longs;t; igitur &longs;i idem lapis <lb/>demittatur ex maiore altitudine, tum ex minore; haud dubiè morus ille <lb/>primus initio e&longs;&longs;et tardior i&longs;to contra experientiam; deinde in &longs;pecu al­<lb/>ti&longs;&longs;ima &longs;ubterranea trahi po&longs;&longs;et corpus virdequaque, &longs;icut in magnete; <lb/>quæ omnia intelligi non po&longs;&longs;unt; denique virtutes illas &longs;eu qualitates <lb/>tractrices refellemus &longs;uo loco. </s></p><p type="main"> | <s>Tertiò non de&longs;unt, qui dicant corpus graue trahi ab ip&longs;a vi quadam <lb/>magneticâ, quod triplici modo fieri pote&longs;t; Primò per qualitatem <lb/>quamdam diffu&longs;am, quod dici non pote&longs;t; quia capillus traheretur faci­<lb/>liùs, quàm ingens &longs;axum, quàm ma&longs;&longs;a, &longs;eu lamina; & faciliùs eadem po­<lb/>tentia motrix minus pondus moueret quàm maius, cæteris paribus; præ­<lb/>terea manum meam æqualiter traheret, &longs;iue &longs;it cum aliquo pondere con­<lb/>iuncta, &longs;iuc &longs;it nuda &longs;ine pondere; deinde illa virtus tractrix ita diffun­<lb/>ditur, vt in maiori di&longs;tantia &longs;it infirmior, fortior in minori; alioqui <lb/>diffunderetur in infinitum, quod dici non pote&longs;t; igitur &longs;i idem lapis <lb/>demittatur ex maiore altitudine, tum ex minore; haud dubiè morus ille <lb/>primus initio e&longs;&longs;et tardior i&longs;to contra experientiam; deinde in &longs;pecu al­<lb/>ti&longs;&longs;ima &longs;ubterranea trahi po&longs;&longs;et corpus vndequaque, &longs;icut in magnete; <lb/>quæ omnia intelligi non po&longs;&longs;unt; denique virtutes illas &longs;eu qualitates <lb/>tractrices refellemus &longs;uo loco. </s></p><p type="main"> |
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| <s>Secundò, aliqui dicunt hoc totum fieri per vim quamdam &longs;ympathi­<lb/>cam, quod etiam fal&longs;i&longs;&longs;imum e&longs;t; tùm quia hæc &longs;ympathia explicari <lb/>non pote&longs;t; tùm quia vel terra ip&longs;a producit aliquid in corpore graui, <lb/>quod in aëre libratur; vel corpus in &longs;e ip&longs;o; &longs;i primum; refellitur ii&longs;­<lb/>dem omninò rationibus, quibus ip&longs;am vim terræ tractricem &longs;uprà expu­<lb/>gnauimus; &longs;i verò &longs;ecundum, hoc ip&longs;um e&longs;t, quod &longs;uprà diximus. </s></p><p type="main"> | <s>Secundò, aliqui dicunt hoc totum fieri per vim quamdam &longs;ympathi­<lb/>cam, quod etiam fal&longs;i&longs;&longs;imum e&longs;t; tùm quia hæc &longs;ympathia explicari <lb/>non pote&longs;t; tùm quia vel terra ip&longs;a producit aliquid in corpore graui, <lb/>quod in aëre libratur; vel corpus in &longs;e ip&longs;o; &longs;i primum; refellitur ii&longs;­<lb/>dem omninò rationibus, quibus ip&longs;am vim terræ tractricem &longs;uprà expu­<lb/>gnauimus; &longs;i verò &longs;ecundum, hoc ip&longs;um e&longs;t, quod &longs;uprà diximus. </s></p><p type="main"> |
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| <s>Secundò, corpus vicinius etiam faciliùs abriperetur. </s></p><p type="main"> | <s>Secundò, corpus vicinius etiam faciliùs abriperetur. </s></p><p type="main"> |
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| <s>Tertiò, numquid flante vento, vel imbre cadente di&longs;&longs;ipantur hæc &longs;i­<lb/>lamenta? </s> | <s>Tertiò, numquid flante vento, vel imbre cadente di&longs;&longs;ipantur hæc fi­<lb/>lamenta? </s> |
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| <s>quod etiam videmus in electro. </s></p><p type="main"> | <s>quod etiam videmus in electro. </s></p><p type="main"> |
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| <s>Sextò, hæc filamenta, quæ deinde reducuntur, debent habere cau­<lb/>&longs;am huius reductionis non extrin&longs;ecam; igitur intrin&longs;ecam; igitur datur <lb/>motus naturalis. </s></p><p type="main"> | <s>Sextò, hæc filamenta, quæ deinde reducuntur, debent habere cau­<lb/>&longs;am huius reductionis non extrin&longs;ecam; igitur intrin&longs;ecam; igitur datur <lb/>motus naturalis. </s></p><p type="main"> |
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| <s>Soptimò, hæc filamenta per mediam flammam non traherent, quod <lb/>etiam fieri videmus in electro. </s></p><p type="main"> | <s>Septimò, hæc filamenta per mediam flammam non traherent, quod <lb/>etiam fieri videmus in electro. </s></p><p type="main"> |
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| <s>Quartò, motus naturalis non e&longs;t à virtute quadam pellente, quam <lb/>cælo quidam affingunt; nam vel ab omni parte cæli deor&longs;um trudere­<lb/>tur, vel ab vnâ; &longs;i ab vna; igitur in omni cæli plaga corpus non fertur <lb/>deor&longs;um; &longs;i ab omni, ergo cum pellatur corpus per plures lineas etiam <lb/>oppo&longs;itas moueri non pote&longs;t: Præterea debilior e&longs;&longs;et hæc vis in maiori <lb/>di&longs;tantiâ; denique vapores, & alia minutiora corpu&longs;cula in aëre fluitan­<lb/>tia faciliùs deor&longs;um truderentur, contra experientiam. </s></p><p type="main"> | <s>Quartò, motus naturalis non e&longs;t à virtute quadam pellente, quam <lb/>cælo quidam affingunt; nam vel ab omni parte cæli deor&longs;um trudere­<lb/>tur, vel ab vnâ; &longs;i ab vna; igitur in omni cæli plaga corpus non fertur <lb/>deor&longs;um; &longs;i ab omni, ergo cum pellatur corpus per plures lineas etiam <lb/>oppo&longs;itas moueri non pote&longs;t: Præterea debilior e&longs;&longs;et hæc vis in maiori <lb/>di&longs;tantiâ; denique vapores, & alia minutiora corpu&longs;cula in aëre fluitan­<lb/>tia faciliùs deor&longs;um truderentur, contra experientiam. </s></p><p type="main"> |
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| <s>Sed non e&longs;t omittendum, quod aliqui putant ex illis filamentis con­<lb/>texi po&longs;&longs;e legitimam rationem, cur atomi etiam plumbeæ materiæ non <lb/>ita facilè de&longs;cendant; quòd &longs;cilicet propter &longs;uam tenuitatem ab illis fi­<lb/>lamentis non ita intercipi vel implicari po&longs;&longs;int; &longs;ed qua&longs;i pi&longs;ces per fo­<lb/>ramina retium euadant; &longs;ed profectò longè alia ratio e&longs;t, qaàm &longs;uo loco <lb/>afferemus, nam etiam plumæ, fe&longs;tucæ, paleæ, & alia corpu&longs;cula longio­<lb/>ra, &longs;ed leui&longs;&longs;ima iis filamentis implicarentur, vt videre e&longs;t in electro. </s></p><p type="main"> | <s>Sed non e&longs;t omittendum, quod aliqui putant ex illis filamentis con­<lb/>texi po&longs;&longs;e legitimam rationem, cur atomi etiam plumbeæ materiæ non <lb/>ita facilè de&longs;cendant; quòd &longs;cilicet propter &longs;uam tenuitatem ab illis fi­<lb/>lamentis non ita intercipi vel implicari po&longs;&longs;int; &longs;ed qua&longs;i pi&longs;ces per fo­<lb/>ramina retium euadant; &longs;ed profectò longè alia ratio e&longs;t, quàm &longs;uo loco <lb/>afferemus, nam etiam plumæ, fe&longs;tucæ, paleæ, & alia corpu&longs;cula longio­<lb/>ra, &longs;ed leui&longs;&longs;ima iis filamentis implicarentur, vt videre e&longs;t in electro. </s></p><p type="main"> |
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| <s>Quintò, aliqui recentiores exi&longs;timant corpora deor&longs;um trudi ab <lb/>ip&longs;a luce, quæ nihil e&longs;t aliud, quam motio æthereæ cuiu&longs;dam &longs;ub&longs;tan­<lb/>tiæ per poros aëris traductæ, vt ip&longs;i volunt; &longs;ed neque hoc probari po­<lb/>te&longs;t. </s> | <s>Quintò, aliqui recentiores exi&longs;timant corpora deor&longs;um trudi ab <lb/>ip&longs;a luce, quæ nihil e&longs;t aliud, quam motio æthereæ cuiu&longs;dam &longs;ub&longs;tan­<lb/>tiæ per poros aëris traductæ, vt ip&longs;i volunt; &longs;ed neque hoc probari po­<lb/>te&longs;t. </s> |
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| <s>Primò quia de nocte corpora æquali motu deor&longs;um feruntur; pe­<lb/>rinde atque de die, nec minùs in ob&longs;curi&longs;&longs;imo conclaui, quàm &longs;ub dio, <lb/>vel aperto cælo. </s> | <s>Primò quia de nocte corpora æquali motu deor&longs;um feruntur; pe­<lb/>rinde atque de die, nec minùs in ob&longs;curi&longs;&longs;imo conclaui, quàm &longs;ub dio, <lb/>vel aperto cælo. </s> |
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| <s>Secundò, in &longs;ubterraneis locis etiam grauia æquè veloci­<lb/>ter de&longs;cendunt; licèr eò lumen non penetret; quod &longs;i aliquis ob&longs;tinatè, <lb/>id a&longs;&longs;ereret; haud dubiè per medium aëra maior huius materiæ copia <lb/>diffunditur, quàm per medias rupes, quis hoc neget; igitur pauci&longs;&longs;imi <lb/>radij v&longs;que ad interius & inferius antrum perueniunt. </s> | <s>Secundò, in &longs;ubterraneis locis etiam grauia æquè veloci­<lb/>ter de&longs;cendunt; licèt eò lumen non penetret; quod &longs;i aliquis ob&longs;tinatè, <lb/>id a&longs;&longs;ereret; haud dubiè per medium aëra maior huius materiæ copia <lb/>diffunditur, quàm per medias rupes, quis hoc neget; igitur pauci&longs;&longs;imi <lb/>radij v&longs;que ad interius & inferius antrum perueniunt. </s> |
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| <s>Tertiò, manum <lb/>meam &longs;iue ponderi coniunctam &longs;iue ab eo <expan abbr="&longs;eparatã">&longs;eparatam</expan> æqualis portio illius <lb/>materiæ deor&longs;um pelleret, vt patet; igitur æquali motus vi. </s> | <s>Tertiò, manum <lb/>meam &longs;iue ponderi coniunctam &longs;iue ab eo <expan abbr="&longs;eparatã">&longs;eparatam</expan> æqualis portio illius <lb/>materiæ deor&longs;um pelleret, vt patet; igitur æquali motus vi. </s> |
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| <s>Nec e&longs;t quod prædicti àuthores confugiant ad experientiam, qua <lb/>&longs;cilicet videmus tripudiantes atomos in radio &longs;olari immer&longs;as; igitur <lb/>agitantur ab ip&longs;o radio, quod maximè accidit in linea v&longs;toria, cuius <lb/>effectus veri&longs;&longs;imam rationem &longs;uo loco afferemus, cum de lumine. </s></p><p type="main"> | <s>Nec e&longs;t quod prædicti àuthores confugiant ad experientiam, qua <lb/>&longs;cilicet videmus tripudiantes atomos in radio &longs;olari immer&longs;as; igitur <lb/>agitantur ab ip&longs;o radio, quod maximè accidit in linea v&longs;toria, cuius <lb/>effectus veri&longs;&longs;imam rationem &longs;uo loco afferemus, cum de lumine. </s></p><p type="main"> |
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| <s>Sextò, &longs;unt denique multi, <expan abbr="ii&qacute;ue">iique</expan> ex &longs;euerioribus Peripateticis, qui <lb/>exi&longs;timant grauia moueri deor&longs;um à generante, quod expre&longs;&longs;rs verbis <lb/>traditum e&longs;t ab <emph type="italics"/>Ari&longs;totele l.<emph.end type="italics"/>8. <emph type="italics"/>phy&longs;. cap.<emph.end type="italics"/>4. <emph type="italics"/>iuxta<emph.end type="italics"/> principium illud vniuer­<lb/>fali&longs;&longs;imum; <emph type="italics"/>Quidquid mouetur; ab alio mouetur<emph.end type="italics"/>; &longs;ed profectò ij ip&longs;i, qui <lb/>motum grauium generanti tribuunt, tanquam principi cau&longs;æ, non ne­<lb/>gant ine&longs;&longs;e grauibus grauitatem, quæ &longs;it principium actiuum minus <lb/>principale motus; ad quem etiam, vt ip&longs;i exi&longs;timant, forma &longs;ub&longs;tantialis <lb/>concurrit; In hoc quippe conueniunt omnes tùm &longs;ectarum Principes, <lb/>tùm recentiores: quidquid &longs;it etiam ex iis ip&longs;is datur motus naturalis, <lb/>qui e&longs;t à virtute proxima intrin&longs;eca; hoc ip&longs;um etiam &longs;en&longs;it Ari&longs;toteles <lb/>lib.4. de cælo cap. | <s>Sextò, &longs;unt denique multi, <expan abbr="ii&qacute;ue">iique</expan> ex &longs;euerioribus Peripateticis, qui <lb/>exi&longs;timant grauia moueri deor&longs;um à generante, quod expre&longs;&longs;is verbis <lb/>traditum e&longs;t ab <emph type="italics"/>Ari&longs;totele l.<emph.end type="italics"/>8. <emph type="italics"/>phy&longs;. cap.<emph.end type="italics"/>4. <emph type="italics"/>iuxta<emph.end type="italics"/> principium illud vniuer­<lb/>&longs;ali&longs;&longs;imum; <emph type="italics"/>Quidquid mouetur; ab alio mouetur<emph.end type="italics"/>; &longs;ed profectò ij ip&longs;i, qui <lb/>motum grauium generanti tribuunt, tanquam principi cau&longs;æ, non ne­<lb/>gant ine&longs;&longs;e grauibus grauitatem, quæ &longs;it principium actiuum minus <lb/>principale motus; ad quem etiam, vt ip&longs;i exi&longs;timant, forma &longs;ub&longs;tantialis <lb/>concurrit; In hoc quippe conueniunt omnes tùm &longs;ectarum Principes, <lb/>tùm recentiores: quidquid &longs;it etiam ex iis ip&longs;is datur motus naturalis, <lb/>qui e&longs;t à virtute proxima intrin&longs;eca; hoc ip&longs;um etiam &longs;en&longs;it Ari&longs;toteles <lb/>lib.4. de cælo cap. |
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| 3. t. </s> | 3. t. </s> |
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| <s><emph type="italics"/>Motus naturalis non e&longs;t immediatè ab ip&longs;a grauitate.<emph.end type="italics"/></s><s> Probatur, &longs;int <lb/>enim eædem hypoth.1.2.3. igitur maior ictus in fine motus, & velocior <lb/>motus debent habere cau&longs;am; &longs;ed hæc grauitas non e&longs;t, quæ &longs;emper ea­<lb/>dem e&longs;t, vt patet, vtrum verò di&longs;tinguatur grauitas ab ip&longs;a corporis <lb/>&longs;ub&longs;tantia di&longs;cutiemus in tractatu &longs;equenti. </s> | <s><emph type="italics"/>Motus naturalis non e&longs;t immediatè ab ip&longs;a grauitate.<emph.end type="italics"/></s><s> Probatur, &longs;int <lb/>enim eædem hypoth.1.2.3. igitur maior ictus in fine motus, & velocior <lb/>motus debent habere cau&longs;am; &longs;ed hæc grauitas non e&longs;t, quæ &longs;emper ea­<lb/>dem e&longs;t, vt patet, vtrum verò di&longs;tinguatur grauitas ab ip&longs;a corporis <lb/>&longs;ub&longs;tantia di&longs;cutiemus in tractatu &longs;equenti. </s> |
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| <s>Fuit aliquis non infunæ no­<lb/>tæ Philo&longs;ophus, qui diceret maiorem illum ictum e&longs;&longs;e ab ipsâ corporis <lb/>&longs;ub&longs;tantiâ; &longs;ed hoc iam refellimus Theoremate 4. lib.1. Adde quod im­<lb/>petu, ad extra producitur ab alio impetu per Th.42.lib.1. Dicebat etiam <lb/>velociorem motum e&longs;&longs;e ab ipsâ grauitate connotante præuium motum, <lb/>quod etiam refellemus infrà. </s></p><p type="main"> | <s>Fuit aliquis non infimæ no­<lb/>tæ Philo&longs;ophus, qui diceret maiorem illum ictum e&longs;&longs;e ab ipsâ corporis <lb/>&longs;ub&longs;tantiâ; &longs;ed hoc iam refellimus Theoremate 4. lib.1. Adde quod im­<lb/>petu, ad extra producitur ab alio impetu per Th.42.lib.1. Dicebat etiam <lb/>velociorem motum e&longs;&longs;e ab ipsâ grauitate connotante præuium motum, <lb/>quod etiam refellemus infrà. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non à &longs;ub&longs;tantia corporis <lb/>grauis per Th. 3. non à grauitace per Th. 4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, à quo &longs;it motus pet definitionem <lb/>3. lib. | <s><emph type="italics"/>Hinc motus naturalis e&longs;t ab impetu.<emph.end type="italics"/></s><s> Probatur; e&longs;t ab aliqua cau&longs;a per <lb/>Ax.8. lib.1. ab aliqua intrin&longs;eca per Th. 1. non à &longs;ub&longs;tantia corporis <lb/>grauis per Th. 3. non à grauitate per Th. 4. igitur ab impetu, quia <lb/>nihil aliud e&longs;&longs;e pote&longs;t intrin&longs;ecum, à quo &longs;it motus per definitionem <lb/>3. lib. |
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| 1. <!-- KEEP S--></s></p><pb xlink:href="026/01/113.jpg" pagenum="81"/><p type="main"> | 1. <!-- KEEP S--></s></p><pb xlink:href="026/01/113.jpg" pagenum="81"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc produci tantùm pote&longs;t ab ip&longs;a &longs;ubstantia corporis grauis; nam graui­<lb/>tas e&longs;t ip&longs;e impetus innatus, de qua infrà:<emph.end type="italics"/> probatur; quia nihil e&longs;t aliud in­<lb/>trin&longs;ecum, à quo produci po&longs;&longs;it; quòd autem non produc tur ab alio im­<lb/>petu ad intra, patet per Th.41. lib. | <s><emph type="italics"/>Hinc produci tantùm pote&longs;t ab ip&longs;a &longs;ubstantia corporis grauis; nam graui­<lb/>tas e&longs;t ip&longs;e impetus innatus, de qua infrà:<emph.end type="italics"/> probatur; quia nihil e&longs;t aliud in­<lb/>trin&longs;ecum, à quo produci po&longs;&longs;it; quòd autem non producatur ab alio im­<lb/>petu ad intra, patet per Th.41. lib. |
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| 1. <!-- KEEP S--></s></p><p type="main"> | 1. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus ille innatus, qui durat &longs;ecundo instanti, con&longs;eruatur ab aiiqua cau­<lb/>&longs;a<emph.end type="italics"/>; e&longs;t certum per Ax. 14.lib.1.num.1. <!-- KEEP S--></s></p><p type="main"> | <s><emph type="italics"/>Impetus ille innatus, qui durat &longs;ecundo instanti, con&longs;eruatur ab aliqua cau­<lb/>&longs;a<emph.end type="italics"/>; e&longs;t certum per Ax. 14.lib.1.num.1. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 11.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Non con&longs;eruatur à cau&longs;a primò productiua.<emph.end type="italics"/></s><s> Probatur per Th.144. lib.1. <lb/>alioquin non po&longs;&longs;et intendi ab eadem cau&longs;a per Th. 146. lib 1. quippè <lb/>con&longs;eruatio nihil e&longs;t aliud, quàm repetita productio, vt con&longs;tat; nam <lb/>cau&longs;a con&longs;eruans verè influit; igitur &longs;i e&longs;t can&longs;a nece&longs;&longs;aria primo, & &longs;e­<lb/>cundo in&longs;tanti æquali ni&longs;u influit; influit enim quantum pote&longs;t per Ax. <!-- REMOVE S--><lb/>12.lib.1.quòd autem impetus intendatur, demon&longs;trabimus infrà; con&longs;ule <lb/>Schol.Th.146.lib.1.in quo habes rationem præclari natura in&longs;tituti; quo <lb/>&longs;cilicet factum e&longs;t, vt qualitates, quæ contrario carent à causâ primò pro­<lb/>ductiua; aliæ verò, quæ contrarium habent, ab alia causà con&longs;er­<lb/>uentur. </s> | <s><emph type="italics"/>Non con&longs;eruatur à cau&longs;a primò productiua.<emph.end type="italics"/></s><s> Probatur per Th.144. lib.1. <lb/>alioquin non po&longs;&longs;et intendi ab eadem cau&longs;a per Th. 146. lib 1. quippè <lb/>con&longs;eruatio nihil e&longs;t aliud, quàm repetita productio, vt con&longs;tat; nam <lb/>cau&longs;a con&longs;eruans verè influit; igitur &longs;i e&longs;t cau&longs;a nece&longs;&longs;aria primo, & &longs;e­<lb/>cundo in&longs;tanti æquali ni&longs;u influit; influit enim quantum pote&longs;t per Ax. <!-- REMOVE S--><lb/>12.lib.1.quòd autem impetus intendatur, demon&longs;trabimus infrà; con&longs;ule <lb/>Schol.Th.146.lib.1.in quo habes rationem præclari natura in&longs;tituti; quo <lb/>&longs;cilicet factum e&longs;t, vt qualitates, quæ contrario carent à causâ primò pro­<lb/>ductiua; aliæ verò, quæ contrarium habent, ab alia causà con&longs;er­<lb/>uentur. </s> |
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| <s>Probatur &longs;ecundò; cre&longs;cit motus grauium in <lb/>libero medio per hypoth. </s> | <s>Probatur &longs;ecundò; cre&longs;cit motus grauium in <lb/>libero medio per hypoth. </s> |
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| <s>1.2.3. igitur cre&longs;cit impetus; quia cum motus <lb/>naturalis &longs;it ab impetu per Th.5. quâ proportionc cre&longs;cit effectus, &longs;cilicet <lb/>&longs;ormalis, & exigentiæ; &longs;ic enim motus e&longs;t effectus impetus per Th. 15. <lb/>lib.1.eàdem cre&longs;cit cau&longs;a per Ax.2. Probatur tertiò, quia corpus graue ex <lb/>maiore altitudine cadens maiorem quoque ictum infligit per hypoth.1. <lb/>igitur maior impetus imprimitur in corpore percu&longs;&longs;o; &longs;ed impetus ad ex­<lb/>tra producitur ab alio impetu per Th.42.lib.1. igitur &longs;i cre&longs;cit productus <lb/>inpetus, cre&longs;cit impetus producens. </s></p><p type="main"> | <s>1.2.3. igitur cre&longs;cit impetus; quia cum motus <lb/>naturalis &longs;it ab impetu per Th.5. quâ proportione cre&longs;cit effectus, &longs;cilicet <lb/>formalis, & exigentiæ; &longs;ic enim motus e&longs;t effectus impetus per Th. 15. <lb/>lib.1.eàdem cre&longs;cit cau&longs;a per Ax.2. Probatur tertiò, quia corpus graue ex <lb/>maiore altitudine cadens maiorem quoque ictum infligit per hypoth.1. <lb/>igitur maior impetus imprimitur in corpore percu&longs;&longs;o; &longs;ed impetus ad ex­<lb/>tra producitur ab alio impetu per Th.42.lib.1. igitur &longs;i cre&longs;cit productus <lb/>inpetus, cre&longs;cit impetus producens. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hinc reiicies quorumdam placitum, qui volunt cau&longs;am velociotis <lb/>motus e&longs;&longs;e grauitatem ip&longs;am, quatenus connotat motum præuium; quia <lb/>&longs;cilicet grauitas non producit illum maiorem impetum ad extra, vt con­<lb/>&longs;tat; nec &longs;ub&longs;tantia ip&longs;ius corporis grauis per Th.40.lib.1.igitur ip&longs;e im­<lb/>petus: præterea &longs;i hoc e&longs;&longs;et, fru&longs;trà requireretur impetus contra Th. 5. <lb/>Denique motus præuius nihil e&longs;t amplius, cum alius &longs;uccedit: Vide Th. <!-- REMOVE S--><lb/>40.lib.1. vbi hæc fusè di&longs;cu&longs;&longs;imus. </s> | <s>Hinc reiicies quorumdam placitum, qui volunt cau&longs;am velocioris <lb/>motus e&longs;&longs;e grauitatem ip&longs;am, quatenus connotat motum præuium; quia <lb/>&longs;cilicet grauitas non producit illum maiorem impetum ad extra, vt con­<lb/>&longs;tat; nec &longs;ub&longs;tantia ip&longs;ius corporis grauis per Th.40.lib.1.igitur ip&longs;e im­<lb/>petus: præterea &longs;i hoc e&longs;&longs;et, fru&longs;trà requireretur impetus contra Th. 5. <lb/>Denique motus præuius nihil e&longs;t amplius, cum alius &longs;uccedit: Vide Th. <!-- REMOVE S--><lb/>40.lib.1. vbi hæc fusè di&longs;cu&longs;&longs;imus. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 14.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si impetus innatus impeditur, ita vt moueri non po&longs;&longs;it corpus graue, &longs;e­<lb/>cundo instanti non producitur nouus impetus.<emph.end type="italics"/></s><s> Probatur primò, non cre&longs;cit <lb/>corporis grauis &longs;eu grauitas, &longs;cu grauitatio, vt con&longs;tat experientiâ; igitur <lb/>non cre&longs;cit impectus; alioquin &longs;i cre&longs;ceret cau&longs;a, cre&longs;ceret effectus per <lb/>Ax.2. igitur de re, quòd &longs;it, certum e&longs;t, atque cuidens; iam demon&longs;tratur <lb/>propter quid &longs;it; impetus &longs;ecundo in&longs;tanti productus e&longs;&longs;et fru&longs;trà; careret <pb xlink:href="026/01/115.jpg" pagenum="83"/>enim &longs;uo fine, vel effectu formali, id e&longs;t motu; igitur e&longs;&longs;et fru&longs;trà, &longs;ed <lb/>quod fru&longs;trà e&longs;t, non e&longs;t per Ax.6.l.1. </s></p><p type="main"> | <s><emph type="italics"/>Si impetus innatus impeditur, ita vt moueri non po&longs;&longs;it corpus graue, &longs;e­<lb/>cundo instanti non producitur nouus impetus.<emph.end type="italics"/></s><s> Probatur primò, non cre&longs;cit <lb/>corporis grauis &longs;eu grauitas, &longs;eu grauitatio, vt con&longs;tat experientiâ; igitur <lb/>non cre&longs;cit impetus; alioquin &longs;i cre&longs;ceret cau&longs;a, cre&longs;ceret effectus per <lb/>Ax.2. igitur de re, quòd &longs;it, certum e&longs;t, atque cuidens; iam demon&longs;tratur <lb/>propter quid &longs;it; impetus &longs;ecundo in&longs;tanti productus e&longs;&longs;et fru&longs;trà; careret <pb xlink:href="026/01/115.jpg" pagenum="83"/>enim &longs;uo fine, vel effectu formali, id e&longs;t motu; igitur e&longs;&longs;et fru&longs;trà, &longs;ed <lb/>quod fru&longs;trà e&longs;t, non e&longs;t per Ax.6.l.1. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;erua quæ&longs;o, quod iam &longs;uprà indicattun e&longs;t, e&longs;&longs;e tres veluti &longs;pecies <lb/>impetus. </s> | <s>Ob&longs;erua quæ&longs;o, quod iam &longs;uprà indicatum e&longs;t, e&longs;&longs;e tres veluti &longs;pecies <lb/>impetus. </s> |
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| <s>Prima e&longs;t impetus naturalis innati. </s> | <s>Prima e&longs;t impetus naturalis innati. </s> |
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| <s>Secunda naturalis acqui&longs;iti. </s> | <s>Secunda naturalis acqui&longs;iti. </s> |
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| <s><lb/>Tertia violenti; innatus e&longs;t qui vel à generante &longs;imul cum corpore <lb/>graui productus e&longs;t; qui&longs;quis tandem &longs;it generans, de quo aliàs; vel ab <lb/>ip&longs;o graui qua&longs;i profunditur, id e&longs;t, producitur in &longs;e ip&longs;o &longs;tatim initio, <lb/>quo e&longs;t; porrò cum in corpore graui duplex qua&longs;i proprietas &longs;en&longs;ibilis <lb/>e&longs;&longs;e videatur, &longs;cilicet grauitas, &longs;eu pondus & motus deor&longs;um; certè de­<lb/>bet e&longs;&longs;e in eo aliquid per quod tùm cogno&longs;ci po&longs;&longs;it eins pondus, tùm in­<lb/>cipiat moueri deor&longs;um; quippe maximè corpora ex pondere cogno&longs;ci­<lb/>mus, vnumque ab alio di&longs;tinguimus; igitur debet e&longs;&longs;e aliquid, quod &longs;en­<lb/>&longs;um afficiat, vt cogno&longs;ci po&longs;&longs;it; atqui illud ip&longs;um non e&longs;t &longs;ub&longs;tantia cor­<lb/>poris; nam corpus graue meæ manui &longs;u&longs;tinenti impetum imptimit; <lb/>immò vim alterius impetus infringit; igitur operâ alterius per Th. 40. <lb/>& 42.lib.1. Præterea illud ip&longs;um, quod agit, &longs;eu deor&longs;um pellit &longs;u&longs;tinen­<lb/>tem manum, e&longs;t illud ip&longs;um quod inclinat corpus graue deor&longs;um imme­<lb/>diatè, &longs;eu quod exigit motum naturalem deor&longs;um; illud autem quod <lb/>immediatè præ&longs;tat hunc motum, nec e&longs;t &longs;ub&longs;tantia corporis grauis per <lb/>Th.3. igitur ip&longs;e impetus per Th.5. adde quod primo in&longs;tanti, quo e&longs;t im­<lb/>petus, non e&longs;t motus ille, quem exigit per Th.34. lib.1. igitur præexi&longs;tit <lb/>&longs;emper impetus, qui ne &longs;it fru&longs;trà, habet primum effectum &longs;uum forma­<lb/>lem, id e&longs;t grauitationem: Ex his dicendum e&longs;t hunc impetum natiuum <lb/>nunquam de&longs;trui, quia nunquam e&longs;t fru&longs;trà, habet enim &longs;emper aliquem <lb/>effectum, primum quidem &longs;i caret &longs;ecundo; &longs;ecundum verò &longs;i caret pri­<lb/>mo; quippe vtrumque &longs;imul habere non pote&longs;t; nam corporis pondus <lb/>cogno&longs;ci non pote&longs;t, dum fertur deor&longs;um accelerato motu, quot verò, <lb/>& quanta commoda ex cognitione ponderis cuiu&longs;libet materiæ proce­<lb/>dant, vix explicari pote&longs;t. </s></p><p type="main"> | <s><lb/>Tertia violenti; innatus e&longs;t qui vel à generante &longs;imul cum corpore <lb/>graui productus e&longs;t; qui&longs;quis tandem &longs;it generans, de quo aliàs; vel ab <lb/>ip&longs;o graui qua&longs;i profunditur, id e&longs;t, producitur in &longs;e ip&longs;o &longs;tatim initio, <lb/>quo e&longs;t; porrò cum in corpore graui duplex qua&longs;i proprietas &longs;en&longs;ibilis <lb/>e&longs;&longs;e videatur, &longs;cilicet grauitas, &longs;eu pondus & motus deor&longs;um; certè de­<lb/>bet e&longs;&longs;e in eo aliquid per quod tùm cogno&longs;ci po&longs;&longs;it eius pondus, tùm in­<lb/>cipiat moueri deor&longs;um; quippe maximè corpora ex pondere cogno&longs;ci­<lb/>mus, vnumque ab alio di&longs;tinguimus; igitur debet e&longs;&longs;e aliquid, quod &longs;en­<lb/>&longs;um afficiat, vt cogno&longs;ci po&longs;&longs;it; atqui illud ip&longs;um non e&longs;t &longs;ub&longs;tantia cor­<lb/>poris; nam corpus graue meæ manui &longs;u&longs;tinenti impetum imprimit; <lb/>immò vim alterius impetus infringit; igitur operâ alterius per Th. 40. <lb/>& 42.lib.1. Præterea illud ip&longs;um, quod agit, &longs;eu deor&longs;um pellit &longs;u&longs;tinen­<lb/>tem manum, e&longs;t illud ip&longs;um quod inclinat corpus graue deor&longs;um imme­<lb/>diatè, &longs;eu quod exigit motum naturalem deor&longs;um; illud autem quod <lb/>immediatè præ&longs;tat hunc motum, nec e&longs;t &longs;ub&longs;tantia corporis grauis per <lb/>Th.3. igitur ip&longs;e impetus per Th.5. adde quod primo in&longs;tanti, quo e&longs;t im­<lb/>petus, non e&longs;t motus ille, quem exigit per Th.34. lib.1. igitur præexi&longs;tit <lb/>&longs;emper impetus, qui ne &longs;it fru&longs;trà, habet primum effectum &longs;uum forma­<lb/>lem, id e&longs;t grauitationem: Ex his dicendum e&longs;t hunc impetum natiuum <lb/>nunquam de&longs;trui, quia nunquam e&longs;t fru&longs;trà, habet enim &longs;emper aliquem <lb/>effectum, primum quidem &longs;i caret &longs;ecundo; &longs;ecundum verò &longs;i caret pri­<lb/>mo; quippe vtrumque &longs;imul habere non pote&longs;t; nam corporis pondus <lb/>cogno&longs;ci non pote&longs;t, dum fertur deor&longs;um accelerato motu, quot verò, <lb/>& quanta commoda ex cognitione ponderis cuiu&longs;libet materiæ proce­<lb/>dant, vix explicari pote&longs;t. </s></p><p type="main"> |
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| <s>Ex his verò concludendum &longs;upere&longs;t impetum innatum e&longs;&longs;e proprie­<lb/>tatem quarto modo, vt vulgò aiunt, corporis grauis; ac proinde ab illo <lb/>in&longs;eparabilem; quid verò fiat de illo, cum corpus graue fit leuc; &longs;i tamen <lb/>hoc aliquando accidit, dicemus cum de grauitate, & grauitatione, iam <lb/>verò &longs;atis e&longs;t ad præ&longs;ens in&longs;titutum impetum innatum ab ip&longs;o corport <lb/>graui nunquam &longs;eparari, quandiu remanet graue. </s></p><p type="main"> | <s>Ex his verò concludendum &longs;upere&longs;t impetum innatum e&longs;&longs;e proprie­<lb/>tatem quarto modo, vt vulgò aiunt, corporis grauis; ac proinde ab illo <lb/>in&longs;eparabilem; quid verò fiat de illo, cum corpus graue fit leue; &longs;i tamen <lb/>hoc aliquando accidit, dicemus cum de grauitate, & grauitatione, iam <lb/>verò &longs;atis e&longs;t ad præ&longs;ens in&longs;titutum impetum innatum ab ip&longs;o corpori <lb/>graui nunquam &longs;eparari, quandiu remanet graue. </s></p><p type="main"> |
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| <s>Impetus naturalis acqui&longs;itus producitur ab codem principio intrin­<lb/>&longs;eco; hinc dicitur naturalis: dicitur verò acqui&longs;itus, quia non e&longs;t inna­<lb/>tus; &longs;ed &longs;eparatur à corpore graui; quod &longs;emper eo caret, quandiu <lb/>quie&longs;cit: &longs;ed innato tantùm accedit ad motus accelerationem, & ad alia <lb/>quamplurima, quæ ex ea &longs;equuntur; putà maiorem percu&longs;&longs;ionem, re&longs;i­<lb/>&longs;tentiam, vim, & ad tollendum totius naturæ languiorem; quo certè af­<lb/>ficeretur, &longs;i corpus grauc tardi&longs;&longs;imo motu deor&longs;um ferretur, de quo in­<lb/>frà; Porrò impetus acqui&longs;itus in multis differt ab innato; primò quia <pb xlink:href="026/01/116.jpg" pagenum="84"/>de&longs;truitur à corpore re&longs;i&longs;tente eo modo, quo diximus, & dicemus infrà. </s> | <s>Impetus naturalis acqui&longs;itus producitur ab codem principio intrin­<lb/>&longs;eco; hinc dicitur naturalis: dicitur verò acqui&longs;itus, quia non e&longs;t inna­<lb/>tus; &longs;ed &longs;eparatur à corpore graui; quod &longs;emper eo caret, quandiu <lb/>quie&longs;cit: &longs;ed innato tantùm accedit ad motus accelerationem, & ad alia <lb/>quamplurima, quæ ex ea &longs;equuntur; putà maiorem percu&longs;&longs;ionem, re&longs;i­<lb/>&longs;tentiam, vim, & ad tollendum totius naturæ langudiorem; quo certè af­<lb/>ficeretur, &longs;i corpus graue tardi&longs;&longs;imo motu deor&longs;um ferretur, de quo in­<lb/>frà; Porrò impetus acqui&longs;itus in multis differt ab innato; primò quia <pb xlink:href="026/01/116.jpg" pagenum="84"/>de&longs;truitur à corpore re&longs;i&longs;tente eo modo, quo diximus, & dicemus infrà. </s> |
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| <s><lb/>Secundò, quia determinari pote&longs;t ad omnem lincam. </s></p><p type="main"> | <s><lb/>Secundò, quia determinari pote&longs;t ad omnem lineam. </s></p><p type="main"> |
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| <s>Impetus violentus e&longs;t, qui e&longs;t ab extrin&longs;eco, de quo agemus infrà, & <lb/>iam &longs;uprà in lib.1. multa &longs;unt de eo demon&longs;trata. </s></p><p type="main"> | <s>Impetus violentus e&longs;t, qui e&longs;t ab extrin&longs;eco, de quo agemus infrà, & <lb/>iam &longs;uprà in lib.1. multa &longs;unt de eo demon&longs;trata. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 16.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc motus naturalis deor&longs;um acceleratur<emph.end type="italics"/>; hoc ip&longs;um &longs;uppo&longs;ui &longs;uprà <lb/>Quod e&longs;&longs;et in hyp.1.2.3. iam verò demon&longs;tro propter quid e&longs;t; &longs;ie cnim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt fæpè monuimus in metho­<lb/>do; igitur probatur hoc Theorema facilè; cre&longs;cit impetus in corpore gra­<lb/>ui, quod tendit deor&longs;um in libero medio per T. 15. igitar cre&longs;cit cau&longs;a <lb/>motus; nam impetus e&longs;t can&longs;a immediata motus naturalis per Th. 51. <lb/>&longs;ed quâ proportione cre&longs;cit cau&longs;a, debet cre&longs;cere effectus per Ax.2. igi­<lb/>tur motus naturalis deor&longs;um cre&longs;cit, id e&longs;t acceleratur, id e&longs;t fit velo­<lb/>cior, quod erat dem: nec e&longs;t quod aliquis exi&longs;timet hic à me committi <lb/>vitio&longs;um argumentationis circulum; quippe probaui &longs;uprà cre&longs;cere im­<lb/>petum, quia cre&longs;cit motus; iam verò probo cre&longs;cere motum, quia cre&longs;­<lb/>cit impetus; nam primò probaui produci nouum impetum in Th.12. eo <lb/>quod &longs;ecundo in&longs;tanti. </s> | <s><emph type="italics"/>Hinc motus naturalis deor&longs;um acceleratur<emph.end type="italics"/>; hoc ip&longs;um &longs;uppo&longs;ui &longs;uprà <lb/>Quod e&longs;&longs;et in hyp.1.2.3. iam verò demon&longs;tro propter quid e&longs;t; &longs;ie enim <lb/>hypothe&longs;is in Theorema conuerti pote&longs;t, vt 6longs;æpè monuimus in metho­<lb/>do; igitur probatur hoc Theorema facilè; cre&longs;cit impetus in corpore gra­<lb/>ui, quod tendit deor&longs;um in libero medio per T. 15. igitur cre&longs;cit cau&longs;a <lb/>motus; nam impetus e&longs;t cau&longs;a immediata motus naturalis per Th. 51. <lb/>&longs;ed quâ proportione cre&longs;cit cau&longs;a, debet cre&longs;cere effectus per Ax.2. igi­<lb/>tur motus naturalis deor&longs;um cre&longs;cit, id e&longs;t acceleratur, id e&longs;t fit velo­<lb/>cior, quod erat dem: nec e&longs;t quod aliquis exi&longs;timet hic à me committi <lb/>vitio&longs;um argumentationis circulum; quippe probaui &longs;uprà cre&longs;cere im­<lb/>petum, quia cre&longs;cit motus; iam verò probo cre&longs;cere motum, quia cre&longs;­<lb/>cit impetus; nam primò probaui produci nouum impetum in Th.12. eo <lb/>quod &longs;ecundo in&longs;tanti. </s> |
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| <s>v.g. <!-- REMOVE S-->&longs;it eadem cau&longs;a nece&longs;&longs;aria applicata non im­<lb/>pedita, igitur tàm debet agere &longs;ecundo quàm primo in&longs;tanti, hæc fuit <lb/>mea probatio à priori; &longs;ecundò verò probaui ex hypothe&longs;i certa; quia <lb/>&longs;cilicet cre&longs;cit motus, cuius veritatem cogno&longs;co &longs;en&longs;ibiliter in &longs;e, vnde <lb/>&longs;uppono tantùm de illa quod &longs;it; igitur nullus committitur circulus; nam <lb/>diuer&longs;a e&longs;t omninò cognitio. </s> | <s>v.g. <!-- REMOVE S-->&longs;it eadem cau&longs;a nece&longs;&longs;aria applicata non im­<lb/>pedita, igitur tàm debet agere &longs;ecundo quàm primo in&longs;tanti, hæc fuit <lb/>mea probatio à priori; &longs;ecundò verò probaui ex hypothe&longs;i certa; quia <lb/>&longs;cilicet cre&longs;cit motus, cuius veritatem cogno&longs;co &longs;en&longs;ibiliter in &longs;e, vnde <lb/>&longs;uppono tantùm de illa quod &longs;it; igitur nullus committitur circulus; nam <lb/>diuer&longs;a e&longs;t omninò cognitio. </s> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis etiam aliud naturæ in&longs;titutum, quo &longs;cilicet factum e&longs;t, vt <pb xlink:href="026/01/117.jpg" pagenum="85"/>corpora grauia motu naturali accelerato deor&longs;um ferantur; &longs;i enim motu <lb/>ferrentur æquabili, vel e&longs;&longs;et æqualis illi quem initio &longs;ui de&longs;cen&longs;us ha­<lb/>bent, qui e&longs;t tardi&longs;&longs;imus, vt con&longs;tat ex ip&longs;a ictuum differentia; atque <lb/>ita infinitum ferè tempus ponerent grauia in minimo etiam de&longs;cen&longs;u, <lb/>quod e&longs;&longs;et maximè incommodum; &longs;i verò motus ille e&longs;&longs;et æqualis mo­<lb/>tui v.g. <!-- REMOVE S-->quem acqui&longs;iuit in fpatio 3. vel 4. perticarum, pondera corpo­<lb/>rum cre&longs;cerent in immen&longs;um, ide&longs;t in ea proportione, qua ictus, qui in­<lb/>fligitur à corpore graui confecto 4. perticarum &longs;patio maior e&longs;t ictu, qui <lb/>infligitur po&longs;t decur&longs;um minimum omnium &longs;patiorum, quod valdè in­<lb/>commodum e&longs;&longs;et. </s> | <s>Ob&longs;eruabis etiam aliud naturæ in&longs;titutum, quo &longs;cilicet factum e&longs;t, vt <pb xlink:href="026/01/117.jpg" pagenum="85"/>corpora grauia motu naturali accelerato deor&longs;um ferantur; &longs;i enim motu <lb/>ferrentur æquabili, vel e&longs;&longs;et æqualis illi quem initio &longs;ui de&longs;cen&longs;us ha­<lb/>bent, qui e&longs;t tardi&longs;&longs;imus, vt con&longs;tat ex ip&longs;a ictuum differentia; atque <lb/>ita infinitum ferè tempus ponerent grauia in minimo etiam de&longs;cen&longs;u, <lb/>quod e&longs;&longs;et maximè incommodum; &longs;i verò motus ille e&longs;&longs;et æqualis mo­<lb/>tui v.g. <!-- REMOVE S-->quem acqui&longs;iuit in &longs;patio 3. vel 4. perticarum, pondera corpo­<lb/>rum cre&longs;cerent in immen&longs;um, ide&longs;t in ea proportione, qua ictus, qui in­<lb/>fligitur à corpore graui confecto 4. perticarum &longs;patio maior e&longs;t ictu, qui <lb/>infligitur po&longs;t decur&longs;um minimum omnium &longs;patiorum, quod valdè in­<lb/>commodum e&longs;&longs;et. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 18.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Qua proportione cre&longs;cit impetus acceleratur motus<emph.end type="italics"/>; quia quæ proportio­<lb/>ne cre&longs;cit cau&longs;a, ctiam cre&longs;cit effectus per Ax.2. </s></p><p type="main"> | <s><emph type="italics"/>Qua proportione cre&longs;cit impetus acceleratur motus<emph.end type="italics"/>; quia quæ proportio­<lb/>ne cre&longs;cit cau&longs;a, etiam cre&longs;cit effectus per Ax.2. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 19.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 19.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc æqualibus temporibus in de&longs;cen&longs;u corpus graue acquirit aqualia ve­<lb/>locitatis, vel acce&longs;erationis momenta<emph.end type="italics"/>; hoc ip&longs;um e&longs;t quod definitionis lo­<lb/>co Galileus in dialogo tertio de motu naturali a&longs;&longs;umit; quod tamen <lb/>meo iudicio fuit antè demon&longs;trandum quàm &longs;upponendum; quare &longs;ic <lb/>demon&longs;tramus, quâ proportione cre&longs;cit impetus, cre&longs;cit motus per Th. <!-- REMOVE S--><lb/>18. &longs;ed temporibus æqualibus acquiruntur æquales impetus gradus per <lb/>Th.17. igitur æqualia velocitatis momenta, vel incrementa. </s> | <s><emph type="italics"/>Hinc æqualibus temporibus in de&longs;cen&longs;u corpus graue acquirit aqualia ve­<lb/>locitatis, vel accelerationis momenta<emph.end type="italics"/>; hoc ip&longs;um e&longs;t quod definitionis lo­<lb/>co Galileus in dialogo tertio de motu naturali a&longs;&longs;umit; quod tamen <lb/>meo iudicio fuit antè demon&longs;trandum quàm &longs;upponendum; quare &longs;ic <lb/>demon&longs;tramus, quâ proportione cre&longs;cit impetus, cre&longs;cit motus per Th. <!-- REMOVE S--><lb/>18. &longs;ed temporibus æqualibus acquiruntur æquales impetus gradus per <lb/>Th.17. igitur æqualia velocitatis momenta, vel incrementa. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 20.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 20.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Spatia que per curruntur motu aquabili æqualibus temporibus &longs;unt æqualia<emph.end type="italics"/>; <lb/>Probatur per Def.2. </s></p><p type="main"> | <s><emph type="italics"/>Spatia que per curruntur motu æquabili æqualibus temporibus &longs;unt æqualia<emph.end type="italics"/>; <lb/>Probatur per Def.2. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 22.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Duo motus æquabiles, quibus percurruntur &longs;patia æqualia &longs;unt vt tempora <lb/>permutande<emph.end type="italics"/>;, patet, quia velocior e&longs;t, quò percurritur &longs;patium æquale <lb/>minori tempore per Def.2. l. <!-- REMOVE S-->1. Igitur eò veiocior, quò minori tem­<lb/>pore. </s> | <s><emph type="italics"/>Duo motus æquabiles, quibus percurruntur &longs;patia æqualia &longs;unt vt tempora <lb/>permutande<emph.end type="italics"/>;, patet, quia velocior e&longs;t, quò percurritur &longs;patium æquale <lb/>minori tempore per Def.2. l. <!-- REMOVE S-->1. Igitur eò velocior, quò minori tem­<lb/>pore. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si idem mobile temporibus æqualibus pereurrat duo &longs;patia motu æquabili, <lb/>&longs;ed inæquali velocitate; &longs;patia erunt vt velocitates, & hæ vt illa; imò &longs;i <lb/>&longs;patia &longs;unt vt velocitates, tempora erunt æqualia<emph.end type="italics"/>; pater etiam per <lb/>Th.25. </s></p><p type="main"> | <s><emph type="italics"/>Si idem mobile temporibus æqualibus percurrat duo &longs;patia motu æquabili, <lb/>&longs;ed inæquali velocitate; &longs;patia erunt vt velocitates, & hæ vt illa; imò &longs;i <lb/>&longs;patia &longs;unt vt velocitates, tempora erunt æqualia<emph.end type="italics"/>; pater etiam per <lb/>Th.25. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si duo mobilia ferantur motu æquabili per diuer&longs;a &longs;patia, & diuer&longs;a velo­<lb/>eitate, tempora erunt in ratione compo&longs;ita ex ratione &longs;paliorum & ratioue <lb/>velocitatum permutata<emph.end type="italics"/>; probatur eodem modo quo &longs;uperius Th. 30. &longs;it <lb/>ratio &longs;patiorum 4/1, velocitatum 4/2; permutetur hæc 1/4; componetur ex <lb/>vtraque 4/1, ide&longs;t 1/2, quæ e&longs;t ratio temporum. </s></p><p type="main"> | <s><emph type="italics"/>Si duo mobilia ferantur motu æquabili per diuer&longs;a &longs;patia, & diuer&longs;a velo­<lb/>citate, tempora erunt in ratione compo&longs;ita ex ratione &longs;patiorum & ratione <lb/>velocitatum permutata<emph.end type="italics"/>; probatur eodem modo quo &longs;uperius Th. 30. &longs;it <lb/>ratio &longs;patiorum 4/1, velocitatum 4/2; permutetur hæc 1/4; componetur ex <lb/>vtraque 4/1, ide&longs;t 1/2, quæ e&longs;t ratio temporum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si duo mobilia æquabili motu ferantur per diuer&longs;a &longs;patia, & inæqualibus <lb/>temporibus; ratio velocitatum erit compo&longs;ita ex ratione &longs;patiorum, & ex ra­<lb/>tione temporum permutata<emph.end type="italics"/>; Probatur eodem modo; &longs;it ratio &longs;patiorum <lb/>4/2 temporum 1/2, permutetur 2/1, compo&longs;ita ex vtraque crit 2/2, ide&longs;t 4. <lb/>quæ e&longs;t ratio velocitatum. </s></p><p type="main"> | <s><emph type="italics"/>Si duo mobilia æquabili motu ferantur per diuer&longs;a &longs;patia, & inæqualibus <lb/>temporibus; ratio velocitatum erit compo&longs;ita ex ratione &longs;patiorum, & ex ra­<lb/>tione temporum permutata<emph.end type="italics"/>; Probatur eodem modo; &longs;it ratio &longs;patiorum <lb/>4/2 temporum 1/2, permutetur 2/1, compo&longs;ita ex vtraque erit 2/2, ide&longs;t 4. <lb/>quæ e&longs;t ratio velocitatum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc &longs;ingalis in&longs;tantibus æqualiter cre&longs;cit & intenditur impetus<emph.end type="italics"/> per Th. <!-- REMOVE S--><lb/>34. igitur æqualiter etiam &longs;ingulis in&longs;tantibus cre&longs;cit velocitas motus <lb/>per Ax.2. </s> | <s><emph type="italics"/>Hinc &longs;ingulis in&longs;tantibus æqualiter cre&longs;cit & intenditur impetus<emph.end type="italics"/> per Th. <!-- REMOVE S--><lb/>34. igitur æqualiter etiam &longs;ingulis in&longs;tantibus cre&longs;cit velocitas motus <lb/>per Ax.2. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc cre&longs;cit impetus iuxta progre&longs;&longs;ionem arithmeticam; cum &longs;ingula in­<lb/>&longs;tantia æqualem impetum addant<emph.end type="italics"/>; &longs;i primo in&longs;tanti &longs;it vnus gradus, crunt <lb/>duo; productus &longs;cilicet alteri additus qui con&longs;eruatur, tertio erunt;. </s> | <s><emph type="italics"/>Hinc cre&longs;cit impetus iuxta progre&longs;&longs;ionem arithmeticam; cum &longs;ingula in­<lb/>&longs;tantia æqualem impetum addant<emph.end type="italics"/>; &longs;i primo in&longs;tanti &longs;it vnus gradus, erunt <lb/>duo; productus &longs;cilicet alteri additus qui con&longs;eruatur, tertio erunt;. </s> |
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| <s><lb/>quarto 4. quinto 5. &c. </s> | <s><lb/>quarto 4. quinto 5. &c. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc &longs;patium qucd acquiritur &longs;ecundo in&longs;tanti e&longs;t duplum illius, qaod ac­<lb/>quiritur primo.<emph.end type="italics"/></s><s> Probatur, quia velocitas e&longs;t dupla per Th 38. igitur &longs;pa­<lb/>tium duplum, & triplum tertio, quadruplum quarto, &c. </s></p><p type="main"> | <s><emph type="italics"/>Hinc &longs;patium qucd acquiritur &longs;ecundo in&longs;tanti e&longs;t duplum illius, quod ac­<lb/>quiritur primo.<emph.end type="italics"/></s><s> Probatur, quia velocitas e&longs;t dupla per Th 38. igitur &longs;pa­<lb/>tium duplum, & triplum tertio, quadruplum quarto, &c. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc &longs;patia cre&longs;cunt &longs;ingulis in&longs;tantibus æqualibus &longs;ecundùm pregre&longs;&longs;io­<lb/>nem arithmeticam<emph.end type="italics"/>; quia cre&longs;cit vt velocitas per Th.40. hæc vt impetus <lb/>per Th.38. hic demum iuxta progre&longs;&longs;ionem arithmeticam per Th. 37. <lb/>igitur &longs;i &longs;patium acqui&longs;itum primo in&longs;tanti &longs;it 1. acqui&longs;itum &longs;ecundo crit <lb/>2. tertio 3. quarto 4. &c. </s> | <s><emph type="italics"/>Hinc &longs;patia cre&longs;cunt &longs;ingulis in&longs;tantibus æqualibus &longs;ecundùm progre&longs;&longs;io­<lb/>nem arithmeticam<emph.end type="italics"/>; quia cre&longs;cit vt velocitas per Th.40. hæc vt impetus <lb/>per Th.38. hic demum iuxta progre&longs;&longs;ionem arithmeticam per Th. 37. <lb/>igitur &longs;i &longs;patium acqui&longs;itum primo in&longs;tanti &longs;it 1. acqui&longs;itum &longs;ecundo erit <lb/>2. tertio 3. quarto 4. &c. </s> |
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| <s>hinc &longs;patia acqui&longs;ita &longs;ingulis in&longs;tantibus &longs;unt <lb/>vt &longs;eries numerorm, qui componunt progre&longs;&longs;ionem &longs;implicem, &longs;cilicet <lb/>1.2.3.4.5.6. &c. </s> | <s>hinc &longs;patia acqui&longs;ita &longs;ingulis in&longs;tantibus &longs;unt <lb/>vt &longs;eries numerorum, qui componunt progre&longs;&longs;ionem &longs;implicem, &longs;cilicet <lb/>1.2.3.4.5.6. &c. </s> |
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| <s>dixi &longs;ingulis in&longs;tantibus æqualibus, quod e&longs;t apprimè <lb/>tenendum; &longs;i enim a&longs;&longs;umantur partes temporis maiores, perturbatur <lb/>hæc progre&longs;&longs;io, de quo infrà. </s></p><pb xlink:href="026/01/121.jpg" pagenum="89"/><p type="main"> | <s>dixi &longs;ingulis in&longs;tantibus æqualibus, quod e&longs;t apprimè <lb/>tenendum; &longs;i enim a&longs;&longs;umantur partes temporis maiores, perturbatur <lb/>hæc progre&longs;&longs;io, de quo infrà. </s></p><pb xlink:href="026/01/121.jpg" pagenum="89"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis primò hanc &longs;patiorum rationem, quæ e&longs;t eadem cum ra­<lb/>tione velocitatum a&longs;&longs;umendam tantùm e&longs;&longs;e in iis &longs;patiis, quæ acquirun­<lb/>tur &longs;ingulis in&longs;tantibus; &longs;i enim accipiantur partes temporis maiores, quæ <lb/>conflentur ex multis in&longs;tantibus; haud dubiè maior erit ratio &longs;patio­<lb/>rum, quàm velocitatum.v.g.&longs;i primo in&longs;tanti acquiratur primo &longs;patium, <lb/>&longs;ecundo, 2.tertio, 3.quarto 4.igitur &longs;i <expan abbr="cõparetur">comparetur</expan> velocitas primi in&longs;tantis <lb/>cum velocitate quarti æqualis erit, vt ratio &longs;patiorum, id e&longs;t, vt 1. ad 4. <lb/>At verò &longs;i accipiatur pars temporis con&longs;tans duobus in&longs;tantibus, hæc 4. <lb/>in&longs;tantia conflabunt tantùm 2. partes temporis æquales; in prima ac­<lb/>quirentur 3.&longs;patia, in &longs;ecunda 7.vt patet: &longs;ed quia velocitas primæ par­<lb/>tis temporis non e&longs;t æquabilis, nec etiam velocitas &longs;ecundæ; addantur <lb/>velocitates primi & &longs;ecundi in&longs;tantis, itemque &longs;eor&longs;im velocitates tertij, <lb/>& quarti; certè ratio collectorum crit vt ratio &longs;patiorum; &longs;i enim velo­<lb/>citas &longs;ecundi in&longs;tantis comparetur cum velocitate quarti e&longs;t tantùm <lb/>1/2 cum tamen primum &longs;patium &longs;it ad &longs;ecundum in ratione 3/7. </s></p><p type="main"> | <s>Ob&longs;eruabis primò hanc &longs;patiorum rationem, quæ e&longs;t eadem cum ra­<lb/>tione velocitatum a&longs;&longs;umendam tantùm e&longs;&longs;e in iis &longs;patiis, quæ acquirun­<lb/>tur &longs;ingulis in&longs;tantibus; &longs;i enim accipiantur partes temporis maiores, quæ <lb/>conflentur ex multis in&longs;tantibus; haud dubiè maior erit ratio &longs;patio­<lb/>rum, quàm velocitatum.v.g.&longs;i primo in&longs;tanti acquiratur primo &longs;patium, <lb/>&longs;ecundo, 2.tertio, 3.quarto 4.igitur &longs;i <expan abbr="cõparetur">comparetur</expan> velocitas primi in&longs;tantis <lb/>cum velocitate quarti æqualis erit, vt ratio &longs;patiorum, id e&longs;t, vt 1. ad 4. <lb/>At verò &longs;i accipiatur pars temporis con&longs;tans duobus in&longs;tantibus, hæc 4. <lb/>in&longs;tantia conflabunt tantùm 2. partes temporis æquales; in prima ac­<lb/>quirentur 3.&longs;patia, in &longs;ecunda 7.vt patet: &longs;ed quia velocitas primæ par­<lb/>tis temporis non e&longs;t æquabilis, nec etiam velocitas &longs;ecundæ; addantur <lb/>velocitates primi & &longs;ecundi in&longs;tantis, itemque &longs;eor&longs;im velocitates tertij, <lb/>& quarti; certè ratio collectorum erit vt ratio &longs;patiorum; &longs;i enim velo­<lb/>citas &longs;ecundi in&longs;tantis comparetur cum velocitate quarti e&longs;t tantùm <lb/>1/2 cum tamen primum &longs;patium &longs;it ad &longs;ecundum in ratione 3/7. </s></p><p type="main"> |
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| <s>Secundò, &longs;i comparentur &longs;patia cum temporibus e&longs;t alia ratio v.g.&longs;pa­<lb/>tium acqui&longs;itum vno in&longs;tanti &longs;e habet ad &longs;patium acqui&longs;itum in duobus <lb/>in&longs;tantibus, vt 1, ad 3.in tribus vt 1.ad 6.in 4. vt 1. ad 10. </s></p><p type="main"> | <s>Secundò, &longs;i comparentur &longs;patia cum temporibus e&longs;t alia ratio v.g.&longs;pa­<lb/>tium acqui&longs;itum vno in&longs;tanti &longs;e habet ad &longs;patium acqui&longs;itum in duobus <lb/>in&longs;tantibus, vt 1, ad 3.in tribus vt 1.ad 6.in 4. vt 1. ad 10. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Collectio &longs;patiorum e&longs;t &longs;umma terminorum huius progre&longs;&longs;ionis arithmeticæ<emph.end type="italics"/>; <lb/>Gùm enim ratio &longs;patiorum &longs;it vt ratio velocitatum; dum &longs;cilicet hæc <lb/>progre&longs;&longs;io accipitur in in&longs;tantibus, & ratio velocitatum vt ratio incre­<lb/>menti impetuum; vt con&longs;tat ex dictis, & hæc &longs;equatur &longs;implicem <lb/>progre&longs;&longs;ionem 1. 2. 3. 4. &c. </s> | <s><emph type="italics"/>Collectio &longs;patiorum e&longs;t &longs;umma terminorum huius progre&longs;&longs;ionis arithmeticæ<emph.end type="italics"/>; <lb/></s> |
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| | <s>Cùm enim ratio &longs;patiorum &longs;it vt ratio velocitatum; dum &longs;cilicet hæc <lb/>progre&longs;&longs;io accipitur in in&longs;tantibus, & ratio velocitatum vt ratio incre­<lb/>menti impetuum; vt con&longs;tat ex dictis, & hæc &longs;equatur &longs;implicem <lb/>progre&longs;&longs;ionem 1. 2. 3. 4. &c. </s> |
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| <s>certè collectio &longs;patiorum e&longs;t &longs;umma ter­<lb/>minorum. </s></p><p type="main"> | <s>certè collectio &longs;patiorum e&longs;t &longs;umma ter­<lb/>minorum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 43.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Data &longs;umma progre&longs;&longs;ionis huius &longs;implicis, inuenietur numerus terminorum, <lb/>&longs;i inueniatur numerus, per quem diuidatur, qui &longs;uperet tantùm vnitate du­<lb/>plum quotientis<emph.end type="italics"/>; quippe habebis in duplo quotientis numerum termino­<lb/>rum v.g. <!-- REMOVE S-->&longs;it &longs;umma 10. diui&longs;or &longs;it 5. quotiens 2. duplus 4. hic e&longs;t nume­<lb/>rus terminorum datæ &longs;ummæ; &longs;it alia &longs;umma 21. diui&longs;or &longs;it 7.quotiens 3. <lb/>numerus terminorum 6. &longs;it alia &longs;umma 36. dini&longs;or &longs;it 9. quotiens 4. nu­<lb/>merus terminorum 8. &longs;it alia &longs;umma 45. partitor &longs;it 10. quotiens 4 1/2, <lb/>numerus terminorum 9. quomodo verò hic partitor inueniri po&longs;&longs;it, vi­<lb/>derint Arithinetici; nec enim e&longs;t huius loci, quamquam datâ &longs;ummâ <lb/>huius progre&longs;&longs;ionis &longs;implicis facilè cogno&longs;ci pote&longs;t numerus termino­<lb/>rum; duplicetur enim, & radix 9. neglecto re&longs;iduo dabit numerum ter­<lb/>minorum v.g. <!-- REMOVE S-->&longs;it &longs;umma 21. duplicetur, erit 42. rad. </s> | <s><emph type="italics"/>Data &longs;umma progre&longs;&longs;ionis huius &longs;implicis, inuenietur numerus terminorum, <lb/>&longs;i inueniatur numerus, per quem diuidatur, qui &longs;uperet tantùm vnitate du­<lb/>plum quotientis<emph.end type="italics"/>; quippe habebis in duplo quotientis numerum termino­<lb/>rum v.g. <!-- REMOVE S-->&longs;it &longs;umma 10. diui&longs;or &longs;it 5. quotiens 2. duplus 4. hic e&longs;t nume­<lb/>rus terminorum datæ &longs;ummæ; &longs;it alia &longs;umma 21. diui&longs;or &longs;it 7.quotiens 3. <lb/>numerus terminorum 6. &longs;it alia &longs;umma 36. dini&longs;or &longs;it 9. quotiens 4. nu­<lb/>merus terminorum 8. &longs;it alia &longs;umma 45. partitor &longs;it 10. quotiens 4 1/2, <lb/>numerus terminorum 9. quomodo verò hic partitor inueniri po&longs;&longs;it, vi­<lb/>derint Arithmetici; nec enim e&longs;t huius loci, quamquam datâ &longs;ummâ <lb/>huius progre&longs;&longs;ionis &longs;implicis facilè cogno&longs;ci pote&longs;t numerus termino­<lb/>rum; duplicetur enim, & radix 9. neglecto re&longs;iduo dabit numerum ter­<lb/>minorum v.g. <!-- REMOVE S-->&longs;it &longs;umma 21. duplicetur, erit 42. rad. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Semper decre&longs;cit proportio incrementi velocitatis, id est maior est proportio <lb/>velocitatis &longs;ecundi in&longs;tantis ad primum quàm tertij ad &longs;ecundum, & maior<emph.end type="italics"/><pb xlink:href="026/01/123.jpg" pagenum="91"/><emph type="italics"/>tertij ad &longs;ecundum quàm quarti ad tertium, atque ita deinceps<emph.end type="italics"/>; &longs;it enim <lb/>primo in&longs;tanti velocitas vt 1.&longs;ecundo erit, vt 2.tertio, vt 3.quarto, vt 4. <lb/>&longs;ed maior e&longs;t proportio 2.ad 1.quàm 3.ad 2. & hæc maior quàm 4. ad 3. <lb/>atque ita deinceps; &longs;imiliter maior e&longs;t proportio &longs;patij quod percurritur <lb/>&longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo, quàm &longs;patij, quod <lb/>percurritur &longs;ecundo in&longs;tanti ad &longs;patium, quod percurtitur primo quàm <lb/>&longs;patij quod percurritur tertio ad &longs;patium, quod percurritur &longs;ecundo, at­<lb/>que ita deinceps; e&longs;t enim eadem ratio &longs;patiorum quæ &longs;ingulis in&longs;tanti­<lb/>bus re&longs;pondent, quæ velocitatum, vt demon&longs;tratum e&longs;t &longs;uprà. </s></p><p type="main"> | <s><emph type="italics"/>Semper decre&longs;cit proportio incrementi velocitatis, id est maior est proportio <lb/>velocitatis &longs;ecundi in&longs;tantis ad primum quàm tertij ad &longs;ecundum, & maior<emph.end type="italics"/><pb xlink:href="026/01/123.jpg" pagenum="91"/><emph type="italics"/>tertij ad &longs;ecundum quàm quarti ad tertium, atque ita deinceps<emph.end type="italics"/>; &longs;it enim <lb/>primo in&longs;tanti velocitas vt 1.&longs;ecundo erit, vt 2.tertio, vt 3.quarto, vt 4. <lb/>&longs;ed maior e&longs;t proportio 2.ad 1.quàm 3.ad 2. & hæc maior quàm 4. ad 3. <lb/>atque ita deinceps; &longs;imiliter maior e&longs;t proportio &longs;patij quod percurritur <lb/>&longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo, quàm &longs;patij, quod <lb/>percurritur &longs;ecundo in&longs;tanti ad &longs;patium, quod percurritur primo quàm <lb/>&longs;patij quod percurritur tertio ad &longs;patium, quod percurritur &longs;ecundo, at­<lb/>que ita deinceps; e&longs;t enim eadem ratio &longs;patiorum quæ &longs;ingulis in&longs;tanti­<lb/>bus re&longs;pondent, quæ velocitatum, vt demon&longs;tratum e&longs;t &longs;uprà. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 45.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 45.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Minor e&longs;t proportio totius &longs;patij, quod acquiritur duobus instantibus ad to, <lb/>tum &longs;patium, quod acquiritur vno, quàm &longs;it illius, quod acquiritur quatuor in­<lb/>&longs;tantibus ad aliud, quod acquiritur duobus<emph.end type="italics"/>; patet-ex dictis; &longs;i enim primo <lb/>in&longs;tanti acquiritur vnum &longs;patium, &longs;ecundo acquiruntur 2.igitur duobus <lb/>&longs;imul acquirantur 3. igitur proportio e&longs;t vt 3.ad 1.Sed &longs;i duobus acqui­<lb/>runtur 3. &longs;patia; certè 4.in&longs;tantibus acquiruntur 10. igitur proportio e&longs;t <lb/>vt 10.ad 3. &longs;ed proportio 10/3 e&longs;t maior 3/1, erit adhuc maior proportio &longs;pa­<lb/>tij quod acquiretur 6. in&longs;tantibus ad illud quod acquiritur tribus; e&longs;t <lb/>enim (21/6) vt patet. </s></p><p type="main"> | <s><emph type="italics"/>Minor e&longs;t proportio totius &longs;patij, quod acquiritur duobus instantibus ad to<lb/>tum &longs;patium, quod acquiritur vno, quàm &longs;it illius, quod acquiritur quatuor in­<lb/>&longs;tantibus ad aliud, quod acquiritur duobus<emph.end type="italics"/>; patet ex dictis; &longs;i enim primo <lb/>in&longs;tanti acquiritur vnum &longs;patium, &longs;ecundo acquiruntur 2.igitur duobus <lb/>&longs;imul acquirantur 3. igitur proportio e&longs;t vt 3.ad 1.Sed &longs;i duobus acqui­<lb/>runtur 3. &longs;patia; certè 4.in&longs;tantibus acquiruntur 10. igitur proportio e&longs;t <lb/>vt 10.ad 3. &longs;ed proportio 10/3 e&longs;t maior 3/1, erit adhuc maior proportio &longs;pa­<lb/>tij quod acquiretur 6. in&longs;tantibus ad illud quod acquiritur tribus; e&longs;t <lb/>enim (21/6) vt patet. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si componatur æquabilis motus ex &longs;ubdupla velocitate maxima, & mini­<lb/>ma, æquali tempore, idem &longs;patium percurretur hoc motu naturaliter aceclera­<lb/>to<emph.end type="italics"/>; &longs;it enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce­<lb/>lerato percurrentur &longs;patia 21. cuius &longs;ummæ termini &longs;unt 6.igitur 6. in­<lb/>&longs;tantibus con&longs;tat hic motus; accipiatur &longs;ubduplum maximæ, & minimæ <lb/>velocitatis, &longs;cilicet 3 1/2. sítque velocitas motus æquabilis in&longs;tantium 6. <lb/>haud dubiè &longs;i ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod &longs;cili­<lb/>cet, vt habeatur &longs;umma progre&longs;&longs;ionis arithmeticæ, debet addi primus <lb/>terminus maximo, & a&longs;&longs;umi &longs;ubduplum totius; illudque ducere in nu­<lb/>merum terminorum per regulam arithmeticam; atqui eadom e&longs;t ratio <lb/>velocitatum, quæ &longs;patiorum; vt dictum e&longs;t &longs;uprà; &longs;cilice, in &longs;ingulis <lb/>in&longs;tantibus. </s></p><p type="main"> | <s><emph type="italics"/>Si componatur æquabilis motus ex &longs;ubdupla velocitate maxima, & mini­<lb/>ma, æquali tempore, idem &longs;patium percurretur hoc motu naturaliter aceclera­<lb/>to<emph.end type="italics"/>; &longs;it enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce­<lb/>lerato percurrentur &longs;patia 21. cuius &longs;ummæ termini &longs;unt 6.igitur 6. in­<lb/>&longs;tantibus con&longs;tat hic motus; accipiatur &longs;ubduplum maximæ, & minimæ <lb/>velocitatis, &longs;cilicet 3 1/2. sítque velocitas motus æquabilis in&longs;tantium 6. <lb/>haud dubiè &longs;i ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod &longs;cili­<lb/>cet, vt habeatur &longs;umma progre&longs;&longs;ionis arithmeticæ, debet addi primus <lb/>terminus maximo, & a&longs;&longs;umi &longs;ubduplum totius; illudque ducere in nu­<lb/>merum terminorum per regulam arithmeticam; atqui eadem e&longs;t ratio <lb/>velocitatum, quæ &longs;patiorum; vt dictum e&longs;t &longs;uprà; &longs;cilice, in &longs;ingulis <lb/>in&longs;tantibus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 47.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si a&longs;&longs;umantur partes temporis majores; quæ &longs;cilicet pluribus in&longs;tantibus <lb/>constent, &longs;erueturque eadem accelerationis progre&longs;&longs;io arithinetica, &longs;patium <lb/>quod ex &longs;umma huius progre&longs;&longs;ionis re&longs;ultabit, erit minus vero,<emph.end type="italics"/> &longs;int enim 6.in­<lb/>&longs;tantia, & cuilibet iuxta progre&longs;&longs;ionem prædictam &longs;uum &longs;patium re&longs;pon­<lb/>deat, haud dubiè &longs;patium &longs;ecundi erit duplum &longs;patij primi, & tertium <lb/>triplum, &c. </s> | <s><emph type="italics"/>Si a&longs;&longs;umantur partes temporis majores; quæ &longs;cilicet pluribus in&longs;tantibus <lb/>constent, &longs;erueturque eadem accelerationis progre&longs;&longs;io arithmetica, &longs;patium <lb/>quod ex &longs;umma huius progre&longs;&longs;ionis re&longs;ultabit, erit minus vero,<emph.end type="italics"/> &longs;int enim 6.in­<lb/>&longs;tantia, & cuilibet iuxta progre&longs;&longs;ionem prædictam &longs;uum &longs;patium re&longs;pon­<lb/>deat, haud dubiè &longs;patium &longs;ecundi erit duplum &longs;patij primi, & tertium <lb/>triplum, &c. </s> |
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| <s>vt con&longs;tat ex dictis; igitur erunt &longs;patia 21. iam verò a&longs;&longs;u­<lb/>mantur 3. partes temporis, quarum quælibet ex 2. con&longs;tet in&longs;tantibus; <lb/>primæ parti tria ex prædictis &longs;patiis re&longs;pondeant; certè &longs;i &longs;eruetur pro­<lb/>gre&longs;&longs;io arithmetica, &longs;ecundæ re&longs;pondebunt 6. & tertiæ 9. igitur totum <lb/>&longs;patium erit 18. minus vero quod erat 21. &longs;i verò a&longs;&longs;umantur tantùm 2. <lb/>partes, quarum quælibet tribus in&longs;tantibus con&longs;tet; primæ parti re&longs;pon-<pb xlink:href="026/01/124.jpg" pagenum="92"/>debunt 6. &longs;ecundæ 12. igitur &longs;umma erit 18. minor vero &longs;patio &longs;cilicet <lb/>21.hinc vides &longs;uppo&longs;ito eodem in&longs;tantium numero &longs;patium e&longs;&longs;e &longs;empet <lb/>æquale, &longs;iue a&longs;&longs;umantur partes maiores temporis, &longs;iuc minores, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;up­<lb/>po&longs;itis 6.in&longs;tantibus, ex quibus totum &longs;patium 21.con&longs;equitur, &longs;iue a&longs;&longs;u­<lb/>mantur tres partes, quarum quælibet con&longs;tet 2. in&longs;tantibus, &longs;iue duæ, <lb/>quarum quælibet con&longs;tet tribus, &longs;patium quod ex illis re&longs;ultat, e&longs;t &longs;em­<lb/>per idem &longs;cilicet 18. a&longs;&longs;umptis verò 8. in&longs;tantibus, & totali &longs;patio, quod <lb/>illis re&longs;pondet 36. &longs;patium quod ex partibus re&longs;ultabit erit 30. &longs;iue &longs;int <lb/>duæ partes, quarum quælibet con&longs;tet 4. in&longs;tantibus, &longs;iue &longs;int 4. quarum <lb/>quælibet con&longs;tet duobus: hinc rur&longs;us vides a&longs;&longs;umpto maiori in&longs;tantium <lb/>numero &longs;patium verum habere maiorem rationem ad non verum, quàm <lb/>a&longs;&longs;umpto minori in&longs;tantium numero, v.g.a&longs;&longs;umantur 4.in&longs;tantia, &longs;umma <lb/>&longs;patiorum erit 10. &longs;i verò a&longs;&longs;umantur 2.partes temporis, quarum quæli­<lb/>bet duobus in&longs;tantibus re&longs;pondeat; &longs;umma &longs;patij erit 9.igitur ratio ve­<lb/>ri &longs;patij ad non verum e&longs;t (10/9). a&longs;&longs;umantur 6. in&longs;tantia &longs;patij veri, &longs;umma <lb/>erit 21.non veri 18. igitur ratio (21/18) &longs;eu 7/6 quæ maior e&longs;t priori: denique <lb/>a&longs;&longs;umantur 8. in&longs;tantia &longs;patij veri, &longs;umma erit 36. non veri 30 igitur ra­<lb/>tio (36/30) &longs;eu 6/3 quæ maior e&longs;t prioribus, atque ita deinceps. </s> | <s>vt con&longs;tat ex dictis; igitur erunt &longs;patia 21. iam verò a&longs;&longs;u­<lb/>mantur 3. partes temporis, quarum quælibet ex 2. con&longs;tet in&longs;tantibus; <lb/>primæ parti tria ex prædictis &longs;patiis re&longs;pondeant; certè &longs;i &longs;eruetur pro­<lb/>gre&longs;&longs;io arithmetica, &longs;ecundæ re&longs;pondebunt 6. & tertiæ 9. igitur totum <lb/>&longs;patium erit 18. minus vero quod erat 21. &longs;i verò a&longs;&longs;umantur tantùm 2. <lb/>partes, quarum quælibet tribus in&longs;tantibus con&longs;tet; primæ parti re&longs;pon-<pb xlink:href="026/01/124.jpg" pagenum="92"/>debunt 6. &longs;ecundæ 12. igitur &longs;umma erit 18. minor vero &longs;patio &longs;cilicet <lb/>21.hinc vides &longs;uppo&longs;ito eodem in&longs;tantium numero &longs;patium e&longs;&longs;e &longs;emper <lb/>æquale, &longs;iue a&longs;&longs;umantur partes maiores temporis, &longs;iuc minores, v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;up­<lb/>po&longs;itis 6.in&longs;tantibus, ex quibus totum &longs;patium 21.con&longs;equitur, &longs;iue a&longs;&longs;u­<lb/>mantur tres partes, quarum quælibet con&longs;tet 2. in&longs;tantibus, &longs;iue duæ, <lb/>quarum quælibet con&longs;tet tribus, &longs;patium quod ex illis re&longs;ultat, e&longs;t &longs;em­<lb/>per idem &longs;cilicet 18. a&longs;&longs;umptis verò 8. in&longs;tantibus, & totali &longs;patio, quod <lb/>illis re&longs;pondet 36. &longs;patium quod ex partibus re&longs;ultabit erit 30. &longs;iue &longs;int <lb/>duæ partes, quarum quælibet con&longs;tet 4. in&longs;tantibus, &longs;iue &longs;int 4. quarum <lb/>quælibet con&longs;tet duobus: hinc rur&longs;us vides a&longs;&longs;umpto maiori in&longs;tantium <lb/>numero &longs;patium verum habere maiorem rationem ad non verum, quàm <lb/>a&longs;&longs;umpto minori in&longs;tantium numero, v.g.a&longs;&longs;umantur 4.in&longs;tantia, &longs;umma <lb/>&longs;patiorum erit 10. &longs;i verò a&longs;&longs;umantur 2.partes temporis, quarum quæli­<lb/>bet duobus in&longs;tantibus re&longs;pondeat; &longs;umma &longs;patij erit 9.igitur ratio ve­<lb/>ri &longs;patij ad non verum e&longs;t (10/9). a&longs;&longs;umantur 6. in&longs;tantia &longs;patij veri, &longs;umma <lb/>erit 21.non veri 18. igitur ratio (21/18) &longs;eu 7/6 quæ maior e&longs;t priori: denique <lb/>a&longs;&longs;umantur 8. in&longs;tantia &longs;patij veri, &longs;umma erit 36. non veri 30 igitur ra­<lb/>tio (36/30) &longs;eu 6/3 quæ maior e&longs;t prioribus, atque ita deinceps. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Datis duabus partibus temporis, & cognito &longs;patio quod percurritur in prima, <lb/>matius &longs;patium re&longs;pondebit &longs;ecundæ quo vtraque in plures partes minores diui­<lb/>detur, &longs;uppofita &longs;emper eadem proare&longs;&longs;ione arithmetica in ip&longs;o incremento<emph.end type="italics"/>; <lb/>&longs;int enim duæ partes temporis &longs;en&longs;ibiles æquales AG. GH. & &longs;pa­<lb/>tium quod percurritur prima parte temporis AG &longs;it HI; in &longs;ecunda <lb/>percurretur IO, id e&longs;t, duplum HI; at verò diuidatur pars temporis <lb/>AG in duas æquales AF, FG, & con&longs;equenter totum tempus AH in 4. <lb/>æquales; haud dubiè in prima AF percurretur NP &longs;ubtripla HI, & in <lb/>&longs;ecunda FG percurretur PK dupla NP; igitur in 4. partibus temporis <lb/>AH percurretur &longs;patium decuplum PN, &longs;ed HO e&longs;t tantùm nouecupla <lb/>NP; igitur re&longs;ultabit maius &longs;patium in 4.partibus temporis, quam in dua­<lb/>bus; licèt duæ æquiualeant 4. iuxta progre&longs;&longs;ionem arithmeticam. </s></p><p type="main"> | <s><emph type="italics"/>Datis duabus partibus temporis, & cognito &longs;patio quod percurritur in prima, <lb/>matius &longs;patium re&longs;pondebit &longs;ecundæ quo vtraque in plures partes minores diui­<lb/>detur, &longs;uppo&longs;ita &longs;emper eadem progre&longs;&longs;ione arithmetica in ip&longs;o incremento<emph.end type="italics"/>; <lb/>&longs;int enim duæ partes temporis &longs;en&longs;ibiles æquales AG. GH. & &longs;pa­<lb/>tium quod percurritur prima parte temporis AG &longs;it HI; in &longs;ecunda <lb/>percurretur IO, id e&longs;t, duplum HI; at verò diuidatur pars temporis <lb/>AG in duas æquales AF, FG, & con&longs;equenter totum tempus AH in 4. <lb/>æquales; haud dubiè in prima AF percurretur NP &longs;ubtripla HI, & in <lb/>&longs;ecunda FG percurretur PK dupla NP; igitur in 4. partibus temporis <lb/>AH percurretur &longs;patium decuplum PN, &longs;ed HO e&longs;t tantùm nonecupla <lb/>NP; igitur re&longs;ultabit maius &longs;patium in 4.partibus temporis, quam in dua­<lb/>bus; licèt duæ æquiualeant 4. iuxta progre&longs;&longs;ionem arithmeticam. </s></p><p type="main"> |
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| <s>Similiter AF diuidatur bifariam in E. & tota AH in 8. æquales AE; <lb/>certè primis 4.percurretur idem &longs;patium ML æquale NK & HI; igitur <lb/>in prima AE percurretur MR. cuius ML &longs;it decupla; nam 4. terminis <lb/>re&longs;pondet &longs;umma 10. &longs;ed 8. terminis id e&longs;t 8.partibus temporis re&longs;pon­<lb/>det &longs;umma; 6. æqualium RM; &longs;ed HO tripla ML e&longs;t tantum 30. <lb/>æqualium MR; igitur in 8.partibus re&longs;ultabit maius &longs;patium, quàm in <lb/>4.quæ æquiualent 8. </s></p><p type="main"> | <s>Similiter AF diuidatur bifariam in E. & tota AH in 8. æquales AE; <lb/>certè primis 4.percurretur idem &longs;patium ML æquale NK & HI; igitur <lb/>in prima AE percurretur MR. cuius ML &longs;it decupla; nam 4. terminis <lb/>re&longs;pondet &longs;umma 10. &longs;ed 8. terminis id e&longs;t 8.partibus temporis re&longs;pon­<lb/>det &longs;umma; 6. æqualium RM; &longs;ed HO tripla ML e&longs;t tantum 30. <lb/>æqualium MR; igitur in 8.partibus re&longs;ultabit maius &longs;patium, quàm in <lb/>4.quæ æquiualent 8. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc quoque ratio maximæ percu&longs;&longs;ionis ex &longs;olo pondere cadentis illius arie­<lb/>tis inflictæ<emph.end type="italics"/>; quâ &longs;cilicet altè infiguntur lignei pali, quibus in mediis <lb/>aquis tanquam iacto &longs;undamini &longs;uperædificatur ingens &longs;æpè ædificij <lb/>moles. </s></p><p type="main"> | <s><emph type="italics"/>Hinc quoque ratio maximæ percu&longs;&longs;ionis ex &longs;olo pondere cadentis illius arie­<lb/>tis inflictæ<emph.end type="italics"/>; quâ &longs;cilicet altè infiguntur lignei pali, quibus in mediis <lb/>aquis tanquam iacto fundamini &longs;uperædificatur ingens &longs;æpè ædificij <lb/>moles. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc ex minima altitudine cadens corpus graue minimum ferè ictum in­<lb/>fligit<emph.end type="italics"/>; quia primus impetus valdè debilis e&longs;t, qui tamen deinde &longs;acta <lb/>acce&longs;&longs;ione maximus ferè euadit. </s></p><p type="main"> | <s><emph type="italics"/>Hinc ex minima altitudine cadens corpus graue minimum ferè ictum in­<lb/>fligit<emph.end type="italics"/>; quia primus impetus valdè debilis e&longs;t, qui tamen deinde facta <lb/>acce&longs;&longs;ione maximus ferè euadit. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc primo in&longs;tanti grauit ationis nullum ferè &longs;entitur pondus,<emph.end type="italics"/> quia mini­<lb/>ma vis e&longs;t, quæ con&longs;equentibus in&longs;tantibus augetur, hinc licèt corpus <lb/>breui tempore quis &longs;u&longs;tineat, paulò po&longs;t tamen ponderi cedit, ratio e&longs;t <lb/>elara ex dictis. </s></p><pb xlink:href="026/01/127.jpg" pagenum="95"/><p type="main"> | <s><emph type="italics"/>Hinc primo in&longs;tanti grauitationis nullum ferè &longs;entitur pondus,<emph.end type="italics"/> quia mini­<lb/>ma vis e&longs;t, quæ con&longs;equentibus in&longs;tantibus augetur, hinc licèt corpus <lb/>breui tempore quis &longs;u&longs;tineat, paulò po&longs;t tamen ponderi cedit, ratio e&longs;t <lb/>clara ex dictis. </s></p><pb xlink:href="026/01/127.jpg" pagenum="95"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Secundò non pote&longs;t ad amu&longs;&longs;im tempus cum tempore componi ad <lb/>æqualitatem, vel aliam datam rationem; licèt enim vnum tempus &longs;en&longs;i­<lb/>bile haberet mille in&longs;tantia &longs;upra aliud; illa tamen inæqualitas &longs;en&longs;u <lb/>minimè perciperetur; idem dico de aliis rationibus, in quo, ni fallor, <lb/>maximè peccant, qui temporum æqualitatem perfectam ob&longs;eruari po&longs;&longs;e <lb/>contendunt. </s></p><p type="main"> | <s>Secundò non pote&longs;t ad amu&longs;&longs;im tempus cum tempore componi ad <lb/>æqualitatem, vel aliam datam rationem; licèt enim vnum tempus &longs;en&longs;i­<lb/>bile haberet mille in&longs;tantia &longs;upra aliud; illa tamen inæqualitas &longs;en&longs;u <lb/>minimè perciperetur; idem dico de aliis rationibus, in quo, ni fallor, <lb/>maximè peccant, qui temporum æqualitatem perfectam ob&longs;eruari po&longs;&longs;e <lb/>contendunt. </s></p><p type="main"> |
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| <s>Tertiò, idem dico de percu&longs;&longs;ionum ratione; quippe non pote&longs;t &longs;en&longs;u <lb/>percipi inæqualitas duarum percu&longs;&longs;ionum, licèt vires vnius præualeant <lb/>mille punctis &longs;eu gradibus in&longs;en&longs;ibilibus; quippe non pote&longs;t di&longs;tingui <lb/>ab alia ni&longs;i vel ex &longs;patio; atqui di&longs;cerni non pote&longs;t, an vnum &longs;patium <lb/>&longs;uperet aliud mille punctis; vel ex &longs;ono; atqui &longs;onus pote&longs;t diuidi in in­<lb/>finitos ferè gradus &longs;en&longs;u minimè perceptibiles; igitur nulla hypothe&longs;is <lb/>in his experimentis &longs;tatui pote&longs;t, quibus æqualitas vel temporum, vel <lb/>&longs;patiorum cogno&longs;ci dicatur; nec dicas aliquot in&longs;tantia parùm di&longs;cti­<lb/>minis importare, nam cùm &longs;ingulis in&longs;tantibus fiat æqualis impetus ac­<lb/>ce&longs;&longs;io, mille in&longs;tantia reddunt percu&longs;&longs;ionem millecuplam grauitationis; <lb/>hinc certum e&longs;t ex numero in&longs;tantium cognito cogno&longs;ci tantùm po&longs;&longs;e <lb/>numerum punctorum, & vici&longs;&longs;im; at certè neuter &longs;en&longs;u percipi pote&longs;t; ne­<lb/>que tanti e&longs;t hoc &longs;cire. </s></p><p type="main"> | <s>Tertiò, idem dico de percu&longs;&longs;ionum ratione; quippe non pote&longs;t &longs;en&longs;u <lb/>percipi inæqualitas duarum percu&longs;&longs;ionum, licèt vires vnius præualeant <lb/>mille punctis &longs;eu gradibus in&longs;en&longs;ibilibus; quippe non pote&longs;t di&longs;tingui <lb/>ab alia ni&longs;i vel ex &longs;patio; atqui di&longs;cerni non pote&longs;t, an vnum &longs;patium <lb/>&longs;uperet aliud mille punctis; vel ex &longs;ono; atqui &longs;onus pote&longs;t diuidi in in­<lb/>finitos ferè gradus &longs;en&longs;u minimè perceptibiles; igitur nulla hypothe&longs;is <lb/>in his experimentis &longs;tatui pote&longs;t, quibus æqualitas vel temporum, vel <lb/>&longs;patiorum cogno&longs;ci dicatur; nec dicas aliquot in&longs;tantia parùm di&longs;eri­<lb/>minis importare, nam cùm &longs;ingulis in&longs;tantibus fiat æqualis impetus ac­<lb/>ce&longs;&longs;io, mille in&longs;tantia reddunt percu&longs;&longs;ionem millecuplam grauitationis; <lb/>hinc certum e&longs;t ex numero in&longs;tantium cognito cogno&longs;ci tantùm po&longs;&longs;e <lb/>numerum punctorum, & vici&longs;&longs;im; at certè neuter &longs;en&longs;u percipi pote&longs;t; ne­<lb/>que tanti e&longs;t hoc &longs;cire. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc &longs;i corpus graue de&longs;cenderet motu æquabili eoque æquali motui primi <lb/>m&longs;tantis; certè vix modicum &longs;patium post multos annos decurreret<emph.end type="italics"/>; &longs;uppo­<lb/>namus enim quod plures habent, licèt accuratè experimento &longs;ubii­<lb/>ci non po&longs;&longs;it, &longs;cilicet vno &longs;ecundo minuto temporis decurri à corpore <lb/>graui deor&longs;um 12. pedes &longs;patij; in &longs;ecundo minuto &longs;upponamus e&longs;&longs;e <lb/>mille in&longs;tantia, quamuis infinita penè contineat; &longs;itque in primo in­<lb/>&longs;tanti motus vnus gradus impetus; &longs;ic enim vocetur illa pars impetus, que <lb/>producitur primo in&longs;tanti; certè po&longs;t mille in&longs;tantia motus, erunt mille <lb/>gradus impetus; iam vcrò &longs;i accipiatur &longs;ubduplum maximæ & minimæ <lb/>velocitatis; id e&longs;t vnius gradus, & mille graduum, &longs;cilicet 500. 1/2 tri­<lb/>buaturque motui æquabili; haud dubiè vno fecundo minuto percur­<lb/>rentur 12. pedes &longs;patij per Th. 46. Igitur &longs;i cum velocitate vt 500, 1/2 <lb/>percurrentur 12. pedes 1.minuto, cum velocitate vt 1. percurrentur <lb/>12. pedes 500.&longs;ecundis minutis, &; 30. tertiis; &longs;i verò accipiantur plura <lb/>in&longs;tantia, v.g. <!-- REMOVE S-->1000000.in&longs;tantia, percurrentur 12. pedes 500000. &longs;e­<lb/>cundis minutis; &longs;i verò 1000000000000. percurremur 500000000000. <lb/>&longs;ecundis, id e&longs;t 8333333333. minutis, id e&longs;t 138888888. horis <pb xlink:href="026/01/128.jpg" pagenum="96"/>id e&longs;t 5787037. diebus id e&longs;t 89031. annis, omitto minutias; atqui lon­<lb/>gè adhuc plura in vno minuto continentur in&longs;tantia. </s> | <s><emph type="italics"/>Hinc &longs;i corpus graue de&longs;cenderet motu æquabili eoque æquali motui primi <lb/>in&longs;tantis; certè vix modicum &longs;patium post multos annos decurreret<emph.end type="italics"/>; &longs;uppo­<lb/>namus enim quod plures habent, licèt accuratè experimento &longs;ubii­<lb/>ci non po&longs;&longs;it, &longs;cilicet vno &longs;ecundo minuto temporis decurri à corpore <lb/>graui deor&longs;um 12. pedes &longs;patij; in &longs;ecundo minuto &longs;upponamus e&longs;&longs;e <lb/>mille in&longs;tantia, quamuis infinita penè contineat; &longs;itque in primo in­<lb/>&longs;tanti motus vnus gradus impetus; &longs;ic enim vocetur illa pars impetus, que <lb/>producitur primo in&longs;tanti; certè po&longs;t mille in&longs;tantia motus, erunt mille <lb/>gradus impetus; iam vcrò &longs;i accipiatur &longs;ubduplum maximæ & minimæ <lb/>velocitatis; id e&longs;t vnius gradus, & mille graduum, &longs;cilicet 500. 1/2 tri­<lb/>buaturque motui æquabili; haud dubiè vno fecundo minuto percur­<lb/>rentur 12. pedes &longs;patij per Th. 46. Igitur &longs;i cum velocitate vt 500, 1/2 <lb/>percurrentur 12. pedes 1.minuto, cum velocitate vt 1. percurrentur <lb/>12. pedes 500.&longs;ecundis minutis, &; 30. tertiis; &longs;i verò accipiantur plura <lb/>in&longs;tantia, v.g. <!-- REMOVE S-->1000000.in&longs;tantia, percurrentur 12. pedes 500000. &longs;e­<lb/>cundis minutis; &longs;i verò 1000000000000. percurremur 500000000000. <lb/>&longs;ecundis, id e&longs;t 8333333333. minutis, id e&longs;t 138888888. horis <pb xlink:href="026/01/128.jpg" pagenum="96"/>id e&longs;t 5787037. diebus id e&longs;t 89031. annis, omitto minutias; atqui lon­<lb/>gè adhuc plura in vno minuto continentur in&longs;tantia. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 60.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si corpus graue de&longs;cenderet motu æquabili, eoque æquali motui vltimi in­<lb/>stantis, duplum ferè &longs;patium æquali tempore conficeret illius quod conficit <lb/>motu accelerato, duplum inquam ferè &longs;cilicet panlò minùs<emph.end type="italics"/>; quia conficit <lb/>idem motu æquabili; cuius velocitas e&longs;t &longs;ubdupla maximæ & minimæ; <lb/>&longs;ed minima velocitas primi in&longs;tantis pro nihilo reputatur; igitur acci­<lb/>piatur tantùm &longs;ubduplum maximæ, igitur cum velocitate æquali maxi­<lb/>mæ, eodem tempore duplum &longs;patium percurretur; igitur in vno minuto <lb/>&longs;ecundo, v.g. <!-- REMOVE S-->24. pedes; igitur in vno minuto primo codem motu æqua­<lb/>bili 1440. pedes percurrentur; igitur in vna hora 86400. pedes; hinc <lb/>non e&longs;t quod aliqui adeo mirentur, &longs;eu potiùs reiiciant hanc motus <lb/>accelerationem quod ex ea tùm tardi&longs;&longs;imus motus, tùm veloci&longs;&longs;imus <lb/>con&longs;equatur. </s> | <s><emph type="italics"/>Si corpus graue de&longs;cenderet motu æquabili, eoque æquali motui vltimi in­<lb/>stantis, duplum ferè &longs;patium æquali tempore conficeret illius quod conficit <lb/>motu accelerato, duplum inquam ferè &longs;cilicet paulò minùs<emph.end type="italics"/>; quia conficit <lb/>idem motu æquabili; cuius velocitas e&longs;t &longs;ubdupla maximæ & minimæ; <lb/>&longs;ed minima velocitas primi in&longs;tantis pro nihilo reputatur; igitur acci­<lb/>piatur tantùm &longs;ubduplum maximæ, igitur cum velocitate æquali maxi­<lb/>mæ, eodem tempore duplum &longs;patium percurretur; igitur in vno minuto <lb/>&longs;ecundo, v.g. <!-- REMOVE S-->24. pedes; igitur in vno minuto primo codem motu æqua­<lb/>bili 1440. pedes percurrentur; igitur in vna hora 86400. pedes; hinc <lb/>non e&longs;t quod aliqui adeo mirentur, &longs;eu potiùs reiiciant hanc motus <lb/>accelerationem quod ex ea tùm tardi&longs;&longs;imus motus, tùm veloci&longs;&longs;imus <lb/>con&longs;equatur. </s> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Secundò reiicies illos, qui volunt accelerationem motus e&longs;&longs;e, vel à vi <lb/>magnetica, quâ terra trahit ad &longs;e omnia grauia; vel ab alia vi occulta, <lb/>quâ cœlum pellit deor&longs;um; vel à cœle&longs;ti illa, imò potiùs fabulosâ mate­<lb/>riâ; vel demum ab ip&longs;a vi fympathicâ, quâ corpus &longs;uo centro propiùs <lb/>factum totas &longs;uas vires exerit, vt ei &longs;e conjungat; quæ omnia gratis di­<lb/>cuntur, & ex dictis plu&longs;quam efficaciter refelli po&longs;&longs;unt, nefru&longs;trà tempus <lb/>in iis iterum refellendis teramus. </s></p><p type="main"> | <s>Secundò reiicies illos, qui volunt accelerationem motus e&longs;&longs;e, vel à vi <lb/>magnetica, quâ terra trahit ad &longs;e omnia grauia; vel ab alia vi occulta, <lb/>quâ cœlum pellit deor&longs;um; vel à cœle&longs;ti illa, imò potiùs fabulosâ mate­<lb/>riâ; vel demum ab ip&longs;a vi &longs;ympathicâ, quâ corpus &longs;uo centro propiùs <lb/>factum totas &longs;uas vires exerit, vt ei &longs;e conjungat; quæ omnia gratis di­<lb/>cuntur, & ex dictis plu&longs;quam efficaciter refelli po&longs;&longs;unt, ne fru&longs;trà tempus <lb/>in iis iterum refellendis teramus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Quartò ex his &longs;ententia Ari&longs;totelica de motu accelerato optunè vin­<lb/>dicatur; quòd &longs;cilicet grauia &longs;ub finem &longs;ui motus velociùs &longs;erantur ver­<lb/>sùs centrum; quod ex dictis, & &longs;implici&longs;&longs;imis, certi&longs;&longs;imi&longs;que principiis <lb/>demon&longs;tratum fuit. </s></p><p type="main"> | <s>Quartò ex his &longs;ententia Ari&longs;totelica de motu accelerato optimè vin­<lb/>dicatur; quòd &longs;cilicet grauia &longs;ub finem &longs;ui motus velociùs &longs;erantur ver­<lb/>sùs centrum; quod ex dictis, & &longs;implici&longs;&longs;imis, certi&longs;&longs;imi&longs;que principiis <lb/>demon&longs;tratum fuit. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium.<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>fique vno in&longs;tanti acquiritur 1. <lb/>&longs;patium, duobus acquiruntur 4. tribus 9. quatuor 16. atque ita deinceps <lb/>per quadrata, quæ omnia ex dictis falfa e&longs;&longs;e con&longs;tat; quippe &longs;i æqualibus <lb/>temporibus acquiruntur æqualia velocitatis momenta; igitur &longs;i primo <lb/>in&longs;tanti e&longs;t 1.gradus, &longs;ecundo erunt 2. igitur &longs;ecundo tempore cum duo­<lb/>bus gradibus velocitatis vel impetus percurrentur duo tantùm &longs;patia, &longs;i <lb/>primò in&longs;tanti æquali cum vno gradu percurritur vnus, &longs;ed de his fusè <lb/>infrà. </s></p><pb xlink:href="026/01/130.jpg" pagenum="98"/><p type="main"> | <s>fique vno in&longs;tanti acquiritur 1. <lb/>&longs;patium, duobus acquiruntur 4. tribus 9. quatuor 16. atque ita deinceps <lb/>per quadrata, quæ omnia ex dictis fal&longs;a e&longs;&longs;e con&longs;tat; quippe &longs;i æqualibus <lb/>temporibus acquiruntur æqualia velocitatis momenta; igitur &longs;i primo <lb/>in&longs;tanti e&longs;t 1.gradus, &longs;ecundo erunt 2. igitur &longs;ecundo tempore cum duo­<lb/>bus gradibus velocitatis vel impetus percurrentur duo tantùm &longs;patia, &longs;i <lb/>primò in&longs;tanti æquali cum vno gradu percurritur vnus, &longs;ed de his fusè <lb/>infrà. </s></p><pb xlink:href="026/01/130.jpg" pagenum="98"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main"> |
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| <s>prop.18.&longs;uæ Bali&longs;ticæ &longs;ub finem; illa <lb/>e&longs;t inquam &longs;ententia, quam hactenus meo iudicio &longs;atis luculenter de­<lb/>mon&longs;trauimus. </s></p><p type="main"> | <s>prop.18.&longs;uæ Bali&longs;ticæ &longs;ub finem; illa <lb/>e&longs;t inquam &longs;ententia, quam hactenus meo iudicio &longs;atis luculenter de­<lb/>mon&longs;trauimus. </s></p><p type="main"> |
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| <s>Sunt tres aliæ &longs;ententiæ, quæ ab eodem Mer&longs;enno referuntur; prima <lb/>e&longs;t quæ progre&longs;&longs;ionem &longs;patiorum eamdem e&longs;&longs;e vult cum eâ, quæ e&longs;t &longs;i­<lb/>nuum ver&longs;orum, centro quadrantis po&longs;ito in centro terræ, & altero ex­<lb/>tremo &longs;inus totius in eo punctò, in quo incipit motus. </s> | <s>Sunt tres aliæ &longs;ententiæ, quæ ab eodem Mer&longs;enno referuntur; prima <lb/>e&longs;t quæ progre&longs;&longs;ionem &longs;patiorum <expan abbr="eãdem">eandem</expan> e&longs;&longs;e vult cum eâ, quæ e&longs;t &longs;i­<lb/>nuum ver&longs;orum, centro quadrantis po&longs;ito in centro terræ, & altero ex­<lb/>tremo &longs;inus totius in eo punctò, in quo incipit motus. </s> |
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| <s>Secunda e&longs;t quo­<lb/>rumdam, qui volunt progre&longs;&longs;ionem &longs;patiorum, quæ &longs;ingulis temporibus <lb/>re&longs;pondent, e&longs;&longs;e in progre&longs;&longs;ione geometrica dupla iuxta hos numeros, <lb/>1.2.4.8.32. Tertia e&longs;t alicuius, qui voluit e&longs;&longs;e iuxta proportionem lineæ <lb/>&longs;ectæ in mediam, & extremam rationem. </s></p><p type="main"> | <s>Secunda e&longs;t quo­<lb/>rumdam, qui volunt progre&longs;&longs;ionem &longs;patiorum, quæ &longs;ingulis temporibus <lb/>re&longs;pondent, e&longs;&longs;e in progre&longs;&longs;ione geometrica dupla iuxta hos numeros, <lb/>1.2.4.8.32. Tertia e&longs;t alicuius, qui voluit e&longs;&longs;e iuxta proportionem lineæ <lb/>&longs;ectæ in mediam, & extremam rationem. </s></p><p type="main"> |
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| <s>Tres vltimæ &longs;ententiæ nullo pror&longs;us nituntur fundamento; igitur vel <lb/>inde maximè confutantur, quòd gratis &longs;ine vllo pror&longs;us vel rationis vel <lb/>experimenti momento excogitatæ &longs;int. </s> | <s>Tres vltimæ &longs;ententiæ nullo pror&longs;us nituntur fundamento; igitur vel <lb/>inde maximè confutantur, quòd gratis &longs;ine vllo pror&longs;us vel rationis vel <lb/>experimenti momento excogitatæ &longs;int. </s> |
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| <s>Igitur in hac di&longs;&longs;ertatione duæ <lb/>tantùm primæ di&longs;cutiendæ &longs;unt Sententiæ Galilei &longs;chema hic habes <lb/>in linea AF, in qua a&longs;&longs;umitur AB, &longs;patium &longs;cilicet, quod dato tempore <pb xlink:href="026/01/131.jpg" pagenum="99"/>corpus graue &longs;uo motu percurrit; & &longs;ecundo tempore æquali BC, quæ <lb/>tripla e&longs;t AB, tertio CD quintupla quarto DE &longs;eptupla, quinto EF <lb/>nouecupla; vides primò &longs;eriem numerorum imparium 1. 3. 5. 7. 9.atque <lb/>ita deinceps. </s> | <s>Igitur in hac di&longs;&longs;ertatione duæ <lb/>tantùm primæ di&longs;cutiendæ &longs;unt Sententiæ Galilei &longs;chema hic habes <lb/>in linea AF, in qua a&longs;&longs;umitur AB, &longs;patium &longs;cilicet, quod dato tempore <pb xlink:href="026/01/131.jpg" pagenum="99"/>corpus graue &longs;uo motu percurrit; & &longs;ecundo tempore æquali BC, quæ <lb/>tripla e&longs;t AB, tertio CD quintupla quarto DE &longs;eptupla, quinto EF <lb/>nonecupla; vides primò &longs;eriem numerorum imparium 1. 3. 5. 7. 9.atque <lb/>ita deinceps. </s> |
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| <s>Secundò vides &longs;patia e&longs;&longs;e in ratione duplicata temporum, <lb/>hoc e&longs;t vt temporum quadrata. </s> | <s>Secundò vides &longs;patia e&longs;&longs;e in ratione duplicata temporum, <lb/>hoc e&longs;t vt temporum quadrata. </s> |
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| <s>Adde quod, vt &longs;e habet tempus, quo de&longs;cendit per totum quadrantem <lb/>DF, ad tempus, quo de&longs;cendit per totum quadrantem EG. &longs;ic &longs;e habet <lb/>tempus, quo de&longs;cendit per arcum DL &longs;ubduplum DF ad tempus, quo <lb/>de&longs;cendit per arcum EI &longs;ubduplum EG; item tempus, quo de&longs;cendit <pb xlink:href="026/01/132.jpg" pagenum="100"/>per arcum DM &longs;ubquadruplum DF.ad tempus, quo de&longs;cendit per arcum <lb/>EK &longs;ubquadruplum EG; denique vt tempus, quo per minimum ar­<lb/>cum quadrantis DF, ad tempus, quo de&longs;cendit per alium proportiona­<lb/>lem, &longs;cilicet quadruplum in quadrante EG; atqui tam parui arcus po&longs;­<lb/>&longs;unt a&longs;&longs;umi, vt &longs;int ad in&longs;tar lineæ rectæ deor&longs;um tangentis &longs;cilicet in D <lb/>& in E; igitur in his rectis de&longs;cendunt grauia iuxta progre&longs;&longs;ionem præ­<lb/>dictam; id e&longs;t, cum arcus minimus a&longs;&longs;umptus ab E, qui æquiualet rectæ, <lb/>&longs;it quadruplus arcus minimi a&longs;&longs;umpti à puncto D, tempus, quo percurri­<lb/>tur ille primus, e&longs;t ad tempus, quo percurritur hic &longs;ubquadruplus, vt tem­<lb/>pus, quo percurritur EG ad tempus, quo percurritur DF vt dictum e&longs;t; <lb/>&longs;ed tempus, quo percurritur EG e&longs;t duplum illius, quo percurritur DF; <lb/>igitur tempus, quo percurritur minimus arcus a&longs;&longs;umptus ab E, & qui e&longs;t <lb/>ad in&longs;tar rectæ, e&longs;t duplum temporis quo percurritur minimus arcus a&longs;­<lb/>&longs;umptus à puncto D &longs;ubquadruplus prioris, & qui e&longs;t etiam ad in&longs;tar re­<lb/>ctæ; igitur &longs;patia &longs;unt vt temporum quadrata. </s></p><p type="main"> | <s>Adde quod, vt &longs;e habet tempus, quo de&longs;cendit per totum quadrantem <lb/>DF, ad tempus, quo de&longs;cendit per totum quadrantem EG. &longs;ic &longs;e habet <lb/>tempus, quo de&longs;cendit per arcum DL &longs;ubduplum DF ad tempus, quo <lb/>de&longs;cendit per arcum EI &longs;ubduplum EG; item tempus, quo de&longs;cendit <pb xlink:href="026/01/132.jpg" pagenum="100"/>per arcum DM &longs;ubquadruplum DF.ad tempus, quo de&longs;cendit per arcum <lb/>EK &longs;ubquadruplum EG; denique vt tempus, quo per minimum ar­<lb/>cum quadrantis DF, ad tempus, quo de&longs;cendit per alium proportiona­<lb/>lem, &longs;cilicet quadruplum in quadrante EG; atqui tam parui arcus po&longs;­<lb/>&longs;unt a&longs;&longs;umi, vt &longs;int ad in&longs;tar lineæ rectæ deor&longs;um tangentis &longs;cilicet in D <lb/>& in E; igitur in his rectis de&longs;cendunt grauia iuxta progre&longs;&longs;ionem præ­<lb/>dictam; id e&longs;t, cum arcus minimus a&longs;&longs;umptus ab E, qui æquiualet rectæ, <lb/>&longs;it quadruplus arcus minimi a&longs;&longs;umpti à puncto D, tempus, quo percurri­<lb/>tur ille primus, e&longs;t ad tempus, quo percurritur hic &longs;ubquadruplus, vt tem­<lb/>pus, quo percurritur EG ad tempus, quo percurritur DF vt dictum e&longs;t; <lb/>&longs;ed tempus, quo percurritur EG e&longs;t duplum illius, quo percurritur DF; <lb/>igitur tempus, quo percurritur minimus arcus a&longs;&longs;umptus ab E, & qui e&longs;t <lb/>ad in&longs;tar rectæ, e&longs;t duplum temporis quo percurritur minimus arcus a&longs;­<lb/>&longs;umptus à puncto D &longs;ubquadruplus prioris, & qui e&longs;t etiam ad in&longs;tar re­<lb/>ctæ; igitur &longs;patia &longs;unt vt temporum quadrata. </s></p><p type="main"> |
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| <s>Quod autem tempus, quo percurritur EG &longs;it duplum illius, quo per­<lb/>curritur DF, patet experientiâ; nam &longs;i numerentur ducentæ vibrationes <lb/>funependuli CD; eodem tempore numerabuntur centum vibrationes <lb/>maioris CE; igitur vibrationum minoris numerus e&longs;t duplus numeri vi­<lb/>brationum maioris, dum &longs;imul vibrantur; igitur eo tempore, quo fiunt <lb/>100.maioris, fient 200. minoris; nam ommes vibrationes eiu&longs;dem fune­<lb/>penduli &longs;unt æquò diuturnæ, licèt fiant per arcus inæquales ciu&longs;dem. </s> | <s>Quod autem tempus, quo percurritur EG &longs;it duplum illius, quo per­<lb/>curritur DF, patet experientiâ; nam &longs;i numerentur ducentæ vibrationes <lb/>funependuli CD; eodem tempore numerabuntur centum vibrationes <lb/>maioris CE; igitur vibrationum minoris numerus e&longs;t duplus numeri vi­<lb/>brationum maioris, dum &longs;imul vibrantur; igitur eo tempore, quo fiunt <lb/>100.maioris, fient 200. minoris; nam omnes vibrationes eiu&longs;dem fune­<lb/>penduli &longs;unt æquò diuturnæ, licèt fiant per arcus inæquales eiu&longs;dem. </s> |
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| <s><lb/>quadrantis, vt &longs;æpè ob&longs;eruatum e&longs;t. </s> | <s><lb/>quadrantis, vt &longs;æpè ob&longs;eruatum e&longs;t. </s> |
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| <s>iudicio, nec <lb/>&longs;inceriùs exponi po&longs;&longs;unt. </s></p><p type="main"> | <s>iudicio, nec <lb/>&longs;inceriùs exponi po&longs;&longs;unt. </s></p><p type="main"> |
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| <s>Antequam rationes, quæ pro hac &longs;ententia facere videntur, propona­<lb/>mus, refellamu&longs;que; oftendo primò quomodo cum his experimentis <lb/>&longs;tare po&longs;&longs;it no&longs;tra hypothe&longs;is; igitur ex iis hypothe&longs;is Galilei rectè de­<lb/>duci non pote&longs;t: quippe hæc e&longs;t certi&longs;&longs;ima regula, quam nemo Philo&longs;o­<lb/>phus negare au&longs;it: Quotie&longs;cumque aliquod experimentum tale e&longs;t, vt <lb/>cum eo &longs;tare po&longs;&longs;int contrariæ hypothe&longs;es; ex eo certè neutra deduci po­<lb/>te&longs;t; igitur ex propo&longs;itis experimentis &longs;uam hypothe&longs;im Galileus non <lb/>legitimè deducit, quod vt clari&longs;&longs;imè o&longs;tendam. </s></p><p type="main"> | <s>Antequam rationes, quæ pro hac &longs;ententia facere videntur, propona­<lb/>mus, refellamu&longs;que; o&longs;tendo primò quomodo cum his experimentis <lb/>&longs;tare po&longs;&longs;it no&longs;tra hypothe&longs;is; igitur ex iis hypothe&longs;is Galilei rectè de­<lb/>duci non pote&longs;t: quippe hæc e&longs;t certi&longs;&longs;ima regula, quam nemo Philo&longs;o­<lb/>phus negare au&longs;it: Quotie&longs;cumque aliquod experimentum tale e&longs;t, vt <lb/>cum eo &longs;tare po&longs;&longs;int contrariæ hypothe&longs;es; ex eo certè neutra deduci po­<lb/>te&longs;t; igitur ex propo&longs;itis experimentis &longs;uam hypothe&longs;im Galileus non <lb/>legitimè deducit, quod vt clari&longs;&longs;imè o&longs;tendam. </s></p><p type="main"> |
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| <s>Suppono, quando dicitur &longs;ecundum &longs;patium e&longs;&longs;e triplum primi &longs;up­<lb/>po&longs;itis æqualibus temporibus, non ita Geometricè, certaque, & acuratâ <lb/>a&longs;&longs;ertione hoc dici; quin vel aliqua puncta in &longs;patiis, vel in&longs;tantia in <lb/>temporibus de&longs;int, vel &longs;uper&longs;int; &longs;i enim quis diceret &longs;patium e&longs;&longs;e tri­<lb/>plum primi minus 100000. punctis, vel &longs;ecundum tempus e&longs;&longs;e maius <lb/>primo 100000. in&longs;tantibus; quis hanc, vel &longs;patij, vel temporis differen­<lb/>tiam &longs;en&longs;u percipiat? </s> | <s>Suppono, quando dicitur &longs;ecundum &longs;patium e&longs;&longs;e triplum primi &longs;up­<lb/>po&longs;itis æqualibus temporibus, non ita Geometricè, certaque, & acuratâ <lb/>a&longs;&longs;ertione hoc dici; quin vel aliqua puncta in &longs;patiis, vel in&longs;tantia in <lb/>temporibus de&longs;int, vel &longs;uper&longs;int; &longs;i enim quis diceret &longs;patium e&longs;&longs;e tri­<lb/>plum primi minus 100000. punctis, vel &longs;ecundum tempus e&longs;&longs;e maius <lb/>primo 100000. in&longs;tantibus; quis hanc, vel &longs;patij, vel temporis differen­<lb/>tiam &longs;en&longs;u percipiat? </s> |
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| <s>cum tamen experimentum omne phy&longs;icum &longs;en&longs;ui <lb/>&longs;ube&longs;&longs;e po&longs;&longs;it; nec e&longs;t quod aliquis dicat hoc idem toties ob&longs;eruatum <lb/>e&longs;&longs;e, tam multis locis temporibus, totque ac tantis etiam te&longs;tibus, vt mi­<lb/>nimè fraus aliqua, vel error &longs;ubrepere potuerit; nam cum parua &longs;it, & <lb/>in&longs;en&longs;ibilis tùm &longs;patiorum, tùm temporum differentia, maius vel minus <lb/>æquali tempus, pro æquali, maius.vel minus triplò &longs;patium pro triplo <pb xlink:href="026/01/133.jpg" pagenum="101"/>facilè accipi pote&longs;t, cum nullum di&longs;erimen &longs;en&longs;ibile e&longs;t. </s></p><p type="main"> | <s>cum tamen experimentum omne phy&longs;icum &longs;en&longs;ui <lb/>&longs;ube&longs;&longs;e po&longs;&longs;it; nec e&longs;t quod aliquis dicat hoc idem toties ob&longs;eruatum <lb/>e&longs;&longs;e, tam multis locis temporibus, totque ac tantis etiam te&longs;tibus, vt mi­<lb/>nimè fraus aliqua, vel error &longs;ubrepere potuerit; nam cum parua &longs;it, & <lb/>in&longs;en&longs;ibilis tùm &longs;patiorum, tùm temporum differentia, maius vel minus <lb/>æquali tempus, pro æquali, maius.vel minus triplò &longs;patium pro triplo <pb xlink:href="026/01/133.jpg" pagenum="101"/>facilè accipi pote&longs;t, cum nullum di&longs;erimen &longs;en&longs;ibile e&longs;t. </s></p><p type="main"> |
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| <s>Adde quod non de&longs;unt viri graui&longs;&longs;uni qui dicant &longs;e vix ob&longs;eruare po­<lb/>tui&longs;&longs;e hanc &longs;patiorum progre&longs;&longs;ionem; plures appellare po&longs;&longs;em; vnus <lb/>Ga&longs;&longs;endus e&longs;t in&longs;tar omnium; qui &longs;anè in ob&longs;eruando fuit acurati&longs;&longs;imus, <lb/>qui literis &longs;criptis, quas ego vidi, expre&longs;&longs;is verbis a&longs;&longs;erit progre&longs;&longs;ionem <lb/>hanc non e&longs;&longs;e omninò iuxta hos numeros 1.3.5.7. &longs;ed &longs;ingulis addendas <lb/>e&longs;&longs;e &longs;uas minutias, quas ip&longs;e habet; &longs;ed ego omitto, quia etiam &longs;ua incer­<lb/>titudine laborant; igitur nullo experimento ad amu&longs;&longs;im concludes, <lb/>vel <expan abbr="æqualitat&etilde;">æqualitatem</expan> vel aliam accuratam tùm temporum tùm &longs;patiorum pro­<lb/>portionem: Equidem &longs;en&longs;u percipio practicam hanc e&longs;&longs;e maiorem pede; <lb/>at tot lineis vel <expan abbr="pũctis">punctis</expan> &longs;uperare ne Argus quidem certò, ac di&longs;tinctè cer­<lb/>neret: Sed efficaciter, meo iudicio, hanc Galilei hypothe&longs;im refello; &longs;int <lb/> 2.partes temporis æquales AE, EF, eæque &longs;en&longs;ibiles; nec enim aliæ a&longs;­<lb/>&longs;iuni po&longs;&longs;unt; &longs;intque minintæ omnium &longs;en&longs;ibilium; haud dubiè con&longs;tant <lb/>&longs;ingulæ infinitis ferè aliis in&longs;en&longs;ibilibus, vt patet; igitur &longs;ic ratiocinatur <lb/>Galileus; in prima parte temporis AE corpus graue percurrit &longs;patium <lb/>GH, & in &longs;ecunda æquali EF percurrit &longs;patium HL triplum prioris; <lb/>igitur &longs;patia &longs;unt vt quadrata temporum, rectè; &longs;ed antequam vlterius <lb/>progrediar; Quæro vel à Galileo, vel à quolibet alro, vtrum &longs;patium <lb/>HL &longs;it omnino triplum? </s> | <s>Adde quod non de&longs;unt viri graui&longs;&longs;imi qui dicant &longs;e vix ob&longs;eruare po­<lb/>tui&longs;&longs;e hanc &longs;patiorum progre&longs;&longs;ionem; plures appellare po&longs;&longs;em; vnus <lb/>Ga&longs;&longs;endus e&longs;t in&longs;tar omnium; qui &longs;anè in ob&longs;eruando fuit acurati&longs;&longs;imus, <lb/>qui literis &longs;criptis, quas ego vidi, expre&longs;&longs;is verbis a&longs;&longs;erit progre&longs;&longs;ionem <lb/>hanc non e&longs;&longs;e omninò iuxta hos numeros 1.3.5.7. &longs;ed &longs;ingulis addendas <lb/>e&longs;&longs;e &longs;uas minutias, quas ip&longs;e habet; &longs;ed ego omitto, quia etiam &longs;ua incer­<lb/>titudine laborant; igitur nullo experimento ad amu&longs;&longs;im concludes, <lb/>vel <expan abbr="æqualitat&etilde;">æqualitatem</expan> vel aliam accuratam tùm temporum tùm &longs;patiorum pro­<lb/>portionem: Equidem &longs;en&longs;u percipio practicam hanc e&longs;&longs;e maiorem pede; <lb/>at tot lineis vel <expan abbr="pũctis">punctis</expan> &longs;uperare ne Argus quidem certò, ac di&longs;tinctè cer­<lb/>neret: Sed efficaciter, meo iudicio, hanc Galilei hypothe&longs;im refello; &longs;int <lb/> 2.partes temporis æquales AE, EF, eæque &longs;en&longs;ibiles; nec enim aliæ a&longs;­<lb/>&longs;umi po&longs;&longs;unt; &longs;intque minimæ omnium &longs;en&longs;ibilium; haud dubiè con&longs;tant <lb/>&longs;ingulæ infinitis ferè aliis in&longs;en&longs;ibilibus, vt patet; igitur &longs;ic ratiocinatur <lb/>Galileus; in prima parte temporis AE corpus graue percurrit &longs;patium <lb/>GH, & in &longs;ecunda æquali EF percurrit &longs;patium HL triplum prioris; <lb/>igitur &longs;patia &longs;unt vt quadrata temporum, rectè; &longs;ed antequam vlterius <lb/>progrediar;</s><s> Quæro vel à Galileo, vel à quolibet alto, vtrum &longs;patium <lb/>HL &longs;it omnino triplum? </s> |
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| <s>& &longs;i aliquis contenderet dec&longs;&longs;e (1/1000000) GH <lb/>vtrum experimento præ&longs;enti conuinci po&longs;&longs;it? </s> | <s>& &longs;i aliquis contenderet dee&longs;&longs;e (1/1000000) GH <lb/>vtrum experimento præ&longs;enti conuinci po&longs;&longs;it? </s> |
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| <s>nemo, vt puto, id a&longs;&longs;erere <lb/>au&longs;it; hoc po&longs;ito, a&longs;&longs;umptaque progre&longs;&longs;ione arithmetica <expan abbr="quã">quam</expan> no&longs;tra &longs;en­<lb/>tentia in &longs;patiis ad&longs;truit; &longs;i prima parte temporis AE percurratur &longs;pa­<lb/>tium GH, &longs;ecunda EF. percurretur tantùm HK duplum GH; igitur <lb/>minus e&longs;t hoc &longs;patium vero &longs;patio 1/4. &longs;cilicet tota KL; res pror&longs;us de­<lb/>mon&longs;trata e&longs;&longs;et, &longs;i termini proportionis vnius e&longs;&longs;ent tantùm 2. id e&longs;t, &longs;i <lb/>progre&longs;&longs;io fieret in partibus temporis &longs;en&longs;ibilibus; at po&longs;ito quod &longs;int <lb/>plures termini, vt reuerâ &longs;unt; nam in totidem terminis fit progre&longs;&longs;io, in <lb/>quibus fit augmentum impetus, vel accelorationis acce&longs;&longs;io; atqui hæc <lb/>fit in &longs;ingulis in&longs;tantibus, licèt finitis, igitur & progre&longs;&longs;ro; Quare duæ <lb/>partes temporis AE, EF diuidantur in 4. æquales AD; certè in duabus <lb/>primis percurretur &longs;patium. </s> | <s>nemo, vt puto, id a&longs;&longs;erere <lb/>au&longs;it; hoc po&longs;ito, a&longs;&longs;umptaque progre&longs;&longs;ione arithmetica <expan abbr="quã">quam</expan> no&longs;tra &longs;en­<lb/>tentia in &longs;patiis ad&longs;truit; &longs;i prima parte temporis AE percurratur &longs;pa­<lb/>tium GH, &longs;ecunda EF. percurretur tantùm HK duplum GH; igitur <lb/>minus e&longs;t hoc &longs;patium vero &longs;patio 1/4. &longs;cilicet tota KL; res pror&longs;us de­<lb/>mon&longs;trata e&longs;&longs;et, &longs;i termini proportionis vnius e&longs;&longs;ent tantùm 2. id e&longs;t, &longs;i <lb/>progre&longs;&longs;io fieret in partibus temporis &longs;en&longs;ibilibus; at po&longs;ito quod &longs;int <lb/>plures termini, vt reuerâ &longs;unt; nam in totidem terminis fit progre&longs;&longs;io, in <lb/>quibus fit augmentum impetus, vel accelerationis acce&longs;&longs;io; atqui hæc <lb/>fit in &longs;ingulis in&longs;tantibus, licèt finitis, igitur & progre&longs;&longs;io; Quare duæ <lb/>partes temporis AE, EF diuidantur in 4. æquales AD; certè in duabus <lb/>primis percurretur &longs;patium. </s> |
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| <s>VQ æquale GH; igitur duabus vltimis per­<lb/>curretur QK, quæ &longs;it ad QV vt 7. ad 3. nam prima parte percurritur 1. <lb/>&longs;patium. </s> | <s>VQ æquale GH; igitur duabus vltimis per­<lb/>curretur QK, quæ &longs;it ad QV vt 7. ad 3. nam prima parte percurritur 1. <lb/>&longs;patium. </s> |
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| <s>&longs;ecunda 2. igitur QV continet tria &longs;patia; tertia verò 3. quarta <lb/>4.ergo hæ duæ vltimæ 7. &longs;ed QM e&longs;t dupla QV; igitur continet 6. igi­<lb/>tur MK e&longs;t 1/3 VQ, vel KL; igitur KM e&longs;t (1/12) GL; igitur 12. L (1/10), vel <lb/>1/6, igitur VK e&longs;t ad GL vt 10.ad 12. igitur totum &longs;patium VK e&longs;t mi­<lb/>nus vero 1/6. Præterea 2. partes temporis AE EF diuidantur in 8. partes <lb/>æquales AE; haud dubiè 4. primis percurretur &longs;patium XT æqualc <lb/>GH, quod debet diuidi in 10. &longs;patia; nam 4. terminis, &longs;eu temporibus <lb/>re&longs;pondent &longs;paria 10. quibus æqualia &longs;unt 40. in teta GL, cuius XT e&longs;t <lb/>(1/14), &longs;ed &longs;i in 4.primis acquiruntur 10. 4. vltimis EF acquiruntur 26.&longs;cili­<lb/>cet T 5; igitur tota X 5. e&longs;t 6. igitur e&longs;t ad GL vt 36. ad 40. &longs;eu 9. ad <lb/>10. igitur X 5. e&longs;t &longs;patium minus vero (1/10). </s></p><p type="main"> | <s>&longs;ecunda 2. igitur QV continet tria &longs;patia; tertia verò 3. quarta <lb/>4.ergo hæ duæ vltimæ 7. &longs;ed QM e&longs;t dupla QV; igitur continet 6. igi­<lb/>tur MK e&longs;t 1/3 VQ, vel KL; igitur KM e&longs;t (1/12) GL; igitur 12. L (1/10), vel <lb/>1/6, igitur VK e&longs;t ad GL vt 10.ad 12. igitur totum &longs;patium VK e&longs;t mi­<lb/>nus vero 1/6. Præterea 2. partes temporis AE EF diuidantur in 8. partes <lb/>æquales AE; haud dubiè 4. primis percurretur &longs;patium XT æquale <lb/>GH, quod debet diuidi in 10. &longs;patia; nam 4. terminis, &longs;eu temporibus <lb/>re&longs;pondent &longs;patia 10. quibus æqualia &longs;unt 40. in teta GL, cuius XT e&longs;t <lb/>(1/14), &longs;ed &longs;i in 4.primis acquiruntur 10. 4. vltimis EF acquiruntur 26.&longs;cili­<lb/>cet T 5; igitur tota X 5. e&longs;t 6. igitur e&longs;t ad GL vt 36. ad 40. &longs;eu 9. ad <lb/>10. igitur X 5. e&longs;t &longs;patium minus vero (1/10). </s></p><p type="main"> |
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| <s>Prærerea diuidatur tempus AF in 16. partes æquales AB; haud dubiè <pb xlink:href="026/01/134.jpg" pagenum="102"/>8 primis acquiritur &longs;patium YS æquale GH; quod debet diuidi in &longs;pa­<lb/>tiola 36, quæ re&longs;poudent 8. temporibus, &longs;eu terminis huius progre&longs;&longs;io­<lb/>nis, quibus æqualia &longs;unt 144. in GL, cuius YS e&longs;t 1/4, &longs;ed &longs;i in 8. primis <lb/>acquiruntur 36. in 8. vltimis acquirentur 100. igitur S 6. e&longs;t 100. igitur <lb/>Y6. e&longs;t 136. igitur e&longs;t ad GL vt 136. ad 144.&longs;eu 17.ad 18.igitur Y6.e&longs;t <lb/>&longs;patium totale minus vero (1/18). </s></p><p type="main"> | <s>Præterea diuidatur tempus AF in 16. partes æquales AB; haud dubiè <pb xlink:href="026/01/134.jpg" pagenum="102"/>8 primis acquiritur &longs;patium YS æquale GH; quod debet diuidi in &longs;pa­<lb/>tiola 36, quæ re&longs;pondent 8. temporibus, &longs;eu terminis huius progre&longs;&longs;io­<lb/>nis, quibus æqualia &longs;unt 144. in GL, cuius YS e&longs;t 1/4, &longs;ed &longs;i in 8. primis <lb/>acquiruntur 36. in 8. vltimis acquirentur 100. igitur S 6. e&longs;t 100. igitur <lb/>Y6. e&longs;t 136. igitur e&longs;t ad GL vt 136. ad 144.&longs;eu 17.ad 18.igitur Y6.e&longs;t <lb/>&longs;patium totale minus vero (1/18). </s></p><p type="main"> |
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| <s>Deinde diuidatur adhuc tempus AF in partes 32. æquales, 16. pri­<lb/>mis acquiritur ZR æquale GH, quod debet diuidi in &longs;patiola 136.quæ <lb/>re&longs;pondent 16. temporibus quibus æqualia &longs;unt 544. in tota GL, cuius <lb/>ZR e&longs;t 1/4 &longs;ed &longs;i in 16. primis temporibus acquiruntur 136. in vltimis <lb/>16. acquiruntur 392. igitur R 7. e&longs;t 392. & ZR 136. igitur Z 7.528. <lb/>igitur Z 7. e&longs;t ad GL, vt 528. ad 544. &longs;eu vt 33. ad 34. igitur Z 7 e&longs;t <lb/>&longs;patium minus verò (1/34) </s></p><p type="main"> | <s>Deinde diuidatur adhuc tempus AF in partes 32. æquales, 16. pri­<lb/>mis acquiritur ZR æquale GH, quod debet diuidi in &longs;patiola 136.quæ <lb/>re&longs;pondent 16. temporibus quibus æqualia &longs;unt 544. in tota GL, cuius <lb/>ZR e&longs;t 1/4 &longs;ed &longs;i in 16. primis temporibus acquiruntur 136. in vltimis <lb/>16. acquiruntur 392. igitur R 7. e&longs;t 392. & ZR 136. igitur Z 7.528. <lb/>igitur Z 7. e&longs;t ad GL, vt 528. ad 544. &longs;eu vt 33. ad 34. igitur Z 7 e&longs;t <lb/>&longs;patium minus verò (1/34) </s></p><p type="main"> |
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| <s>Præterea &longs;i diai­<lb/>datur velocitas EF, & eius &longs;ubdupla ducatur in tempus AE; habebitur <lb/>rectangulum æquale triangulo AFE, vt con&longs;tat. </s> | <s>Præterea &longs;i diai­<lb/>datur velocitas EF, & eius &longs;ubdupla ducatur in tempus AE; habebitur <lb/>rectangulum æquale triangulo AFE, vt con&longs;tat. </s> |
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| <s>Re&longs;pondeo facilè ex di­<lb/>ctis, hoc ip&longs;um etiam ex no&longs;tra hypothe&longs;i proxime &longs;equi; &longs;int enim duo <lb/>in&longs;tantia; haud dubie &longs;i non cre&longs;cit velocitas, &longs;ecundo in&longs;tanti æquale <lb/>&longs;patium percurretur; &longs;i vero &longs;ecundo in&longs;tanti cre&longs;cat, percurrentur illo <lb/>motu 3.&longs;patia; & cùm velocitas <expan abbr="&longs;ecũdi">&longs;ecundi</expan> <expan abbr="in&longs;tãtis">in&longs;tantis</expan> &longs;it dupla velocitatis primi <lb/>in&longs;tantis, primo in&longs;tanti &longs;it 1.gradus v.g. <!-- REMOVE S-->&longs;ecundo crunt 2. gradus; igi­<lb/>tur moueatur per duo in&longs;tantia motu æquabili veloci vt 2. percurrentur <lb/>4. &longs;patia; igitur totum &longs;patium, quod percurritur motu veloci vt 2. per <lb/>2.in&longs;tantia e&longs;t ad totum &longs;patium, quod percurritur æquali tempore mo-<pb xlink:href="026/01/140.jpg" pagenum="108"/>tu naturaliter accelerato vt 4. ad 3. igitur continet illud 1. (11/3); &longs;i verò <lb/>&longs;int 3. in&longs;tantis continet illud, 1/2; &longs;i 4. continet 1. 3/5, &longs;i 5. continet 1.2/3 <lb/>&longs;i 5. continet 1 2/3. &longs;i 6. continet 1 5/7. &longs;i 7. continet 1 3/4. &longs;i 8. continet <lb/>1 7/9. &longs;i 9. continet 1 (4/11). &longs;i 10. continet 1 9/5 &longs;ic quo plura crunt in&longs;tantia <lb/>accedet propiùs ad rationem duplam, nunquam tamen ad illam perue­<lb/>niet. </s> | <s>Re&longs;pondeo facilè ex di­<lb/>ctis, hoc ip&longs;um etiam ex no&longs;tra hypothe&longs;i proxime &longs;equi; &longs;int enim duo <lb/>in&longs;tantia; haud dubie &longs;i non cre&longs;cit velocitas, &longs;ecundo in&longs;tanti æquale <lb/>&longs;patium percurretur; &longs;i vero &longs;ecundo in&longs;tanti cre&longs;cat, percurrentur illo <lb/>motu 3.&longs;patia; & cùm velocitas <expan abbr="&longs;ecũdi">&longs;ecundi</expan> <expan abbr="in&longs;tãtis">in&longs;tantis</expan> &longs;it dupla velocitatis primi <lb/>in&longs;tantis, primo in&longs;tanti &longs;it 1.gradus v.g. <!-- REMOVE S-->&longs;ecundo erunt 2. gradus; igi­<lb/>tur moueatur per duo in&longs;tantia motu æquabili veloci vt 2. percurrentur <lb/>4. &longs;patia; igitur totum &longs;patium, quod percurritur motu veloci vt 2. per <lb/>2.in&longs;tantia e&longs;t ad totum &longs;patium, quod percurritur æquali tempore mo-<pb xlink:href="026/01/140.jpg" pagenum="108"/>tu naturaliter accelerato vt 4. ad 3. igitur continet illud 1. (11/3); &longs;i verò <lb/>&longs;int 3. in&longs;tantis continet illud, 1/2; &longs;i 4. continet 1. 3/5, &longs;i 5. continet 1.2/3 <lb/>&longs;i 5. continet 1 2/3. &longs;i 6. continet 1 5/7. &longs;i 7. continet 1 3/4. &longs;i 8. continet <lb/>1 7/9. &longs;i 9. continet 1 (4/11). &longs;i 10. continet 1 9/5 &longs;ic quo plura erunt in&longs;tantia <lb/>accedet propiùs ad rationem duplam, nunquam tamen ad illam perue­<lb/>niet. </s> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Etiam &longs;i non &longs;int infiniti tarditatis gradus, vt con&longs;tat ex dictis, &longs;ed fi­<lb/>niti; in ordine tamen ad praxim eodem modo &longs;e habent, ac &longs;i e&longs;&longs;ent in­<lb/>&longs;initi; quia non pote&longs;t di&longs;tingui primus, & minimus ab omnibus <lb/>al is. </s></p><p type="main"> | <s>Etiam &longs;i non &longs;int infiniti tarditatis gradus, vt con&longs;tat ex dictis, &longs;ed fi­<lb/>niti; in ordine tamen ad praxim eodem modo &longs;e habent, ac &longs;i e&longs;&longs;ent in­<lb/>finiti; quia non pote&longs;t di&longs;tingui primus, & minimus ab omnibus <lb/>aliis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Licèt hypothe&longs;is Galilei &longs;it fal&longs;a in hypothe&longs;i in&longs;tantium finitorum; <lb/>nam &longs;ingulis in&longs;tantibus noua fit velocitatis acce&longs;&longs;io; phy&longs;icè tamen lo­<lb/>quendo eodem modo &longs;e habet, ac &longs;i e&longs;&longs;et vera; quia cum non po&longs;&longs;it pro­<lb/>bari, ni&longs;i in partibus temporis &longs;en&longs;ibilibus; certà, cùm quælibet pars <lb/>&longs;en&longs;ibilis innumera ferè in&longs;tantia contineat, in quibus fit progre&longs;&longs;io; <lb/>differentia vtriu&longs;que &longs;en&longs;ibilis e&longs;&longs;e non pote&longs;t; igitur linea denticulata <lb/> eodem modo &longs;e habet phy&longs;icè, hoc e&longs;t &longs;en&longs;ibiliter, ac &longs;i e&longs;&longs;et recta; &longs;ic­<lb/>que progre&longs;&longs;io arithmetica in multis terminis-reducitur &longs;en&longs;ibiliter ad <lb/>Geometriam in paucioribus terminis; immò in communi illa &longs;ententia. </s> | <s>Licèt hypothe&longs;is Galilei &longs;it fal&longs;a in hypothe&longs;i in&longs;tantium finitorum; <lb/>nam &longs;ingulis in&longs;tantibus noua fit velocitatis acce&longs;&longs;io; phy&longs;icè tamen lo­<lb/>quendo eodem modo &longs;e habet, ac &longs;i e&longs;&longs;et vera; quia cum non po&longs;&longs;it pro­<lb/>bari, ni&longs;i in partibus temporis &longs;en&longs;ibilibus; certà, cùm quælibet pars <lb/>&longs;en&longs;ibilis innumera ferè in&longs;tantia contineat, in quibus fit progre&longs;&longs;io; <lb/>differentia vtriu&longs;que &longs;en&longs;ibilis e&longs;&longs;e non pote&longs;t; igitur linea denticulata <lb/> eodem modo &longs;e habet phy&longs;icè, hoc e&longs;t &longs;en&longs;ibiliter, ac &longs;i e&longs;&longs;et recta; &longs;ic­<lb/>que progre&longs;&longs;io arithmetica in multis terminis reducitur &longs;en&longs;ibiliter ad <lb/>Geometriam in paucioribus terminis; immò in communi illa &longs;ententia. </s> |
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| <s><lb/>in qua dicitur tempus con&longs;tare ex partibus actu infinitis, progre&longs;&longs;io Ga­<lb/>lilei tantùm locum habere pete&longs;t; igitur hæc e&longs;to clauis huius difficul­<lb/>tatis; progre&longs;&longs;io &longs;implex principium phy&longs;icum habet, non experimen­<lb/>tum; progre&longs;&longs;io numerorum imparium experimentum non principium; <lb/>vtramque cum principio & experimento componimus; prima enim &longs;i. </s> | <s><lb/>in qua dicitur tempus con&longs;tare ex partibus actu infinitis, progre&longs;&longs;io Ga­<lb/>lilei tantùm locum habere pete&longs;t; igitur hæc e&longs;to clauis huius difficul­<lb/>tatis; progre&longs;&longs;io &longs;implex principium phy&longs;icum habet, non experimen­<lb/>tum; progre&longs;&longs;io numerorum imparium experimentum non principium; <lb/>vtramque cum principio & experimento componimus; prima enim &longs;i. </s> |
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| <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Corollarium<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Similiter cognito &longs;patio quod percurrit 4. &longs;ecundis minutis, cogno­<lb/>&longs;ues &longs;patium, quod percurret 2. vel 1. v.g. <!-- REMOVE S-->percurrit 4. &longs;ecundis 192. pe-<pb xlink:href="026/01/141.jpg" pagenum="109"/>des; accipe 9.4. id e&longs;t 16. & per 16. diuide 192. quotíens dabit 12. pro <lb/>primo &longs;ecundo: accipe 9.2. id e&longs;t, 4. & diuide 192. per 4.quotiens dabit <lb/>48. pro duobus minutis, atque ita deinceps. </s> | <s>Similiter cognito &longs;patio quod percurrit 4. &longs;ecundis minutis, cogno­<lb/>&longs;ces &longs;patium, quod percurret 2. vel 1. v.g. <!-- REMOVE S-->percurrit 4. &longs;ecundis 192. pe-<pb xlink:href="026/01/141.jpg" pagenum="109"/>des; accipe 9.4. id e&longs;t 16. & per 16. diuide 192. quotíens dabit 12. pro <lb/>primo &longs;ecundo: accipe 9.2. id e&longs;t, 4. & diuide 192. per 4.quotiens dabit <lb/>48. pro duobus minutis, atque ita deinceps. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Tertia objectio. </s> | <s>Tertia objectio. </s> |
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| <s>Sed inquies, igitur &longs;ecundo tempore æquali primo <lb/>acquiruntur 2.gradus velocitatis, vel impetus; igitur tria &longs;patia &longs;ecun­<lb/>do tempore percurruntur, quod e&longs;t contra hypothe&longs;im; quippc duo gra­<lb/>dus impetus accedunt primo, &longs;imiliter tertio tempore producentur tres <lb/>gradus impetus; qui &longs;i iungantur tribus præcedentibus, erunt 6. Igitur <lb/>percurrentur tertio tempore 6. &longs;patia, & quarto 10.quinto 15. quia &longs;in­<lb/>gulis in&longs;tantibus debet produci impetus; e&longs;t enim cau&longs;a nece&longs;&longs;aria ap­<lb/>plicata. </s></p><p type="main"> | <s>Sed inquies, igitur &longs;ecundo tempore æquali primo <lb/>acquiruntur 2.gradus velocitatis, vel impetus; igitur tria &longs;patia &longs;ecun­<lb/>do tempore percurruntur, quod e&longs;t contra hypothe&longs;im; quippe duo gra­<lb/>dus impetus accedunt primo, &longs;imiliter tertio tempore producentur tres <lb/>gradus impetus; qui &longs;i iungantur tribus præcedentibus, erunt 6. Igitur <lb/>percurrentur tertio tempore 6. &longs;patia, & quarto 10.quinto 15. quia &longs;in­<lb/>gulis in&longs;tantibus debet produci impetus; e&longs;t enim cau&longs;a nece&longs;&longs;aria ap­<lb/>plicata. </s></p><p type="main"> |
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| <s>Re&longs;pondço, equidem eo in&longs;tanti, quo percurritur &longs;patium BD, pro­<lb/>duci aliquid impetus, & aliquid eo in&longs;tanti, quo percurritur &longs;patium <lb/>DC; ita vt tamen totus ille impetus, qui producitur his duobus in&longs;tan­<lb/>tibus, &longs;it æqualis illi, qui producitur primo in&longs;tanti, quo &longs;cilicet percurri­<lb/>tur &longs;patium AB; quia duo illa in&longs;tantia &longs;unul &longs;umpta faciunt tempus <lb/>æquale primo in&longs;tanti; atqui temporibus æqualibus eadem cau&longs;a nece&longs;­<lb/>&longs;aria non impedita æqualem effectum producit per Ax.3.hinc vides &longs;in­<lb/>gulis in&longs;tantibus eadem proportione decre&longs;cere impetum in perfectio­<lb/>ne, qua tempus e&longs;t breuius, &longs;eu velocior motus; &longs;ed de hoc infrà. </s></p><p type="main"> | <s>Re&longs;pond&ecedil;o, equidem eo in&longs;tanti, quo percurritur &longs;patium BD, pro­<lb/>duci aliquid impetus, & aliquid eo in&longs;tanti, quo percurritur &longs;patium <lb/>DC; ita vt tamen totus ille impetus, qui producitur his duobus in&longs;tan­<lb/>tibus, &longs;it æqualis illi, qui producitur primo in&longs;tanti, quo &longs;cilicet percurri­<lb/>tur &longs;patium AB; quia duo illa in&longs;tantia &longs;imul &longs;umpta faciunt tempus <lb/>æquale primo in&longs;tanti; atqui temporibus æqualibus eadem cau&longs;a nece&longs;­<lb/>&longs;aria non impedita æqualem effectum producit per Ax.3.hinc vides &longs;in­<lb/>gulis in&longs;tantibus eadem proportione decre&longs;cere impetum in perfectio­<lb/>ne, qua tempus e&longs;t breuius, &longs;eu velocior motus; &longs;ed de hoc infrà. </s></p><p type="main"> |
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| <s>Quarta objectio; &longs;i impetus &longs;ingulis in&longs;tuitibus cre&longs;ceret, vel intende­<lb/>retur, augeretur grauitatio: quippe &longs;i grauitas primo in&longs;tanti producat <lb/>vnum gradum impetus; &longs;ecundo æqualem producet, & rertio, atque ita <lb/>deinceps, quod e&longs;&longs;et ab&longs;urdum; alioqui minima atomus quodlibet cor­<lb/>pus graue adæquaret, quod e&longs;t ab&longs;urdum. </s></p><p type="main"> | <s>Quarta objectio; &longs;i impetus &longs;ingulis in&longs;titutibus cre&longs;ceret, vel intende­<lb/>retur, augeretur grauitatio: quippe &longs;i grauitas primo in&longs;tanti producat <lb/>vnum gradum impetus; &longs;ecundo æqualem producet, & tertio, atque ita <lb/>deinceps, quod e&longs;&longs;et ab&longs;urdum; alioqui minima atomus quodlibet cor­<lb/>pus graue adæquaret, quod e&longs;t ab&longs;urdum. </s></p><p type="main"> |
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| <s>Re&longs;pondeo nunquam impetum intendi, ni&longs;i &longs;it motus, qui e&longs;t illius fi­<lb/>nis; alioquin fru&longs;tra e&longs;&longs;et per plura in&longs;tantia; igitur de&longs;trui deberet; nec <lb/>dicas impetum naturalem etiam fru&longs;trà e&longs;&longs;e &longs;ine motu; quia cum mo­<lb/>tus non &longs;it eius finis adæquatus; non mirum e&longs;t &longs;i po&longs;&longs;it e&longs;&longs;e &longs;ine motu; <lb/>atqui iam diximus &longs;uprà habere duos fines, quorum alterum &longs;emper ha-<pb xlink:href="026/01/143.jpg" pagenum="111"/>bet; primus e&longs;t grauitatio, &longs;eu ni&longs;us ver&longs;us centrum; &longs;ecundus motus <lb/>deor&longs;um; cùm tamen impetus addititius motum tantùm pro fine habeat; <lb/>igitur &longs;i impeditur totus motus, non producitur hic impetus. </s></p><p type="main"> | <s>Re&longs;pondeo nunquam impetum intendi, ni&longs;i &longs;it motus, qui e&longs;t illius fi­<lb/>nis; alioquin fru&longs;tra e&longs;&longs;et per plura in&longs;tantia; igitur de&longs;trui deberet; nec <lb/>dicas impetum naturalem etiam fru&longs;trà e&longs;&longs;e &longs;ine motu; quia cum mo­<lb/>tus non &longs;it eius finis adæquatus; non mirum e&longs;t &longs;i po&longs;&longs;it e&longs;&longs;e &longs;ine motu; <lb/>atqui iam diximus &longs;uprà habere duos fines, quorum alterum &longs;emper ha-<pb xlink:href="026/01/143.jpg" pagenum="111"/>bet; primus e&longs;t grauitatio, &longs;eu ni&longs;us ver&longs;us centrum; &longs;ecundus motus <lb/>deor&longs;um; cùm tamen impetus additivius motum tantùm pro fine habeat; <lb/>igitur &longs;i impeditur totus motus, non producitur hic impetus. </s></p><p type="main"> |
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| <s>Quinta objectio; &longs;i impetum &longs;uum intendit corpus graue; &longs;imiliter <lb/>Ignis diceretur intendere calorem; Sol lucem, &c. </s> | <s>Quinta objectio; &longs;i impetum &longs;uum intendit corpus graue; &longs;imiliter <lb/>Ignis diceretur intendere calorem; Sol lucem, &c. </s> |
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| <s>Re&longs;pondeo primò, non po&longs;&longs;e dari infinitam il­<lb/>lam di&longs;tantiam. </s> | <s>Re&longs;pondeo primò, non po&longs;&longs;e dari infinitam il­<lb/>lam di&longs;tantiam. </s> |
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| <s>Secundò etiani&longs;i daretur lapis, ex ea non caderet; fru&longs;trà <lb/>enim e&longs;&longs;et ille motus: Tertiò, &longs;i daretur motus infinitus, haud dubiè e&longs;&longs;et <lb/>æquabilis; qualis e&longs;t motus circularis corporum cœle&longs;tium; at verò <lb/>motus naturalis deor&longs;um corporum grauium debet e&longs;&longs;e acceleratus ne <lb/>vel de&longs;cenderent tardiùs, &longs;i cum primo tantùm velocitatis gradu de&longs;cen­<lb/>derent; vel &longs;u&longs;tineri vix po&longs;&longs;ent, &longs;i impetum innatum intontiorem habe­<lb/>rent; vtrum verò &longs;emper intendatur, & ex quacumque altitudine cadat <lb/>corpus graue, videbimus infrà. </s></p><p type="main"> | <s>Secundò etiam&longs;i daretur lapis, ex ea non caderet; fru&longs;trà <lb/>enim e&longs;&longs;et ille motus: Tertiò, &longs;i daretur motus infinitus, haud dubiè e&longs;&longs;et <lb/>æquabilis; qualis e&longs;t motus circularis corporum cœle&longs;tium; at verò <lb/>motus naturalis deor&longs;um corporum grauium debet e&longs;&longs;e acceleratus ne <lb/>vel de&longs;cenderent tardiùs, &longs;i cum primo tantùm velocitatis gradu de&longs;cen­<lb/>derent; vel &longs;u&longs;tineri vix po&longs;&longs;ent, &longs;i impetum innatum intentiorem habe­<lb/>rent; vtrum verò &longs;emper intendatur, & ex quacumque altitudine cadat <lb/>corpus graue, videbimus infrà. </s></p><p type="main"> |
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| <s>Ex dictis hactenus facilè refelluntur aliæ &longs;ententiæ de proportione <lb/>motus naturaliter accelerati. </s></p><p type="main"> | <s>Ex dictis hactenus facilè refelluntur aliæ &longs;ententiæ de proportione <lb/>motus naturaliter accelerati. </s></p><p type="main"> |
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| <s>Tertiò reiicitur illa quoque &longs;ententia, quæ proportionem lineæ &longs;ectæ <lb/>in mediam, & extremam rationem huic lineæ tribuit, quam ferè in his <lb/>numeris vides 1.2.3.5.8, 13. 21. 34. 55. quæ &longs;ub finem etiam longi&longs;&longs;imè <lb/>aberrat, vt videre e&longs;t, quare ii&longs;dem rationibus impugnatur, quibus iam <lb/>aliam impugnauimus. </s></p><p type="main"> | <s>Tertiò reiicitur illa quoque &longs;ententia, quæ proportionem lineæ &longs;ectæ <lb/>in mediam, & extremam rationem huic lineæ tribuit, quam ferè in his <lb/>numeris vides 1.2.3.5.8, 13. 21. 34. 55. quæ &longs;ub finem etiam longi&longs;&longs;imè <lb/>aberrat, vt videre e&longs;t, quare ii&longs;dem rationibus impugnatur, quibus iam <lb/>aliam impugnauimus. </s></p><p type="main"> |
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| <s>Scio e&longs;&longs;e alias multas rationes, quibus aliqui recentiores motus natu­<lb/>ralis accelerationem explicare nituntur, &longs;ed iam &longs;uprà &longs;atis &longs;uperque re­<lb/>iectæ fuerunt, vel profectò eæ &longs;unt, quæ ne quidem inter fabulo&longs;a poë­<lb/>tarum commenta locum aliquem habere po&longs;&longs;int: Et verò ni&longs;i me ani­<lb/>mus fallit in re clari&longs;&longs;ima, rationem huius effectus ex communibus <lb/>principiis deductam cum ip&longs;is etiam experimentis con&longs;entire hactenus <lb/>ita demon&longs;trauimus, vt iam vix vllus dubitationi locus relinquatur; &longs;ed <lb/>interrruptam Theorematum &longs;eriem tandem repetimus. </s></p><p type="main"> | <s>Scio e&longs;&longs;e alias multas rationes, quibus aliqui recentiores motus natu­<lb/>ralis accelerationem explicare nituntur, &longs;ed iam &longs;uprà &longs;atis &longs;uperque re­<lb/>iectæ fuerunt, vel profectò eæ &longs;unt, quæ ne quidem inter fabulo&longs;a poë­<lb/>tarum commenta locum aliquem habere po&longs;&longs;int: Et verò ni&longs;i me ani­<lb/>mus fallit in re clari&longs;&longs;ima, rationem huius effectus ex communibus <lb/>principiis deductam cum ip&longs;is etiam experimentis con&longs;entire hactenus <lb/>ita demon&longs;trauimus, vt iam vix vllus dubitationi locus relinquatur; &longs;ed <lb/>interruptam Theorematum &longs;eriem tandem repetimus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main"> |
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| <s>faciant &longs;emper tempora æqualia, quia temporibus æqualibus æ­<lb/>qualia acquiruntur velocitatis momenta? </s> | <s>faciant &longs;emper tempora æqualia, quia temporibus æqualibus æ­<lb/>qualia acquiruntur velocitatis momenta? </s> |
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| <s>igitur &longs;i primo in&longs;tanti per­<lb/>curritur vnum &longs;patium; &longs;ecundo tempore æquali percurruntur duo &longs;pa­<lb/>tia æqualia primo, & tertio, tria; atque deinceps; &longs;ed vt &longs;uprà dictum e&longs;t <lb/>in re&longs;pon&longs;.ad obiect primam, vno, & <expan abbr="cod&etilde;">codem</expan> in&longs;tanti non pote&longs;t idem cor­<lb/>pus percurrere duo &longs;patia, ne &longs;imul e&longs;&longs;et in duobus locis; igitur &longs;ingula <lb/>&longs;patia re&longs;pondent &longs;ingulis in&longs;tantibus licèt minoribus; &longs;ed &longs;ecundo tem­<lb/>pore æquali primo in&longs;tanti percurruntur duo &longs;patia æqualia primo &longs;pa­<lb/>tio; igitur &longs;ecundum, & tertium in&longs;tans debent &longs;imul &longs;umpta adæquare <pb xlink:href="026/01/145.jpg" pagenum="113"/>primum, &longs;ed non &longs;unt æqualia, vt con&longs;tat; alioquin duobus illis in&longs;tanti <lb/>bus motus e&longs;&longs;et æquabilis; igitur &longs;ecundum e&longs;t maius tertio, ita vt tamen <lb/>ex vtroque tempus fiat æquale primo in&longs;tanti. </s></p><p type="main"> | <s>igitur &longs;i primo in&longs;tanti per­<lb/>curritur vnum &longs;patium; &longs;ecundo tempore æquali percurruntur duo &longs;pa­<lb/>tia æqualia primo, & tertio, tria; atque deinceps; &longs;ed vt &longs;uprà dictum e&longs;t <lb/>in re&longs;pon&longs;. ad obiect. primam, vno, & <expan abbr="eod&etilde;">eodem</expan> in&longs;tanti non pote&longs;t idem cor­<lb/>pus percurrere duo &longs;patia, ne &longs;imul e&longs;&longs;et in duobus locis; igitur &longs;ingula <lb/>&longs;patia re&longs;pondent &longs;ingulis in&longs;tantibus licèt minoribus; &longs;ed &longs;ecundo tem­<lb/>pore æquali primo in&longs;tanti percurruntur duo &longs;patia æqualia primo &longs;pa­<lb/>tio; igitur &longs;ecundum, & tertium in&longs;tans debent &longs;imul &longs;umpta adæquare <pb xlink:href="026/01/145.jpg" pagenum="113"/>primum, &longs;ed non &longs;unt æqualia, vt con&longs;tat; alioquin duobus illis in&longs;tanti <lb/>bus motus e&longs;&longs;et æquabilis; igitur &longs;ecundum e&longs;t maius tertio, ita vt tamen <lb/>ex vtroque tempus fiat æquale primo in&longs;tanti. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Non decre&longs;cunt illa in&longs;tantia &longs;ecundum lineam &longs;extam in extremam & <lb/>mediam rationrm propagatam; ita vt primum &longs;it ad &longs;ecundum, vt &longs;ecundum <lb/>ad tertium, tertium ad quartum, quartum ad quintum at que ita deinceps<emph.end type="italics"/>; <lb/>&longs;it enim aliqua &longs;eries numerorum, qui aliquo modo accedant ad prædi­<lb/>ctam proportionem 1.2.3.5.8.13.21.34.55. &longs;itque primum in&longs;tans vlti­<lb/>mus numerus 55. &longs;ecundum 34.tertium 21. atque ita deinceps: Equidem <lb/>&longs;ecundum, & tertium adæquant primum; at verò quartum, quintum, <lb/>&longs;extum nullo modo adæquant; immò ne quidem eius &longs;ubduplum, & <lb/>multò minus 3. alij addito primo: immò &longs;i linea data duodecies propor­<lb/>tionaliter diuidatur, vltimum &longs;egmentum vix e&longs;&longs;et &longs;ubcentuplum primi, <lb/>vt con&longs;tar; igitur reiici debet hæc propo&longs;itio. </s></p><p type="main"> | <s><emph type="italics"/>Non decre&longs;cunt illa in&longs;tantia &longs;ecundum lineam &longs;extam in extremam & <lb/>mediam rationem propagatam; ita vt primum &longs;it ad &longs;ecundum, vt &longs;ecundum <lb/>ad tertium, tertium ad quartum, quartum ad quintum at que ita deinceps<emph.end type="italics"/>; <lb/>&longs;it enim aliqua &longs;eries numerorum, qui aliquo modo accedant ad prædi­<lb/>ctam proportionem 1.2.3.5.8.13.21.34.55. &longs;itque primum in&longs;tans vlti­<lb/>mus numerus 55. &longs;ecundum 34.tertium 21. atque ita deinceps: Equidem <lb/>&longs;ecundum, & tertium adæquant primum; at verò quartum, quintum, <lb/>&longs;extum nullo modo adæquant; immò ne quidem eius &longs;ubduplum, & <lb/>multò minus 3. alij addito primo: immò &longs;i linea data duodecies propor­<lb/>tionaliter diuidatur, vltimum &longs;egmentum vix e&longs;&longs;et &longs;ubcentuplum primi, <lb/>vt con&longs;tat; igitur reiici debet hæc propo&longs;itio. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main"> |
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| <s>item 4. alij, qui &longs;equuntur, item 5. item 6. &c. </s> | <s>item 4. alij, qui &longs;equuntur, item 5. item 6. &c. </s> |
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| <s><lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->pote&longs;t dari linea AG con&longs;tans tribus partibus æqualibus, &longs;cilicet <lb/>AB, BC, CG, & &longs;ecunda BC duabus BD maiore, & DC minore, & ter­<lb/>tia tribus prima CE minore ED, &longs;ed maiore EF, &longs;ecunda EF maiore F <lb/>G, atque ita deinceps; addi pote&longs;t quartum &longs;egmentum æquale AB; quod <lb/>&longs;ubdiuidetur in 4. partes, quarum prima &longs;it maior &longs;ecunda, & hçc tertia <lb/>& hæc quarta, & omnes minores FG; ita autem &longs;uperant primæ &longs;equen­<lb/>tes, vt differentia primæ, & &longs;ecundæ &longs;it maior differentia &longs;ecundæ, & <pb xlink:href="026/01/146.jpg" pagenum="114"/>tertiæ, & hæc maior differentia tertiæ, & quartæ; atque ita deinceps, nec <lb/>aliter res e&longs;&longs;e pote&longs;t. </s> | <s><lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->pote&longs;t dari linea AG con&longs;tans tribus partibus æqualibus, &longs;cilicet <lb/>AB, BC, CG, & &longs;ecunda BC duabus BD maiore, & DC minore, & ter­<lb/>tia tribus prima CE minore ED, &longs;ed maiore EF, &longs;ecunda EF maiore F <lb/>G, atque ita deinceps; addi pote&longs;t quartum &longs;egmentum æquale AB; quod <lb/>&longs;ubdiuidetur in 4. partes, quarum prima &longs;it maior &longs;ecunda, & <expan abbr="h&ecedil;c">haec</expan> tertia <lb/>& hæc quarta, & omnes minores FG; ita autem &longs;uperant primæ &longs;equen­<lb/>tes, vt differentia primæ, & &longs;ecundæ &longs;it maior differentia &longs;ecundæ, & <pb xlink:href="026/01/146.jpg" pagenum="114"/>tertiæ, & hæc maior differentia tertiæ, & quartæ; atque ita deinceps, nec <lb/>aliter res e&longs;&longs;e pote&longs;t. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc qua preportione decre&longs;cunt instantia, decre&longs;cit etiam per&longs;ectio <lb/>impetus<emph.end type="italics"/>; quia temporibus æqualibus eadem cau&longs;a nece&longs;&longs;aria æqualem ef­<lb/>fectum producit per Ax. tertium igitur inæqualem inæqualibus, per Ax. <!-- REMOVE S--><lb/>13. num.4. igitur minorem minore tempore; igitur minorem in eadem <lb/>proportione, in qua tempus e&longs;t; igitur qua proportione, &c. </s> | <s><emph type="italics"/>Hinc qua proportione decre&longs;cunt instantia, decre&longs;cit etiam perfectio <lb/>impetus<emph.end type="italics"/>; quia temporibus æqualibus eadem cau&longs;a nece&longs;&longs;aria æqualem ef­<lb/>fectum producit per Ax. tertium igitur inæqualem inæqualibus, per Ax. <!-- REMOVE S--><lb/>13. num.4. igitur minorem minore tempore; igitur minorem in eadem <lb/>proportione, in qua tempus e&longs;t; igitur qua proportione, &c. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc vides quâm &longs;it nece&longs;&longs;aria illa diuer &longs;a perfestio impetus, quam indi­<lb/>cauimus lib.<emph.end type="italics"/>1. hinc impetus productus &longs;ecundo, & tertio in&longs;tanti adæ­<lb/>quat impetum productum primo, quem etiam adæquat productus quar­<lb/>to, quinto, &longs;exto, item productus &longs;eptimo, octauo, nono; decimo, atque ita <lb/>deinceps; hinc e&longs;t eadem differentia impetuum, quæ <expan abbr="in&longs;tãtium">in&longs;tantium</expan>; hinc &longs;in­<lb/>gulis &longs;patiis æqualibus primo &longs;patio, quod percurritur primo in&longs;tanti; <lb/>re&longs;pondent &longs;ingula in&longs;tantia, & &longs;ingulis in&longs;tantibus &longs;inguli, & &longs;ingulares <lb/>impetus; hinc non e&longs;t quod primo in&longs;tanti dicantur produci plura pun­<lb/>cta impetus in eodem puncto corporis grauis; &longs;ed vnicum tantùm pun­<lb/>ctum talis perfectionis &longs;cilicet phy&longs;icum; cur enim potius duo puncta, <lb/>quam tria? </s> | <s><emph type="italics"/>Hinc vides quâm &longs;it nece&longs;&longs;aria illa diuer&longs;a perfectio impetus, quam indi­<lb/>cauimus lib.<emph.end type="italics"/>1. hinc impetus productus &longs;ecundo, & tertio in&longs;tanti adæ­<lb/>quat impetum productum primo, quem etiam adæquat productus quar­<lb/>to, quinto, &longs;exto, item productus &longs;eptimo, octauo, nono; decimo, atque ita <lb/>deinceps; hinc e&longs;t eadem differentia impetuum, quæ <expan abbr="in&longs;tãtium">in&longs;tantium</expan>; hinc &longs;in­<lb/>gulis &longs;patiis æqualibus primo &longs;patio, quod percurritur primo in&longs;tanti; <lb/>re&longs;pondent &longs;ingula in&longs;tantia, & &longs;ingulis in&longs;tantibus &longs;inguli, & &longs;ingulares <lb/>impetus; hinc non e&longs;t quod primo in&longs;tanti dicantur produci plura pun­<lb/>cta impetus in eodem puncto corporis grauis; &longs;ed vnicum tantùm pun­<lb/>ctum talis perfectionis &longs;cilicet phy&longs;icum; cur enim potius duo puncta, <lb/>quam tria? </s> |
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| <s>&longs;ed quod vnum e&longs;t determinatum e&longs;t per Ax. 5. lib. | <s>&longs;ed quod vnum e&longs;t determinatum e&longs;t per Ax. 5. lib. |
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| 1. hinc <lb/>optima ratio cur potius tali in&longs;tanti producatur impetus talis perfectie­<lb/>nis quàm alterius? </s> | 1. hinc <lb/>optima ratio cur potius tali in&longs;tanti producatur impetus talis perfectio­<lb/>nis quàm alterius? </s> |
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| <s>quippe perfectio impetus &longs;equitur perfectionem in­<lb/>&longs;tantis quo producitur; hinc dicendum videtur omnia puncta impetus <lb/>e&longs;&longs;e diuer&longs;æ perfectionis, vel heterogenea; vt vulgò aiunt Philo&longs;ophi; <lb/>cuius rationem demon&longs;tratiuam afferemus lib. | <s>quippe perfectio impetus &longs;equitur perfectionem in­<lb/>&longs;tantis quo producitur; hinc dicendum videtur omnia puncta impetus <lb/>e&longs;&longs;e diuer&longs;æ perfectionis, vel heterogenea; vt vulgò aiunt Philo&longs;ophi; <lb/>cuius rationem demon&longs;tratiuam afferemus lib. |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si a&longs;&longs;umantur &longs;patia &longs;en&longs;ibilia æqualia, tempora &longs;unt ferè in ratione &longs;ubdu­<lb/>plicata &longs;patiorum<emph.end type="italics"/>; crun enim &longs;patia &longs;int vt quadrata <expan abbr="t&etilde;porum">temporum</expan> &longs;en&longs;ibiliter; <lb/>certè tempora &longs;unt, vt radices i&longs;torum quadtatorum, &longs;cilicet &longs;patiorum; <lb/>&longs;int enim quæcunque &longs;patia æqualia in linea AF; &longs;intque &longs;patia AC 4. <lb/>AE 16. radix quadr.4. e&longs;t 2.16. verò 4. igitur tempora &longs;unt vt 4.2.&longs;i ve­<lb/>rò accipiatur primum &longs;patium, quod vno tempore percurritur; tempus <lb/>quo percurruntur duo &longs;patia æqualia primum e&longs;t v.2.quo percurruntur <lb/>tria v.3.quo percurruntur 4.&longs;patia, 2. atque ita deinceps; igitur in praxi <lb/>quæ tantùm fit in &longs;patiis &longs;en&longs;ibilibus hæc progre&longs;&longs;io adhibenda e&longs;t, il­<lb/>lamque deinceps, &longs;i quando opus e&longs;t, adhibebimus. </s></p><p type="main"> | <s><emph type="italics"/>Si a&longs;&longs;umantur &longs;patia &longs;en&longs;ibilia æqualia, tempora &longs;unt ferè in ratione &longs;ubdu­<lb/>plicata &longs;patiorum<emph.end type="italics"/>; crun enim &longs;patia &longs;int vt quadrata <expan abbr="t&etilde;porum">temporum</expan> &longs;en&longs;ibiliter; <lb/>certè tempora &longs;unt, vt radices i&longs;torum quadratorum, &longs;cilicet &longs;patiorum; <lb/>&longs;int enim quæcunque &longs;patia æqualia in linea AF; &longs;intque &longs;patia AC 4. <lb/>AE 16. radix quadr.4. e&longs;t 2.16. verò 4. igitur tempora &longs;unt vt 4.2.&longs;i ve­<lb/>rò accipiatur primum &longs;patium, quod vno tempore percurritur; tempus <lb/>quo percurruntur duo &longs;patia æqualia primum e&longs;t v.2.quo percurruntur <lb/>tria v.3.quo percurruntur 4.&longs;patia, 2. atque ita deinceps; igitur in praxi <lb/>quæ tantùm fit in &longs;patiis &longs;en&longs;ibilibus hæc progre&longs;&longs;io adhibenda e&longs;t, il­<lb/>lamque deinceps, &longs;i quando opus e&longs;t, adhibebimus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 71.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 72.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus naturalis addititius de&longs;truitur<emph.end type="italics"/>; patet experientiâ; quippe pila <lb/>deor&longs;um cadens tandem quie&longs;cit, licèt à terra reflectatur ratione impe­<lb/>dimenti, ex quo re&longs;ultat duplex determinatio, ratione cuius idem im­<lb/>petus &longs;ibi aliquo modo redditur <expan abbr="cõtrarius">contrarius</expan>; &longs;ed de his fusè in primo libro <lb/>à Th.148. ad finem v&longs;que libri: nam reuerâ duæ determinationes op­<lb/>po&longs;itæ pugnant pro rata per Ax. 15.l.1. & quotie&longs;cunque idem impetus <lb/>e&longs;t ad lineas oppo&longs;itas determinatus eodem modo &longs;e habet, ac &longs;i duplex <lb/>e&longs;&longs;et, & quilibet &longs;uæ &longs;ube&longs;&longs;et determinationi; atqui &longs;i duplex e&longs;&longs;et oppo­<lb/>&longs;itus, pugnarent pro rata; igitur tàm pugnant duæ determinationes op­<lb/>po&longs;itæ in codem impetu, quàm duo impetus ad oppo&longs;itas lincas deter­<lb/>minati; igitur impetus naturalis aduentitius de&longs;truitur, &c. </s></p><p type="main"> | <s><emph type="italics"/>Impetus naturalis addititius de&longs;truitur<emph.end type="italics"/>; patet experientiâ; quippe pila <lb/>deor&longs;um cadens tandem quie&longs;cit, licèt à terra reflectatur ratione impe­<lb/>dimenti, ex quo re&longs;ultat duplex determinatio, ratione cuius idem im­<lb/>petus &longs;ibi aliquo modo redditur <expan abbr="cõtrarius">contrarius</expan>; &longs;ed de his fusè in primo libro <lb/>à Th.148. ad finem v&longs;que libri: nam reuerâ duæ determinationes op­<lb/>po&longs;itæ pugnant pro rata per Ax. 15.l.1. & quotie&longs;cunque idem impetus <lb/>e&longs;t ad lineas oppo&longs;itas determinatus eodem modo &longs;e habet, ac &longs;i duplex <lb/>e&longs;&longs;et, & quilibet &longs;uæ &longs;ube&longs;&longs;et determinationi; atqui &longs;i duplex e&longs;&longs;et oppo­<lb/>&longs;itus, pugnarent pro rata; igitur tàm pugnant duæ determinationes op­<lb/>po&longs;itæ in codem impetu, quàm duo impetus ad oppo&longs;itas lineas deter­<lb/>minati; igitur impetus naturalis aduentitius de&longs;truitur, &c. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 73.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 73.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Dices lignum vi extrin&longs;eca in aqua immer&longs;um &longs;ua &longs;ponte a&longs;cendit; <lb/>igitur ille gradus impetus grauitationis de&longs;truitur, & alius producitur; <lb/>hæc quæ&longs;tio ad præ&longs;ens in&longs;titutum non pertinet, &longs;ed ad librum de gra­<lb/>uitate, & leuitate. </s> | <s>Dices lignum vi extrin&longs;eca in aqua immer&longs;um &longs;ua &longs;ponte a&longs;cendit; <lb/>igitur ille gradus impetus grauitationis de&longs;truitur, & alius producitur; <lb/>hæc quæ&longs;tio ad præ&longs;ens in&longs;titutum non pertinet, &longs;ed ad librum de gra­<lb/>uitate, & leuitate. </s> |
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| <s>Igitur breuiter re&longs;pondeo illum impetum nunquam <lb/>de&longs;trui, quandiu mobile grauitat, vel grauitatione &longs;ingulari, (&longs;ic corpus <lb/>grauitat in manum &longs;u&longs;tinentis,) vel grauitatione communi, (&longs;ic lignum <lb/>humori innatans grauitat, non quidem in aquam, at &longs;imul cum aqua;) <lb/>&longs;ed de grauitate, & grauitatione in Tomo de &longs;tatibus corporum &longs;en&longs;ibi-<pb xlink:href="026/01/148.jpg" pagenum="116"/>libus, in quo o&longs;tendemus ideo lignum &longs;ur&longs;um emergere, quia ab aqua <lb/>extenditur, & idco corpora &longs;ur&longs;um ire, quia alia dcor&longs;um eunt. </s></p><p type="main"> | <s>Igitur breuiter re&longs;pondeo illum impetum nunquam <lb/>de&longs;trui, quandiu mobile grauitat, vel grauitatione &longs;ingulari, (&longs;ic corpus <lb/>grauitat in manum &longs;u&longs;tinentis,) vel grauitatione communi, (&longs;ic lignum <lb/>humori innatans grauitat, non quidem in aquam, at &longs;imul cum aqua;) <lb/>&longs;ed de grauitate, & grauitatione in Tomo de &longs;tatibus corporum &longs;en&longs;ibi-<pb xlink:href="026/01/148.jpg" pagenum="116"/>libus, in quo o&longs;tendemus ideo lignum &longs;ur&longs;um emergere, quia ab aqua <lb/>extenditur, & idco corpora &longs;ur&longs;um ire, quia alia deor&longs;um eunt. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 74.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Quando lapis de&longs;cendit per medium aëra, impeditur aliquantulum eius <lb/>motus<emph.end type="italics"/>: Probatur primò experientiâ, quæ certa e&longs;t; tàm enim aër impe­<lb/>dit motum deor&longs;um, quàm &longs;ur&longs;um, vt videre e&longs;t in mobili leuiore &longs;eu ra­<lb/>riore, quod etiam flante vento ob&longs;eruare omnes po&longs;&longs;unt; quomodo ve­<lb/>rò impediat, dicemus aliàs; &longs;ecundò corpus immobile, in quod mobile <lb/>impingitur, motum illius impedit; &longs;ed in diuer&longs;as partes aëris corpus <lb/>graue impingitur in de&longs;cen&longs;u; igitur aliquantulum impeditur eius <lb/>inotus. </s></p><p type="main"> | <s><emph type="italics"/>Quando lapis de&longs;cendit per medium aëra, impeditur aliquantulum eius <lb/>motus<emph.end type="italics"/>: Probatur primò experientiâ, quæ certa e&longs;t; tàm enim aër impe­<lb/>dit motum deor&longs;um, quàm &longs;ur&longs;um, vt videre e&longs;t in mobili leuiore &longs;eu ra­<lb/>riore, quod etiam flante vento ob&longs;eruare omnes po&longs;&longs;unt; quomodo ve­<lb/>rò impediat, dicemus aliàs; &longs;ecundò corpus immobile, in quod mobile <lb/>impingitur, motum illius impedit; &longs;ed in diuer&longs;as partes aëris corpus <lb/>graue impingitur in de&longs;cen&longs;u; igitur aliquantulum impeditur eius <lb/>motus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 75.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc etiam impetus producitur imperfectior<emph.end type="italics"/>; quia ex imperfectione ef­<lb/>fectus requiritur imperfectic cau&longs;æ per Ax. 13.l. </s> | <s><emph type="italics"/>Hinc etiam impetus producitur imperfectior<emph.end type="italics"/>; quia ex imperfectione ef­<lb/>fectus requiritur imperfectio cau&longs;æ per Ax. 13.l. </s> |
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| <s>1. & quâ proportione <lb/>e&longs;t tardior motus eâdem impetus e&longs;t imperfectior, per Ax. <!-- REMOVE S-->5. excipe ta­<lb/>men impetum innatum, qui &longs;emper habet cundem effectum grauitatio­<lb/>nis, vel &longs;ingularis, quâ grauitas cum ip&longs;o medio, &longs;i reuerâ medium gra­<lb/>uitat, de quo aliàs. </s> | <s>1. & quâ proportione <lb/>e&longs;t tardior motus eâdem impetus e&longs;t imperfectior, per Ax. <!-- REMOVE S-->5. excipe ta­<lb/>men impetum innatum, qui &longs;emper habet eundem effectum grauitatio­<lb/>nis, vel &longs;ingularis, quâ grauitas cum ip&longs;o medio, &longs;i reuerâ medium gra­<lb/>uitat, de quo aliàs. </s> |
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| <s>Ob&longs;erua e&longs;&longs;e aliqua corpora minus den&longs;a, quæ motum omninò im­<lb/>pediunt; quippe certum e&longs;t aquam e&longs;&longs;e den&longs;iorem ligno; atqui li­<lb/>gnum de&longs;cen&longs;um lapidis impedit, non verò aqua; quia &longs;cilicet lignum <lb/>non e&longs;t medium, vt aqua; vt enim aliquod corpus &longs;it medium, debet e&longs;&longs;e <lb/>liquidum, vt, aqua & alij liquores; vel &longs;pirabile vt aër, vapor, &c. </s> | <s>Ob&longs;erua e&longs;&longs;e aliqua corpora minus den&longs;a, quæ motum omninò im­<lb/>pediunt; quippe certum e&longs;t aquam e&longs;&longs;e den&longs;iorem ligno; atqui li­<lb/>gnum de&longs;cen&longs;um lapidis impedit, non verò aqua; quia &longs;cilicet lignum <lb/>non e&longs;t medium, vt aqua; vt enim aliquod corpus &longs;it medium, debet e&longs;&longs;e <lb/>liquidum, vt, aqua & alij liquores; vel &longs;pirabile vt aër, vapor, &c. </s> |
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| <s>ratio <lb/>e&longs;t, quia partes ligni, vel alterius corpotis durioris, ita &longs;unt inter &longs;e con­<lb/>junctæ, vel implicatæ, vt omnem tran&longs;itum intercludant, ni&longs;i corpus ip­<lb/>&longs;um graue valido ictu vel impetu &longs;ibi viam aperiat; igitur vt corpus ali­<lb/>quod vice medij defungatur, debet in eo &longs;tatu e&longs;&longs;e, in quo eius partes <pb xlink:href="026/01/149.jpg" pagenum="117"/>modico ferè ni&longs;u &longs;eiungantur, & loco cedant; &longs;ed de his &longs;tatibus cor­<lb/>porum fusè agemus Tomo 5. adde quod ad medium &longs;ufficit vacuum &longs;i <lb/>motus in vacuo e&longs;&longs;e pote&longs;t, de quo alibi; quod certè e&longs;t omnium me­<lb/>diorum optimum, cum nullo modo re&longs;i&longs;tar mobili. </s></p><p type="main"> | <s>ratio <lb/>e&longs;t, quia partes ligni, vel alterius corporis durioris, ita &longs;unt inter &longs;e con­<lb/>junctæ, vel implicatæ, vt omnem tran&longs;itum intercludant, ni&longs;i corpus ip­<lb/>&longs;um graue valido ictu vel impetu &longs;ibi viam aperiat; igitur vt corpus ali­<lb/>quod vice medij defungatur, debet in eo &longs;tatu e&longs;&longs;e, in quo eius partes <pb xlink:href="026/01/149.jpg" pagenum="117"/>modico ferè ni&longs;u &longs;eiungantur, & loco cedant; &longs;ed de his &longs;tatibus cor­<lb/>porum fusè agemus Tomo 5. adde quod ad medium &longs;ufficit vacuum &longs;i <lb/>motus in vacuo e&longs;&longs;e pote&longs;t, de quo alibi; quod certè e&longs;t omnium me­<lb/>diorum optimum, cum nullo modo re&longs;i&longs;tar mobili. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Ob&longs;erua den&longs;itatem medij cogno&longs;ci ex eius grauitate; illud enim <lb/>den&longs;ius e&longs;t, quod e&longs;t grauius & vici&longs;&longs;im; quod fusè explicabimus &longs;uo lo­<lb/>co; e&longs;t enim grauitas quædam <emph type="italics"/>den&longs;itas, vt ait<emph.end type="italics"/> Philo&longs;ophus <emph type="italics"/>tùm l.<emph.end type="italics"/>4.<emph type="italics"/>pb.c.<emph.end type="italics"/><lb/>9.<emph type="italics"/>t.<emph.end type="italics"/>85. & 86. <emph type="italics"/>den&longs;um & rarum,<emph.end type="italics"/> inquit, <emph type="italics"/>&longs;unt lationis efficientia,<emph.end type="italics"/> & paulò &longs;u­<lb/>periùs; <emph type="italics"/>e&longs;t autem den&longs;um graue, rarum verò leue, & l.<emph.end type="italics"/>8.<emph type="italics"/>c.<emph.end type="italics"/>7.<emph type="italics"/>t.<emph.end type="italics"/>55. <emph type="italics"/>hæc habet, <lb/>graue & leue; molle & durum den&longs;itates quædam e&longs;&longs;e, & raritates videntur,<emph.end type="italics"/><lb/>quæ adnotare volui, vt vel inde con&longs;tet doctrinam hanc cum Peripate­<lb/>tica optimè con&longs;entire. </s></p><p type="main"> | <s>Ob&longs;erua den&longs;itatem medij cogno&longs;ci ex eius grauitate; illud enim <lb/>den&longs;ius e&longs;t, quod e&longs;t grauius & vici&longs;&longs;im; quod fusè explicabimus &longs;uo lo­<lb/>co; e&longs;t enim grauitas quædam <emph type="italics"/>den&longs;itas, vt ait<emph.end type="italics"/> Philo&longs;ophus <emph type="italics"/>tùm l.<emph.end type="italics"/>4.<emph type="italics"/>pb.c.<emph.end type="italics"/><lb/>9.<emph type="italics"/>t.<emph.end type="italics"/>85. & 86. <emph type="italics"/>den&longs;um & rarum,<emph.end type="italics"/> inquit, <emph type="italics"/>&longs;unt lationis efficientia,<emph.end type="italics"/> & paulò &longs;u­<lb/>periùs; <emph type="italics"/>e&longs;t autem den&longs;um graue, rarum verò leue, & l.<emph.end type="italics"/>8.<emph type="italics"/>c.<emph.end type="italics"/>7.<emph type="italics"/>t.<emph.end type="italics"/>55. <emph type="italics"/>hæc habet, <lb/>graue & leue; molle & durum den&longs;itates quædam e&longs;&longs;e, & raritates videntur,<emph.end type="italics"/><lb/>quæ adnotare volui, vt vel inde con&longs;tet doctrinam hanc cum Peripate­<lb/>tica optimè con&longs;entire. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis ctiam hîc à me non di&longs;cuti, in quo con&longs;i&longs;tat den&longs;itas, vel <lb/>raritas, grauitas, vel leuitas; &longs;uppono tantùm graue illud e&longs;&longs;e, quod ten­<lb/>dit deor&longs;um; leue illud, quod tendit &longs;ur&longs;um &longs;iue pellatur à grauiori, &longs;iue <lb/>non, den&longs;um verò e&longs;&longs;e id quod multùm materia habet &longs;ub parua exten­<lb/>&longs;ione, rarum è contrario; quorum omnium cau&longs;as, & rationes &longs;uo loco <lb/>explicabimus. </s></p><p type="main"> | <s>Ob&longs;eruabis etiam hîc à me non di&longs;cuti, in quo con&longs;i&longs;tat den&longs;itas, vel <lb/>raritas, grauitas, vel leuitas; &longs;uppono tantùm graue illud e&longs;&longs;e, quod ten­<lb/>dit deor&longs;um; leue illud, quod tendit &longs;ur&longs;um &longs;iue pellatur à grauiori, &longs;iue <lb/>non, den&longs;um verò e&longs;&longs;e id quod multùm materia habet &longs;ub parua exten­<lb/>&longs;ione, rarum è contrario; quorum omnium cau&longs;as, & rationes &longs;uo loco <lb/>explicabimus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Sub medium leuius corpus graue de&longs;cendit<emph.end type="italics"/>; certa e&longs;t hypothe&longs;is, ni&longs;i for­<lb/>tè aliquando per accidens &longs;ecus accidat; ratio porrò petitur ex ip&longs;a <lb/>grauitatis natura, quâ corpus graue tendit deor&longs;um; nihil enim aliud <lb/>grauitas e&longs;t, quidquid tandem illa &longs;it; quippe corpus graue de&longs;cendit, <lb/>quando medium liberum habet, idemque leuius, per quod de&longs;cendat; <lb/>quod certè &longs;i grauius e&longs;&longs;et, haud dubiè non de&longs;cenderet; &longs;ic ferrum, & <lb/>&longs;axum plumbo liquato innatant; cum tamen per mediam aquam de­<lb/>fcendant; fic lignum aquæ &longs;upernatat, quod per liberum aëra de&longs;cendit; <lb/>ratio e&longs;t, quia grauius de&longs;cendit &longs;ub medium leuius; cur autem id fiat <lb/>fusè alibi explicabo; id tantùm obiter indico. </s> | <s><emph type="italics"/>Sub medium leuius corpus graue de&longs;cendit<emph.end type="italics"/>; certa e&longs;t hypothe&longs;is, ni&longs;i for­<lb/>tè aliquando per accidens &longs;ecus accidat; ratio porrò petitur ex ip&longs;a <lb/>grauitatis natura, quâ corpus graue tendit deor&longs;um; nihil enim aliud <lb/>grauitas e&longs;t, quidquid tandem illa &longs;it; quippe corpus graue de&longs;cendit, <lb/>quando medium liberum habet, idemque leuius, per quod de&longs;cendat; <lb/>quod certè &longs;i grauius e&longs;&longs;et, haud dubiè non de&longs;cenderet; &longs;ic ferrum, & <lb/>&longs;axum plumbo liquato innatant; cum tamen per mediam aquam de­<lb/>&longs;cendant; fic lignum aquæ &longs;upernatat, quod per liberum aëra de&longs;cendit; <lb/>ratio e&longs;t, quia grauius de&longs;cendit &longs;ub medium leuius; cur autem id fiat <lb/>fusè alibi explicabo; id tantùm obiter indico. </s> |
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| <s>Omnis motus, qui fit à <lb/>principio intrin&longs;eco per lineam rectam propter locum e&longs;t, vt patet; quis <lb/>enim neget corpus graue ideo de&longs;cendere &longs;ub leuius, vt occupet aliquem <lb/>locum quo prius carebat, qui tamen illi connaturalis e&longs;t in hoc rerum <lb/>ordine? </s> | <s>Omnis motus, qui fit à <lb/>principio intrin&longs;eco per lineam rectam propter locum e&longs;t, vt patet; quis <lb/>enim neget corpus graue ideo de&longs;cendere &longs;ub leuius, vt occupet aliquem <lb/>locum quo prius carebat, qui tamen illi connaturalis e&longs;t in hoc rerum <lb/>ordine? </s> |
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| <s>cum à natura acceperit vim illam intrin&longs;ecam, quâ in eum lo­<lb/>cum &longs;e&longs;e recipere pote&longs;t; quam certè vim intrin&longs;ecam nunquam à na­<lb/>tura rebus creatis in&longs;itam e&longs;&longs;e con&longs;tat, ni&longs;i ad eum finem con&longs;equendum, <lb/>cui à natura de&longs;tinantur; cur verò locus connaturalis corporis grauio­<lb/>ris &longs;it ille, in quo leuiori &longs;ube&longs;t, non diu hærebit animus, quin &longs;tatim ra­<lb/>tio affulgeat; cum enim corpus, quod e&longs;t &longs;uprà, &longs;u&longs;tineatur ab eo quod e&longs;t <lb/>infrà; illud certè infra e&longs;&longs;e connaturalius e&longs;t, quod aptius e&longs;t ad &longs;u&longs;tinen-<pb xlink:href="026/01/150.jpg" pagenum="118"/>dum; atqui den&longs;um aptius e&longs;t ad id munus, quia plures partes &longs;u&longs;tinentis <lb/>pauciores &longs;u&longs;tinent alterius leuioris, &longs;eu rarioris, vt con&longs;tat; v.g. <!-- REMOVE S-->certum <lb/>e&longs;t camdem aëris partem pluribus aquæ partibus re&longs;pondere; &longs;ed de hoc <lb/>alias fusè; hæc interim &longs;ufficiat indica&longs;&longs;e, vt vel aliqua ratio affulgeat; <lb/>cur &longs;cilicet corpus graue &longs;ub medium leuius &longs;ua &longs;ponte de&longs;cendat; adde <lb/>quod cum omne corpus graue tendat deor&longs;um, tunc vnum infra aliud de­<lb/>&longs;cendit, cum &longs;unt plures partes pellentis, quàm pul&longs;i; denique per va­<lb/>cuum modicum &longs;ine vlla re&longs;i&longs;tentia de&longs;cenderet. </s> | <s>cum à natura acceperit vim illam intrin&longs;ecam, quâ in eum lo­<lb/>cum &longs;e&longs;e recipere pote&longs;t; quam certè vim intrin&longs;ecam nunquam à na­<lb/>tura rebus creatis in&longs;itam e&longs;&longs;e con&longs;tat, ni&longs;i ad eum finem con&longs;equendum, <lb/>cui à natura de&longs;tinantur; cur verò locus connaturalis corporis grauio­<lb/>ris &longs;it ille, in quo leuiori &longs;ube&longs;t, non diu hærebit animus, quin &longs;tatim ra­<lb/>tio affulgeat; cum enim corpus, quod e&longs;t &longs;uprà, &longs;u&longs;tineatur ab eo quod e&longs;t <lb/>infrà; illud certè infra e&longs;&longs;e connaturalius e&longs;t, quod aptius e&longs;t ad &longs;u&longs;tinen-<pb xlink:href="026/01/150.jpg" pagenum="118"/>dum; atqui den&longs;um aptius e&longs;t ad id munus, quia plures partes &longs;u&longs;tinentis <lb/>pauciores &longs;u&longs;tinent alterius leuioris, &longs;eu rarioris, vt con&longs;tat; v.g. <!-- REMOVE S-->certum <lb/>e&longs;t <expan abbr="cãdem">eandem</expan> aëris partem pluribus aquæ partibus re&longs;pondere; &longs;ed de hoc <lb/>alias fusè; hæc interim &longs;ufficiat indica&longs;&longs;e, vt vel aliqua ratio affulgeat; <lb/>cur &longs;cilicet corpus graue &longs;ub medium leuius &longs;ua &longs;ponte de&longs;cendat; adde <lb/>quod cum omne corpus graue tendat deor&longs;um, tunc vnum infra aliud de­<lb/>&longs;cendit, cum &longs;unt plures partes pellentis, quàm pul&longs;i; denique per va­<lb/>cuum modicum &longs;ine vlla re&longs;i&longs;tentia de&longs;cenderet. </s> |
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| <s>&longs;upponunt etiam reliqui <lb/>omnes, præ&longs;ertim recentior Galileus; &longs;i enim æqualis &longs;uperat æqualem, <lb/>ergo inæqualis pro rata; &longs;cilicet &longs;ubdupla &longs;ubduplum &longs;ubtripla, &c. </s> | <s>&longs;upponunt etiam reliqui <lb/>omnes, præ&longs;ertim recentior Galileus; &longs;i enim æqualis &longs;uperat æqualem, <lb/>ergo inæqualis pro rata; &longs;cilicet &longs;ubdupla &longs;ubduplum &longs;ubtripla, &c. </s> |
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| <s>Præ­<lb/>terca, cum detrahat aliquam partem grauitationis maioris per Th.85.nec <lb/>detrahat inæqualem maiorem, per Th.80.nec inæqualem minorem; cur <lb/>enim potius vnam minorem quam aliam? </s> | <s>Præ­<lb/>terea, cum detrahat aliquam partem grauitationis maioris per Th.85.nec <lb/>detrahat inæqualem maiorem, per Th.80.nec inæqualem minorem; cur <lb/>enim potius vnam minorem quam aliam? </s> |
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| <s>certè æqualem tantùm <lb/>detrahere pote&longs;t, quod &longs;uo loco per Principium po&longs;itiuum demon&longs;tra­<lb/>bimus. </s></p><p type="main"> | <s>certè æqualem tantùm <lb/>detrahere pote&longs;t, quod &longs;uo loco per Principium po&longs;itiuum demon&longs;tra­<lb/>bimus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 87.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc ratio cur grauia de&longs;cendant tardius in aqua, quàm in aëre, & in <lb/>aëre, quàm in vacuo<emph.end type="italics"/>; hinc etiam maioris &longs;unt ponderis in aëre quam in <lb/>aqua; hinc &longs;i grauitas alicuius corporis &longs;it ad grauitatem aëris vt 100. <lb/>ad 1. haud dubiè decre&longs;cet eius pondus in aëre (1/100); id e&longs;t, &longs;i penderet 100. <lb/>libras in vacuo, in aëre penderet 99. & eo tempore quo in vacuo decur­<lb/>reret 100. pa&longs;&longs;us, in aëre decurreret 99. &longs;i nulla &longs;it aliunde re&longs;i&longs;tentia, <lb/>qualis reuerâ e&longs;t, vt dicam infrà; &longs;imiliter &longs;i grauitas alicuius corporis <lb/>&longs;it ad grauitatem aquæ, vt 10. ad 1. decre&longs;cet eius pondus in aqua (1/<gap/>), & <lb/>co tempore quo decurreret in vacuo 10. palmos &longs;patij, in aqua decurre <pb xlink:href="026/01/152.jpg" pagenum="120"/>ret tantùm 9. po&longs;ito quod non &longs;it aliud quod re&longs;i&longs;tat; quanta verò &longs;it <lb/>grauitas omnium corporum tùm duriorum, qualia &longs;unt metall<gap/>, tùm li­<lb/>quidorum, tùm &longs;pirabilium, dicemus &longs;uo loco; illorum tabulas habes <lb/>apud Gethaldum, & Mer&longs;ennum. </s></p><p type="main"> | <s><emph type="italics"/>Hinc ratio cur grauia de&longs;cendant tardius in aqua, quàm in aëre, & in <lb/>aëre, quàm in vacuo<emph.end type="italics"/>; hinc etiam maioris &longs;unt ponderis in aëre quam in <lb/>aqua; hinc &longs;i grauitas alicuius corporis &longs;it ad grauitatem aëris vt 100. <lb/>ad 1. haud dubiè decre&longs;cet eius pondus in aëre (1/100); id e&longs;t, &longs;i penderet 100. <lb/>libras in vacuo, in aëre penderet 99. & eo tempore quo in vacuo decur­<lb/>reret 100. pa&longs;&longs;us, in aëre decurreret 99. &longs;i nulla &longs;it aliunde re&longs;i&longs;tentia, <lb/>qualis reuerâ e&longs;t, vt dicam infrà; &longs;imiliter &longs;i grauitas alicuius corporis <lb/>&longs;it ad grauitatem aquæ, vt 10. ad 1. decre&longs;cet eius pondus in aqua (1/<gap/>), & <lb/>co tempore quo decurreret in vacuo 10. palmos &longs;patij, in aqua decurre <pb xlink:href="026/01/152.jpg" pagenum="120"/>ret tantùm 9. po&longs;ito quod non &longs;it aliud quod re&longs;i&longs;tat; quanta verò &longs;it <lb/>grauitas omnium corporum tùm duriorum, qualia &longs;unt metalla, tùm li­<lb/>quidorum, tùm &longs;pirabilium, dicemus &longs;uo loco; illorum tabulas habes <lb/>apud Gethaldum, & Mer&longs;ennum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 88.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 88.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis dictum e&longs;&longs;e hactenus; &longs;i nihil aliud de&longs;cen&longs;um corporis <lb/>grauis impedit; nam certè aliud e&longs;t, de quo infrà, ex cuius ignoratione <lb/>plures haud dubiè in inue&longs;tigandis grauitatum medij rationibus hallu­<lb/>cinarentur; cum enim ob&longs;eruatum &longs;it globum plumbeum, cuius graui­<lb/>tas e&longs;t ferè dodecupla grauitatis aquæ, conficere in libero aëre 48. pedes <lb/>&longs;patij tempore duorum &longs;ecundorum, in aqua verò 12. pedes codem tem­<lb/>pore; certè in vacuo ip&longs;o moueretur tardiùs quàm in aëre; quia eo tem­<lb/>pore, quo conficit in aqua 12.pedes in vacuo conficeret (13 1/21), &longs;i tantùm <lb/>detrahitur (1/12) grauitationis, & de&longs;cen&longs;us; atqui in aëre codem tempore <lb/>conficit 48. pedes; igitur velociùs moueretur in aëre quàm in vacuo; <lb/>igitur e&longs;t aliquid aliud quod impedit motum; vt enim optimè monet <lb/>Mer&longs;ennus, &longs;i grauitas aquæ &longs;it ad grauitatem aëris vt 400 ad 1.& graui­<lb/>tas plumbi ad grauitatem aquæ vt 12. ad 1.eadem grauitas plumbi e&longs;t ad <lb/>grauitatem aëris vt 4800. igitur &longs;i &longs;patium, quod decurrit plumbum in <lb/>vacuo diuidatur in 4800. partes, decurret in aëre 4799. partes; in aqua <lb/>verò 4400. quod e&longs;t contra experientiam; nam &longs;patium, quod decurrit <lb/>in aëre e&longs;t maius &longs;patio, quod decurrit in aqua 3/4; quippe conficit 12. <lb/>pedes in aqua eodem tempore, quo in aëre conficir 48; igitur in aqua <lb/>amittit 3/4 &longs;uæ grauitationis, & &longs;ui motus; igitur 3600. partes; igitur <lb/>plumbi grauitas e&longs;&longs;et ad grauitatem aquæ vt 4.ad 3.& ad grauitatem aë­<lb/>ris vt 3600. ad 1. atqui vtrumque fal&longs;um e&longs;&longs;e con&longs;tat; igitur e&longs;t aliquid <lb/>aliud, quod etiam impedit motum; nec ex motu diuer&longs;o per diuer&longs;a me­<lb/>dia cogno&longs;ci pote&longs;t eorum grauitas. </s></p><p type="main"> | <s>Ob&longs;eruabis dictum e&longs;&longs;e hactenus; &longs;i nihil aliud de&longs;cen&longs;um corporis <lb/>grauis impedit; nam certè aliud e&longs;t, de quo infrà, ex cuius ignoratione <lb/>plures haud dubiè in inue&longs;tigandis grauitatum medij rationibus hallu­<lb/>cinarentur; cum enim ob&longs;eruatum &longs;it globum plumbeum, cuius graui­<lb/>tas e&longs;t ferè dodecupla grauitatis aquæ, conficere in libero aëre 48. pedes <lb/>&longs;patij tempore duorum &longs;ecundorum, in aqua verò 12. pedes codem tem­<lb/>pore; certè in vacuo ip&longs;o moueretur tardiùs quàm in aëre; quia eo tem­<lb/>pore, quo conficit in aqua 12.pedes in vacuo conficeret (13 1/21), &longs;i tantùm <lb/>detrahitur (1/12) grauitationis, & de&longs;cen&longs;us; atqui in aëre codem tempore <lb/>conficit 48. pedes; igitur velociùs moueretur in aëre quàm in vacuo; <lb/>igitur e&longs;t aliquid aliud quod impedit motum; vt enim optimè monet <lb/>Mer&longs;ennus, &longs;i grauitas aquæ &longs;it ad grauitatem aëris vt 400 ad 1.& graui­<lb/>tas plumbi ad grauitatem aquæ vt 12. ad 1.eadem grauitas plumbi e&longs;t ad <lb/>grauitatem aëris vt 4800. igitur &longs;i &longs;patium, quod decurrit plumbum in <lb/>vacuo diuidatur in 4800. partes, decurret in aëre 4799. partes; in aqua <lb/>verò 4400. quod e&longs;t contra experientiam; nam &longs;patium, quod decurrit <lb/>in aëre e&longs;t maius &longs;patio, quod decurrit in aqua 3/4; quippe conficit 12. <lb/>pedes in aqua eodem tempore, quo in aëre conficit 48; igitur in aqua <lb/>amittit 3/4 &longs;uæ grauitationis, & &longs;ui motus; igitur 3600. partes; igitur <lb/>plumbi grauitas e&longs;&longs;et ad grauitatem aquæ vt 4.ad 3.& ad grauitatem aë­<lb/>ris vt 3600. ad 1. atqui vtrumque fal&longs;um e&longs;&longs;e con&longs;tat; igitur e&longs;t aliquid <lb/>aliud, quod etiam impedit motum; nec ex motu diuer&longs;o per diuer&longs;a me­<lb/>dia cogno&longs;ci pote&longs;t eorum grauitas. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 89.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 89.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc potiori iure reiicies illerum &longs;ententiam, qui volunt impediri motum <lb/>corporis de&longs;cendentis per diuer&longs;a media pro diuer&longs;aratione grauitatum vtriu&longs;­<lb/>que medy<emph.end type="italics"/>; quod certè fal&longs;um e&longs;t; nam aqua &longs;it ad grauitatem aëris vt <lb/>400. ad 1. deberet omne corpus de&longs;cendere velociùs in aëre quadrin-<pb xlink:href="026/01/153.jpg" pagenum="121"/>gente&longs;ies, quàm in aqua, quod fal&longs;um e&longs;t; cum aliquod corpus nullo mo­<lb/>do de&longs;cendat in aqua, quod de&longs;cendit in aëre, vt lignum. </s></p><p type="main"> | <s><emph type="italics"/>Hinc potiori iure reiicies illorum &longs;ententiam, qui volunt impediri motum <lb/>corporis de&longs;cendentis per diuer&longs;a media pro diuer&longs;a ratione grauitatum vtriu&longs;­<lb/>que medy<emph.end type="italics"/>; quod certè fal&longs;um e&longs;t; nam aqua &longs;it ad grauitatem aëris vt <lb/>400. ad 1. deberet omne corpus de&longs;cendere velociùs in aëre quadrin-<pb xlink:href="026/01/153.jpg" pagenum="121"/>gente&longs;ies, quàm in aqua, quod fal&longs;um e&longs;t; cum aliquod corpus nullo mo­<lb/>do de&longs;cendat in aqua, quod de&longs;cendit in aëre, vt lignum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 90.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 90.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 92.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc aliqua tantùm partes medij loco cedunt<emph.end type="italics"/>; probatur, quia vel totum <lb/>medium, vel aliquæ eius partes, per Th.90.non primum per Th.91.igitut <lb/>&longs;ecundum, in his certè non e&longs;t vlla difficultas. </s></p><p type="main"> | <s><emph type="italics"/>Hinc aliqua tantùm partes medij loco cedunt<emph.end type="italics"/>; probatur, quia vel totum <lb/>medium, vel aliquæ eius partes, per Th.90.non primum per Th.91. igitur <lb/>&longs;ecundum, in his certè non e&longs;t vlla difficultas. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 93.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 93.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis vmonem continuatiuam corporum aliquando po&longs;itam <lb/>e&longs;&longs;e in plexu, vel implicatione partium, vt videmus in fune, ligno, carne, <lb/>o&longs;&longs;ibus, &c. </s> | <s>Ob&longs;eruabis vnionem continuatiuam corporum aliquando po&longs;itam <lb/>e&longs;&longs;e in plexu, vel implicatione partium, vt videmus in fune, ligno, carne, <lb/>o&longs;&longs;ibus, &c. </s> |
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| <s>aliquando in vacui metu; &longs;ic aqua, vt &longs;uo va&longs;i adhæreat, <lb/>a&longs;cendit, vel &longs;ur&longs;um attollitur, ne detur vacuum; aliquando in coitione <lb/>quadam magnetica; porrò hic plexus con&longs;tat ex infinitis ferè tenui&longs;&longs;i­<lb/>morum filamentorum voluminibus, vel aduncis &longs;iue hamatis partibus, <lb/>&longs;eu corpu&longs;culis: Vtrum verò præter hæc requiratur alius vnionis mo­<lb/>dus, di&longs;cutiemus fusè Tomo 5. quidquid &longs;it; certum e&longs;t medium illud, <lb/>cuius partes arctiori maiorique nexu copulantur, longè difficiliùs per­<lb/>aurri po&longs;&longs;e, &longs;eu perrumpi. </s></p><p type="main"> | <s>aliquando in vacui metu; &longs;ic aqua, vt &longs;uo va&longs;i adhæreat, <lb/>a&longs;cendit, vel &longs;ur&longs;um attollitur, ne detur vacuum; aliquando in coitione <lb/>quadam magnetica; porrò hic plexus con&longs;tat ex infinitis ferè tenui&longs;&longs;i­<lb/>morum filamentorum voluminibus, vel aduncis &longs;iue hamatis partibus, <lb/>&longs;eu corpu&longs;culis: Vtrum verò præter hæc requiratur alius vnionis mo­<lb/>dus, di&longs;cutiemus fusè Tomo 5. quidquid &longs;it; certum e&longs;t medium illud, <lb/>cuius partes arctiori maiorique nexu copulantur, longè difficiliùs per­<lb/>curri po&longs;&longs;e, &longs;eu perrumpi. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 99.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 99.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc non modò aqua detrahit plumbo<emph.end type="italics"/> (1/22) <emph type="italics"/>&longs;ui motus, quod &longs;cilicet plumbi græ­<lb/>uitas &longs;it dedecupla grauitatis aquæ, verùm etiam propter re&longs;istentiam petitam <lb/>ex alio capite aliquid adhuc detrabere pote&longs;t<emph.end type="italics"/>; &longs;cilicet quia partes aquæ non <lb/>po&longs;&longs;unt amoueri, ni&longs;i ab aliis &longs;eparentur; atqui maiore vi opus e&longs;t ad­<lb/>&longs;oiuendum &longs;trictiorem nexum; immò licèt partes aquæ nullo penitus <lb/>nexu vniantur, &longs;ed tantùm vel vacui metu, vel alio modo, quod alibi ex­<lb/>plicabimus; omninò detraherent adhuc plumbo (1/12) motus; igitur, &longs;i <lb/>præter illud impedimentum, quod petitur à comparatione grauitatis <lb/>corporis mobilis cum grauitate medij, addatur aliud longè robu&longs;tius; <lb/>non mirum e&longs;t, &longs;i maior inde &longs;equatur effectus, id e&longs;t maior imminutio <lb/>motus, qui qua&longs;i frangitur ab impedimento. </s></p><p type="main"> | <s><emph type="italics"/>Hinc non modò aqua detrahit plumbo<emph.end type="italics"/> (1/22) <emph type="italics"/>&longs;ui motus, quod &longs;cilicet plumbi gra­<lb/>uitas &longs;it dedecupla grauitatis aquæ, verùm etiam propter re&longs;istentiam petitam <lb/>ex alio capite aliquid adhuc detrahere pote&longs;t<emph.end type="italics"/>; &longs;cilicet quia partes aquæ non <lb/>po&longs;&longs;unt amoueri, ni&longs;i ab aliis &longs;eparentur; atqui maiore vi opus e&longs;t ad­<lb/>&longs;oluendum &longs;trictiorem nexum; immò licèt partes aquæ nullo penitus <lb/>nexu vniantur, &longs;ed tantùm vel vacui metu, vel alio modo, quod alibi ex­<lb/>plicabimus; omninò detraherent adhuc plumbo (1/12) motus; igitur, &longs;i <lb/>præter illud impedimentum, quod petitur à comparatione grauitatis <lb/>corporis mobilis cum grauitate medij, addatur aliud longè robu&longs;tius; <lb/>non mirum e&longs;t, &longs;i maior inde &longs;equatur effectus, id e&longs;t maior imminutio <lb/>motus, qui qua&longs;i frangitur ab impedimento. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 100.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc petitur ratio illius experimenti, &longs;i verum e&longs;t, duobus &longs;ecundis per­<lb/>currere plumbeam pilam in aëre<emph.end type="italics"/> 48. <emph type="italics"/>&longs;patij pedes, in aqua verò<emph.end type="italics"/> 12. <emph type="italics"/>pedes<emph.end type="italics"/>; hinc <lb/>tenui nexu partes aëris copulantur; partes verò aquæ firmiori; hinc aër <lb/>minùs re&longs;i&longs;tit etiam motibus violentis; hinc vix pote&longs;t qui&longs;piam in aqua <lb/>currere propter maiorem aquæ re&longs;i&longs;tentiam; hinc pote&longs;t dici quota parte <lb/>firmior &longs;it nexus vnius corporis quàm alterius; hinc non tantùm copu­<lb/>lantur partes metu vacui; alioquin æquè re&longs;i&longs;terent partes aëris, ac par­<lb/>tes aquæ ratione nexus; hinc videntur guttulæ illæ &longs;phericæ inuolui te­<lb/>nui qua&longs;i membranula, &longs;eu &longs;uperficie, cuius analogiam videmus in aqua<gap/><pb xlink:href="026/01/155.jpg" pagenum="123"/>feruente; in bullis, quæ ex guttis pluuiæ re&longs;ilientibus na&longs;ci videntur; in <lb/>bullis etiam illis &longs;aponariis, quas leui calamo pueri inter ludendum in­<lb/>flant; hinc ex minimo ferè contactu guttula &longs;pargitur, ni&longs;i fortè cum <lb/>multo a&longs;per&longs;a puluere cru&longs;tam quamdam induit &longs;olidiorem; &longs;ic bullæ il­<lb/>læ ad minimum etiam contactum di&longs;&longs;ipantur; hinc ip&longs;a &longs;uperficies <lb/>aquæ plus videtur re&longs;i&longs;tere quod multis experimentis comprobatur; &longs;ed <lb/>illo maximè, quo videmus findi à remo cum quodam qua&longs;i &longs;tridulo cre­<lb/>pitu re&longs;i&longs;tentiæ maioris te&longs;te; immò cum ab ip&longs;a naui qua&longs;i &longs;ulcatur, <lb/>idem &longs;tridor auditur, maximè in iis tractibus; in quibus nullis fluctibus <lb/>agitata læuigati&longs;&longs;imam faciem præfert; habes analogiam in illa cru&longs;ta, <lb/>quæ concre&longs;cit in &longs;uperficie liquorum, &longs;ed præ&longs;ertim offarum:adde quod <lb/>aër paulò compre&longs;&longs;ior vndique guttulam premens æquali ni&longs;u eam miri­<lb/>ficè tornat: hæc tantùm tumultuatim conge&longs;ta alibi fusè pertractabi­<lb/>mus, & ex &longs;implici&longs;&longs;imis principiis demon&longs;trabimus; plura hîc de graui­<lb/>tate crant dicenda, & de grauitatione, quæ tantùm indica&longs;&longs;e &longs;ufficiat, vt <lb/>deinde Tomo quinto fusè explicentur. </s></p><p type="main"> | <s><emph type="italics"/>Hinc petitur ratio illius experimenti, &longs;i verum e&longs;t, duobus &longs;ecundis per­<lb/>currere plumbeam pilam in aëre<emph.end type="italics"/> 48. <emph type="italics"/>&longs;patij pedes, in aqua verò<emph.end type="italics"/> 12. <emph type="italics"/>pedes<emph.end type="italics"/>; hinc <lb/>tenui nexu partes aëris copulantur; partes verò aquæ firmiori; hinc aër <lb/>minùs re&longs;i&longs;tit etiam motibus violentis; hinc vix pote&longs;t qui&longs;piam in aqua <lb/>currere propter maiorem aquæ re&longs;i&longs;tentiam; hinc pote&longs;t dici quota parte <lb/>firmior &longs;it nexus vnius corporis quàm alterius; hinc non tantùm copu­<lb/>lantur partes metu vacui; alioquin æquè re&longs;i&longs;terent partes aëris, ac par­<lb/>tes aquæ ratione nexus; hinc videntur guttulæ illæ &longs;phericæ inuolui te­<lb/>nui qua&longs;i membranula, &longs;eu &longs;uperficie, cuius analogiam videmus in aqua<gap/><pb xlink:href="026/01/155.jpg" pagenum="123"/>feruente; in bullis, quæ ex guttis pluuiæ re&longs;ilientibus na&longs;ci videntur; in <lb/>bullis etiam illis &longs;aponariis, quas leui calamo pueri inter ludendum in­<lb/>flant; hinc ex minimo ferè contactu guttula &longs;pargitur, ni&longs;i fortè cum <lb/>multo a&longs;per&longs;a puluere cru&longs;tam quamdam induit &longs;olidiorem; &longs;ic bullæ il­<lb/>læ ad minimum etiam contactum di&longs;&longs;ipantur; hinc ip&longs;a &longs;uperficies <lb/>aquæ plus videtur re&longs;i&longs;tere quod multis experimentis comprobatur; &longs;ed <lb/>illo maximè, quo videmus findi à remo cum quodam qua&longs;i &longs;tridulo cre­<lb/>pitu re&longs;i&longs;tentiæ maioris te&longs;te; immò cum ab ip&longs;a naui qua&longs;i &longs;ulcatur, <lb/>idem &longs;tridor auditur, maximè in iis tractibus; in quibus nullis fluctibus <lb/>agitata læuigati&longs;&longs;imam faciem præfert; habes analogiam in illa cru&longs;ta, <lb/>quæ concre&longs;cit in &longs;uperficie liquorum, &longs;ed præ&longs;ertim o&longs;&longs;arum: adde quod <lb/>aër paulò compre&longs;&longs;ior vndique guttulam premens æquali ni&longs;u eam miri­<lb/>ficè tornat: hæc tantùm tumultuatim conge&longs;ta alibi fusè pertractabi­<lb/>mus, & ex &longs;implici&longs;&longs;imis principiis demon&longs;trabimus; plura hîc de graui­<lb/>tate crant dicenda, & de grauitatione, quæ tantùm indica&longs;&longs;e &longs;ufficiat, vt <lb/>deinde Tomo quinto fusè explicentur. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 101.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 102.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 102.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc quo &longs;unt plures partes diuidendæ, quæ antè uniebantur, maior e&longs;t re&longs;i­<lb/>&longs;tentia<emph.end type="italics"/>; igitur maiore vi opus e&longs;t, igitur maiore grauitate; &longs;ed in medio <lb/>den&longs;iore ab codem mobili plures &longs;eparantur quàm in rariore; quia &longs;ci­<lb/>licet corpus den&longs;um plures habet &longs;ub minori exten&longs;ione, & rarum è con­<lb/>trario, vt videbimus &longs;uo loco; igitur in medio den&longs;iore idem mobile ma­<lb/>jorem re&longs;i&longs;tentiam inuenit, quàm in rariore; licèt vtriu&longs;que partes <lb/>æquali nexu &longs;eu fibula copulentur; quia &longs;cilicet plures &longs;unt diuidendæ <lb/>in den&longs;iore; quia plures &longs;cilicet in æquali &longs;patio occurrunt, quàm in ra­<lb/>tiore; igitur maiore vi grauitatis opus e&longs;t. </s></p><p type="main"> | <s><emph type="italics"/>Hinc quo &longs;unt plures partes diuidendæ, quæ antè uniebantur, maior e&longs;t re&longs;i­<lb/>&longs;tentia<emph.end type="italics"/>; igitur maiore vi opus e&longs;t, igitur maiore grauitate; &longs;ed in medio <lb/>den&longs;iore ab codem mobili plures &longs;eparantur quàm in rariore; quia &longs;ci­<lb/>licet corpus den&longs;um plures habet &longs;ub minori exten&longs;ione, & rarum è con­<lb/>trario, vt videbimus &longs;uo loco; igitur in medio den&longs;iore idem mobile ma­<lb/>jorem re&longs;i&longs;tentiam inuenit, quàm in rariore; licèt vtriu&longs;que partes <lb/>æquali nexu &longs;eu fibula copulentur; quia &longs;cilicet plures &longs;unt diuidendæ <lb/>in den&longs;iore; quia plures &longs;cilicet in æquali &longs;patio occurrunt, quàm in ra­<lb/>riore; igitur maiore vi grauitatis opus e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 103.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 103.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc medium pote&longs;t comparari cum alio in<emph.end type="italics"/> 2. <emph type="italics"/>capitibus<emph.end type="italics"/>; Primum e&longs;t in <lb/>grauitate, vel den&longs;itate, nam reuerâ ex maiori den&longs;itate maiorem gra­<lb/>uitatem reducimus; Secundum e&longs;t in maiori, vel minori partium nexu, <lb/>ex quo 4. &longs;equuntur combinationes 2.mediorum; nam vel &longs;unt eiu&longs;dem <lb/>grauitatis, & mollitiei; vel eiu&longs;dem grauitatis & diuer&longs;æ mollitiei; vel <lb/>ciu&longs;dem mollitici, & diuer&longs;æ grauitatis; vel diuer&longs;æ grauitatis, & ciu&longs;­<lb/>dem mollitici; mollius autem illud appello, cuius partes laxiori nexu <lb/>copulantur; porrò 4.i &longs;tæ combinationes &longs;upponunt <expan abbr="id&etilde;">idem</expan> mobile <expan abbr="invtroq;">invtroque</expan> <lb/>medio; &longs;i &longs;it prima combinatio, motus e&longs;t æqualis in vtroque; &longs;i &longs;ecunda <pb xlink:href="026/01/156.jpg" pagenum="124"/>maior e&longs;t in molliori; &longs;i tertia maior in grauiori; &longs;i verò quarta &longs;ubdi­<lb/>uidi pote&longs;t in duas; nam vel grauius e&longs;t conjunctum cum maiori molli­<lb/>tie, vel leuius; &longs;i leuius, haud dubiè maior e&longs;t motus in leuiore; &longs;i gra­<lb/>uius & mollities compen&longs;et grauitatem, id e&longs;t, &longs;i vt &longs;e habet grauitas gra­<lb/>uioris ad leuitatem leuioris; ita &longs;e habet mollities illius ad mollitiem <lb/>huius, æqualis e&longs;t in vtroque; &longs;i &longs;ecus, pro rata; hinc pote&longs;t e&longs;&longs;e æqualis <lb/>motus in grauiore & leuiore medio, & in æquè graui pote&longs;t e&longs;&longs;e maior <lb/>in grauiore; & minor; maior quidem, &longs;i maior &longs;it ratio mollitici gra­<lb/>uioris ad mollitiem leuioris, quàm grauitatis ad grauitatem; minor ve­<lb/>rò, &longs;i maior &longs;itratio grauitatis ad grauitatem, quàm mollitici ad molli­<lb/>tiem; æqualis denique &longs;i æqualis ratio; & his regulis cuncta facilè ex­<lb/>plicari po&longs;&longs;unt; hîc porrò &longs;uppono idem mobile, quod per vtrumque me­<lb/>dium de&longs;cendere po&longs;&longs;it, id e&longs;t, quod &longs;it vtroque grauius, medium autem <lb/>appello illud, per quod mobile grauius per &longs;e de&longs;cendit; dixi per &longs;e quia <lb/>nonnunquam accidit, vt vel ratione figuræ, vel alterius impedimenti non <lb/>de&longs;cendat. </s></p><p type="main"> | <s><emph type="italics"/>Hinc medium pote&longs;t comparari cum alio in<emph.end type="italics"/> 2. <emph type="italics"/>capitibus<emph.end type="italics"/>; Primum e&longs;t in <lb/>grauitate, vel den&longs;itate, nam reuerâ ex maiori den&longs;itate maiorem gra­<lb/>uitatem reducimus; Secundum e&longs;t in maiori, vel minori partium nexu, <lb/>ex quo 4. &longs;equuntur combinationes 2.mediorum; nam vel &longs;unt eiu&longs;dem <lb/>grauitatis, & mollitiei; vel eiu&longs;dem grauitatis & diuer&longs;æ mollitiei; vel <lb/>eiu&longs;dem mollitiei, & diuer&longs;æ grauitatis; vel diuer&longs;æ grauitatis, & eiu&longs;­<lb/>dem mollitiei; mollius autem illud appello, cuius partes laxiori nexu <lb/>copulantur; porrò 4. i&longs;tæ combinationes &longs;upponunt <expan abbr="id&etilde;">idem</expan> mobile <expan abbr="invtroq;">in vtroque</expan> <lb/>medio; &longs;i &longs;it prima combinatio, motus e&longs;t æqualis in vtroque; &longs;i &longs;ecunda <pb xlink:href="026/01/156.jpg" pagenum="124"/>maior e&longs;t in molliori; &longs;i tertia maior in grauiori; &longs;i verò quarta &longs;ubdi­<lb/>uidi pote&longs;t in duas; nam vel grauius e&longs;t conjunctum cum maiori molli­<lb/>tie, vel leuius; &longs;i leuius, haud dubiè maior e&longs;t motus in leuiore; &longs;i gra­<lb/>uius & mollities compen&longs;et grauitatem, id e&longs;t, &longs;i vt &longs;e habet grauitas gra­<lb/>uioris ad leuitatem leuioris; ita &longs;e habet mollities illius ad mollitiem <lb/>huius, æqualis e&longs;t in vtroque; &longs;i &longs;ecus, pro rata; hinc pote&longs;t e&longs;&longs;e æqualis <lb/>motus in grauiore & leuiore medio, & in æquè graui pote&longs;t e&longs;&longs;e maior <lb/>in grauiore; & minor; maior quidem, &longs;i maior &longs;it ratio mollitiei gra­<lb/>uioris ad mollitiem leuioris, quàm grauitatis ad grauitatem; minor ve­<lb/>rò, &longs;i maior &longs;itratio grauitatis ad grauitatem, quàm mollitiei ad molli­<lb/>tiem; æqualis denique &longs;i æqualis ratio; & his regulis cuncta facilè ex­<lb/>plicari po&longs;&longs;unt; hîc porrò &longs;uppono idem mobile, quod per vtrumque me­<lb/>dium de&longs;cendere po&longs;&longs;it, id e&longs;t, quod &longs;it vtroque grauius, medium autem <lb/>appello illud, per quod mobile grauius per &longs;e de&longs;cendit; dixi per &longs;e quia <lb/>nonnunquam accidit, vt vel ratione figuræ, vel alterius impedimenti non <lb/>de&longs;cendat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 104.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 104.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Sunt tres combinationes mobilis cum medio<emph.end type="italics"/>; prima, &longs;i &longs;it idem mobile <lb/>cum diuer&longs;is mediis; &longs;ecunda, &longs;i idem medium cum diuer&longs;is mobilibus; <lb/>tertia &longs;i diuer&longs;a mobïlia cum diuer&longs;is mediis; de primâ actum e&longs;t iam <lb/>fuprà; &longs;ecunda &longs;ube&longs;t 4. combinationibus. </s> | <s><emph type="italics"/>Sunt tres combinationes mobilis cum medio<emph.end type="italics"/>; prima, &longs;i &longs;it idem mobile <lb/>cum diuer&longs;is mediis; &longs;ecunda, &longs;i idem medium cum diuer&longs;is mobilibus; <lb/>tertia &longs;i diuer&longs;a mobïlia cum diuer&longs;is mediis; de primâ actum e&longs;t iam <lb/>&longs;uprà; &longs;ecunda &longs;ube&longs;t 4. combinationibus. </s> |
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| <s>Prima &longs;i mobilia &longs;int eiu&longs;­<lb/>dem materiæ, &longs;ed diuer&longs;æ figuræ; Secunda eiu&longs;dem figuræ & diuer&longs;æ <lb/>materiæ. </s> | <s>Prima &longs;i mobilia &longs;int eiu&longs;­<lb/>dem materiæ, &longs;ed diuer&longs;æ figuræ; Secunda eiu&longs;dem figuræ & diuer&longs;æ <lb/>materiæ. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 105.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 105.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si mobilia duo eiu&longs;dem materiæ, figuræ, & grauitatis in eodem medio de­<lb/>&longs;<gap/>endant, æquali motu feruntur<emph.end type="italics"/> dem. </s> | <s><emph type="italics"/>Si mobilia duo eiu&longs;dem materiæ, figuræ, & grauitatis in eodem medio de­<lb/>&longs;cendant, æquali motu feruntur<emph.end type="italics"/> dem. </s> |
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| <s>vbi e&longs;t eadem proportio cau&longs;æ & re&longs;i­<lb/>&longs;bentiæ ibi e&longs;t idem effectus, per Ax. 5. &longs;ed in hoc ca&longs;u eadem e&longs;t illa pro­<lb/>portio; nam e&longs;t æqualis cau&longs;a, &longs;cilicet grauitas; idem medium æqualiter <lb/>vtrique re&longs;i&longs;tens, cum non plures medij partes re&longs;i&longs;tant vni, quam alteri; <lb/>igitur æqualis proportio. </s></p><p type="main"> | <s>vbi e&longs;t eadem proportio cau&longs;æ & re&longs;i­<lb/>&longs;tentiæ ibi e&longs;t idem effectus, per Ax. 5. &longs;ed in hoc ca&longs;u eadem e&longs;t illa pro­<lb/>portio; nam e&longs;t æqualis cau&longs;a, &longs;cilicet grauitas; idem medium æqualiter <lb/>vtrique re&longs;i&longs;tens, cum non plures medij partes re&longs;i&longs;tant vni, quam alteri; <lb/>igitur æqualis proportio. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 106.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si diuidatur cubus in cubos minores, ratio &longs;uperficierum erit duplicat a la­<lb/>terum, & ratio &longs;olidorum triplicata,<emph.end type="italics"/> con&longs;tat ex Geometria, &longs;it enim cubus </s></p><p type="main"> | <s><emph type="italics"/>Si diuidatur cubus in cubos minores, ratio &longs;uperficierum erit duplicat a la­<lb/>terum, & ratio &longs;olidorum triplicata,<emph.end type="italics"/> con&longs;tat ex Geometria, &longs;it enim cubus </s></p><p type="main"> |
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| <s><arrow.to.target n="note2"/><lb/>GK, nam in gratiam corum qui Geometriam ignorant hoc ip&longs;um ocu­<lb/>lis &longs;ubiiciendum e&longs;&longs;e videtur; diuidantur 6. eius facies in 4. quadrata <lb/>æqualia v. <!-- REMOVE S-->g. <!-- REMOVE S-->facies AI in quad. </s> | <s><arrow.to.target n="note2"/><lb/>GK, nam in gratiam eorum qui Geometriam ignorant hoc ip&longs;um ocu­<lb/>lis &longs;ubiiciendum e&longs;&longs;e videtur; diuidantur 6. eius facies in 4. quadrata <lb/>æqualia v. <!-- REMOVE S-->g. <!-- REMOVE S-->facies AI in quad. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 111.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 111.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc plùs minuitur grauitas, quàm re&longs;i&longs;tentia minoris cubi<emph.end type="italics"/>; quia grauitas <lb/>re&longs;pondet &longs;olido, & re&longs;i&longs;tentia primç facici; re&longs;i&longs;tentia <expan abbr="inquā">inquam</expan> ratione par­<lb/>tium medij; &longs;ed &longs;olidum plus miuuitur quàm facies, vt dictum e&longs;t; igitur <lb/>plus minuitur grauitas, quæ e&longs;t cau&longs;a virium quàm hæc re&longs;i&longs;tentia; crgo <lb/>decre&longs;cunt vires in maiore proportione quàm hæc re&longs;i&longs;tentia, quod be­<lb/>nè ob&longs;eruauit Galileus in dìalogis. </s></p><p type="main"> | <s><emph type="italics"/>Hinc plùs minuitur grauitas, quàm re&longs;i&longs;tentia minoris cubi<emph.end type="italics"/>; quia grauitas <lb/>re&longs;pondet &longs;olido, & re&longs;i&longs;tentia prim&ecedil; faciei; re&longs;i&longs;tentia <expan abbr="inquā">inquam</expan> ratione par­<lb/>tium medij; &longs;ed &longs;olidum plus miuuitur quàm facies, vt dictum e&longs;t; igitur <lb/>plus minuitur grauitas, quæ e&longs;t cau&longs;a virium quàm hæc re&longs;i&longs;tentia; ergo <lb/>decre&longs;cunt vires in maiore proportione quàm hæc re&longs;i&longs;tentia, quod be­<lb/>nè ob&longs;eruauit Galileus in dìalogis. </s></p><p type="main"> |
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| <s>Hinc concludit Galileus duos cubos eiu&longs;dem materiæ, &longs;ed inæquales <lb/>de&longs;cendere inæquali motu; maiorem &longs;cilicet velociùs minori; demon­<lb/>ftrare videtur, quia maior habet maiorem proportionem virium ad re­<lb/>&longs;i&longs;tentiam, quàm minor; igitur maiorem habet effectum per Ax. 5. igi­<lb/>tur maiorem, & velociorem motum. </s></p><p type="main"> | <s>Hinc concludit Galileus duos cubos eiu&longs;dem materiæ, &longs;ed inæquales <lb/>de&longs;cendere inæquali motu; maiorem &longs;cilicet velociùs minori; demon­<lb/>&longs;trare videtur, quia maior habet maiorem proportionem virium ad re­<lb/>&longs;i&longs;tentiam, quàm minor; igitur maiorem habet effectum per Ax. 5. igi­<lb/>tur maiorem, & velociorem motum. </s></p><p type="main"> |
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| <s>Scio non dee&longs;&longs;e multos viros doctos qui acriter in hanc &longs;ententiam <pb xlink:href="026/01/158.jpg" pagenum="126"/>in&longs;urgant: Obiicient fortè primò, experientiam e&longs;&longs;e contrariam; &longs;i enim <lb/>accipiantur duo cubi maior, & minor eiu&longs;dem materiæ, & dimittantur <lb/>ex eadem altitudine codem pror&longs;us momento terram ferient; Re&longs;ponde­<lb/>ri pote&longs;t momentum illud &longs;en&longs;u percipi non po&longs;&longs;e; &longs;i enim dicam ma­<lb/>iorem tangere terram 1000. in&longs;tantibus ante minorem, an fortè &longs;en&longs;u <lb/>hoc percipies, vi&longs;u &longs;cilicet vel auditu? </s> | <s>Scio non dee&longs;&longs;e multos viros doctos qui acriter in hanc &longs;ententiam <pb xlink:href="026/01/158.jpg" pagenum="126"/>in&longs;urgant: Obiicient fortè primò, experientiam e&longs;&longs;e contrariam; &longs;i enim <lb/>accipiantur duo cubi maior, & minor eiu&longs;dem materiæ, & dimittantur <lb/>ex eadem altitudine codem pror&longs;us momento terram ferient; Re&longs;ponde­<lb/>ri pote&longs;t momentum illud &longs;en&longs;u percipi non po&longs;&longs;e; &longs;i enim dicam ma­<lb/>iorem tangere terram 1000. in&longs;tantibus ante minorem, an fortè &longs;en&longs;u <lb/>hoc percipies, vi&longs;u &longs;cilicet vel auditu? </s> |
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| <s>Secundò obiicient, &longs;i &longs;uperponatur cubus minor maiori in &longs;uo motu <lb/>nunquam &longs;eparantur; igitur æquali motu de&longs;cendunt. </s> | <s>Secundò obiicient, &longs;i &longs;uperponatur cubus minor maiori in &longs;uo motu <lb/>nunquam &longs;eparantur; igitur æquali motu de&longs;cendunt. </s> |
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| <s>Re&longs;p. videri po­<lb/>te&longs;t equidem æquali motu de&longs;cendere quia &longs;unt veluti partes ciu&longs;dem <lb/>corporis, & grauitant grauitatione communi, neque minor habet &longs;ingu­<lb/>larem re&longs;i&longs;tentiam &longs;uperandam; immò &longs;i &longs;uperponatur minor maiori, <lb/>vel maior minori, motus e&longs;t velocior quàm e&longs;&longs;et &longs;olius maioris; quia <lb/>cum non &longs;it maior re&longs;i&longs;tentia, maiores illi vires opponuntur; igitur fa­<lb/>ciliùs &longs;uperatur. </s></p><p type="main"> | <s>Re&longs;p. videri po­<lb/>te&longs;t equidem æquali motu de&longs;cendere quia &longs;unt veluti partes eiu&longs;dem <lb/>corporis, & grauitant grauitatione communi, neque minor habet &longs;ingu­<lb/>larem re&longs;i&longs;tentiam &longs;uperandam; immò &longs;i &longs;uperponatur minor maiori, <lb/>vel maior minori, motus e&longs;t velocior quàm e&longs;&longs;et &longs;olius maioris; quia <lb/>cum non &longs;it maior re&longs;i&longs;tentia, maiores illi vires opponuntur; igitur fa­<lb/>ciliùs &longs;uperatur. </s></p><p type="main"> |
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| <s>Tertiò obiicient; e&longs;t eadem &longs;pecie grauitas; igitur eadem grauitatio, <lb/>idemque motus deor&longs;um; Re&longs;ponderi po&longs;&longs;et concedendo antecedens, <lb/>vnde in vacuo omnia grauia æquè velociter de&longs;cenderent, &longs;i in eo mo­<lb/>tus e&longs;&longs;et; at verò altera duarum cau&longs;arum eiu&longs;dem &longs;peciei, quæ habet mi­<lb/>norem proportionem actiuitatis ad re&longs;i&longs;tentiam, profectò minùs agit, <lb/>quod certum e&longs;t. </s></p><p type="main"> | <s>Tertiò obiicient; e&longs;t eadem &longs;pecie grauitas; igitur eadem grauitatio, <lb/>idemque motus deor&longs;um; Re&longs;ponderi po&longs;&longs;et concedendo antecedens, <lb/>vnde in vacuo omnia grauia æquè velociter de&longs;cenderent, &longs;i in eo mo­<lb/>tus e&longs;&longs;et; at verò altera duarum cau&longs;arum eiu&longs;dem &longs;peciei, quæ habet mi­<lb/>norem proportionem actiuitatis ad re&longs;i&longs;tentiam, profectò minùs agit, <lb/>quod certum e&longs;t. </s></p><p type="main"> |
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| <s>igitur obiectiones illæ non cuertunt Gali­<lb/>lei &longs;ententiam. </s></p><p type="main"> | <s>igitur obiectiones illæ non euertunt Gali­<lb/>lei &longs;ententiam. </s></p><p type="main"> |
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| <s>Inde idem Galilcus o&longs;tendere videtur cur atomi materiæ etiam gra­<lb/>ui&longs;&longs;imæ, &longs;eu granula pulueris motu tardi&longs;&longs;imo de&longs;cendant in aëre vel in <lb/>aqua; quia &longs;cilicet per illam diui&longs;ionem ita imminutæ &longs;unt vires graui­<lb/>tatis, vt iam re&longs;i&longs;tentiam medij &longs;uperare non po&longs;&longs;int. </s></p><p type="main"> | <s>Inde idem Galileus o&longs;tendere videtur cur atomi materiæ etiam gra­<lb/>ui&longs;&longs;imæ, &longs;eu granula pulueris motu tardi&longs;&longs;imo de&longs;cendant in aëre vel in <lb/>aqua; quia &longs;cilicet per illam diui&longs;ionem ita imminutæ &longs;unt vires graui­<lb/>tatis, vt iam re&longs;i&longs;tentiam medij &longs;uperare non po&longs;&longs;int. </s></p><p type="main"> |
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| <s>Sed videtur e&longs;&longs;e graui&longs;&longs;ima difficultas, &longs;int enim duo cubi, maior B <lb/>F, minor GM, & vterque innatet medio liquido duplo grauiori; certè ex­<lb/>tabit maior toto rectangulo CA æquali CF, & minor toto rectangulo <lb/>KH æquali KM; igitur e&longs;t eadem proportio grauitatis maioris ad re&longs;i­<lb/>&longs;tentiam medij in grauitatione, quæ e&longs;t minoris; igitur & in motu. </s></p><p type="main"> | <s>Sed videtur e&longs;&longs;e graui&longs;&longs;ima difficultas, &longs;int enim duo cubi, maior B <lb/>F, minor GM, & vterque innatet medio liquido duplo grauiori; certè ex­<lb/>tabit maior toto rectangulo CA æquali CF, & minor toto rectangulo <lb/>KH æquali KM; igitur e&longs;t eadem proportio grauitatis maioris ad re&longs;i­<lb/>&longs;tentiam medij in grauitatione, quæ e&longs;t minoris; igitur & in motu. </s></p><p type="main"> |
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| <s>Vt &longs;olui po&longs;&longs;it præ&longs;ens difficultas, quæ cettè maxima e&longs;t, totam rem <lb/>i&longs;tam paulò fu&longs;iùs e&longs;&longs;e explicandam iudico. </s> | <s>Vt &longs;olui po&longs;&longs;it præ&longs;ens difficultas, quæ cettè maxima e&longs;t, totam rem <lb/>i&longs;tam paulò fu&longs;iùs e&longs;&longs;e explicandam iudico. </s> |
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| <s>Primò itaque certum e&longs;t <lb/>partes medij, quæ prius in fronte erant, retroire; hoc ip&longs;um videmus in <lb/>naui quæ &longs;ulcat aquas, hoc ip&longs;um accidit in omni corpore natante etiam <lb/>immobili, quippe partes aquæ retinentur ab illa membranula, de qua &longs;u­<lb/>prà; &longs;ic enim &longs;æpè a&longs;&longs;urgunt, & intume&longs;cunt &longs;upra labra va&longs;is; cur verò <lb/>continui penè circulares limbi dilatentur: Re&longs;p. nullo flante vento <lb/>vix aliquem circulum huiu&longs;inodi in &longs;uperficie aquæ apparere à fronte, <lb/>&longs;ed tantùm à tergo, & lateribus, qua&longs;i ad in&longs;tar pyramidis; &longs;ed de his aliàs <lb/>fusè. </s></p><p type="main"> | <s>Primò itaque certum e&longs;t <lb/>partes medij, quæ prius in fronte erant, retroire; hoc ip&longs;um videmus in <lb/>naui quæ &longs;ulcat aquas, hoc ip&longs;um accidit in omni corpore natante etiam <lb/>immobili, quippe partes aquæ retinentur ab illa membranula, de qua &longs;u­<lb/>prà; &longs;ic enim &longs;æpè a&longs;&longs;urgunt, & intume&longs;cunt &longs;upra labra va&longs;is; cur verò <lb/>continui penè circulares limbi dilatentur: Re&longs;p. nullo flante vento <lb/>vix aliquem circulum huiu&longs;modi in &longs;uperficie aquæ apparere à fronte, <lb/>&longs;ed tantùm à tergo, & lateribus, qua&longs;i ad in&longs;tar pyramidis; &longs;ed de his aliàs <lb/>fusè. </s></p><p type="main"> |
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| <s>Secundò certum e&longs;t numerum partium, quas impellit maior cubus A <lb/>E; e&longs;&longs;e quadruplum numeri partium, quas impellit cubus BG: &longs;int autem <lb/>v.g.8. partes re&longs;i&longs;tentes cubo maiori, &longs;unt duæ re&longs;i&longs;tentes cubo minoris; <lb/>&longs;ed vires cubi maioris &longs;unt ad vires cubi minoris vt 8. ad 1. igitur vires <lb/>vt 8. &longs;uperabunt faciliùs re&longs;i&longs;tentiam vt 8. quam vires vt 1. re&longs;i&longs;tentiam <lb/>vt 2.vnde duplò velociùs moueretur, ni&longs;i aër duplò velociori motu amo­<lb/>uendus e&longs;&longs;et, quod vt clarius explicetur;</s></p><p type="main"> | <s>Secundò certum e&longs;t numerum partium, quas impellit maior cubus A <lb/>E; e&longs;&longs;e quadruplum numeri partium, quas impellit cubus BG: &longs;int autem <lb/>v.g.8. partes re&longs;i&longs;tentes cubo maiori, &longs;unt duæ re&longs;i&longs;tentes cubo minoris; <lb/>&longs;ed vires cubi maioris &longs;unt ad vires cubi minoris vt 8. ad 1. igitur vires <lb/>vt 8. &longs;uperabunt faciliùs re&longs;i&longs;tentiam vt 8. quam vires vt 1. re&longs;i&longs;tentiam <lb/>vt 2.vnde duplò velociùs moueretur, ni&longs;i aër duplò velociori motu amo­<lb/>uendus e&longs;&longs;et, quod vt clarius explicetur;</s></p><p type="main"> |
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| <s>Sit cubus maior AF octuplus cubi GI, vt iam dictum e&longs;t; haud <lb/>dubiè aër qui &longs;ub&longs;tat cubo AF e&longs;t quadruplus aëris, qui &longs;ub&longs;tat cubo GI, <lb/>vnde &longs;i vires cubi AF e&longs;&longs;ent quadruplæ virium cubi GI, e&longs;&longs;et æqualis <lb/>proportio in vtroque virium, & re&longs;i&longs;tentiæ; &longs;ed &longs;unt octuplæ; igitur faci­<lb/>liùs vincetur re&longs;i&longs;tentia; igitur amouebitur aër faciliùs; &longs;it autem aër <lb/>expre&longs;&longs;us in globulis EFB, &c. </s> | <s>Sit cubus maior AF octuplus cubi GI, vt iam dictum e&longs;t; haud <lb/>dubiè aër qui &longs;ub&longs;tat cubo AF e&longs;t quadruplus aëris, qui &longs;ub&longs;tat cubo GI, <lb/>vnde &longs;i vires cubi AF e&longs;&longs;ent quadruplæ virium cubi GI, e&longs;&longs;et æqualis <lb/>proportio in vtroque virium, & re&longs;i&longs;tentiæ; &longs;ed &longs;unt octuplæ; igitur faci­<lb/>liùs vincetur re&longs;i&longs;tentia; igitur amouebitur aër faciliùs; &longs;it autem aër <lb/>expre&longs;&longs;us in globulis EFB, &c. </s> |
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| <s>cuius &longs;uperficies cum relinquatur retrò <lb/>ver&longs;us AB, & occupetur illa quæ e&longs;t in fronte EF; haud dubiè partes <lb/>hinc inde diuiduntur in D, & fegmentum NB tran&longs;it in locum relicti <lb/>loci BC, FN tran&longs;it in NB, & DF, in FN; idem dico de &longs;egmentis oppo­<lb/>fitis; idem pror&longs;us dico de minori globo; nam MH tran&longs;it in HQ, & H <lb/>Q in QG, & QG in GL, idem dico de &longs;egmentis oppo&longs;itis; igitur hæc <lb/>e&longs;t circuitio partium medij, quàm &longs;uprà indicauimus; hinc aër, qui amo­<lb/>uetur à corpore graui de&longs;cendente moueri debet nece&longs;&longs;ariò velociùs <lb/>quàm ip&longs;um corpus grauc, quod de&longs;cendit. </s></p><p type="main"> | <s>cuius &longs;uperficies cum relinquatur retrò <lb/>ver&longs;us AB, & occupetur illa quæ e&longs;t in fronte EF; haud dubiè partes <lb/>hinc inde diuiduntur in D, & &longs;egmentum NB tran&longs;it in locum relicti <lb/>loci BC, FN tran&longs;it in NB, & DF, in FN; idem dico de &longs;egmentis oppo­<lb/>&longs;itis; idem pror&longs;us dico de minori globo; nam MH tran&longs;it in HQ, & H <lb/>Q in QG, & QG in GL, idem dico de &longs;egmentis oppo&longs;itis; igitur hæc <lb/>e&longs;t circuitio partium medij, quàm &longs;uprà indicauimus; hinc aër, qui amo­<lb/>uetur à corpore graui de&longs;cendente moueri debet nece&longs;&longs;ariò velociùs <lb/>quàm ip&longs;um corpus graue, quod de&longs;cendit. </s></p><p type="main"> |
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| <s>In hoc porrò ob&longs;erua &longs;egmentum MH moueri tardiùs quàm DF; quia <lb/>conficit &longs;ubduplum &longs;patium, eo tempore, quo DF conficit duplum; <pb xlink:href="026/01/160.jpg" pagenum="128"/>nam DF & FN &longs;unt duplæ MH & & <expan abbr="Hq;">Hque</expan> igitur dupla vi motrice opus <lb/>e&longs;t; &longs;ed vires cubi AF &longs;unt ad vires cubi GI, vt 8. ad 1. partes verò aëris, <lb/>quas impellit AF, &longs;unt ad partes aëris, quas impellit GI, vt 4.ad 1. igitur <lb/>&longs;i partes aëris mouerentur æquali motu cum ip&longs;is cubis, à quibus mo­<lb/>uentur; certè maior moueretur motu velociori; vt autem moueantur par­<lb/>tes DF duplò velociore motu, quàm partes MH; debent vires, quæ mo­<lb/>nent DF, e&longs;&longs;e in ratione dupla ad illas, quæ mouent MH, id e&longs;teo tem­<lb/>pore, quo vires vt 8.mouebunt mobile vt 4. motu vt 2. vires vt 1.moue­<lb/>bunt mobile vt 1. motu vt 1. licèt enim &longs;uperficies aëris EF moueatur <lb/>deor&longs;um; attamen ab alio aëere inferiore ita reperlitur, vt &longs;ur&longs;um ver&longs;us <lb/>FN repellatur. </s></p><p type="main"> | <s>In hoc porrò ob&longs;erua &longs;egmentum MH moueri tardiùs quàm DF; quia <lb/>conficit &longs;ubduplum &longs;patium, eo tempore, quo DF conficit duplum; <pb xlink:href="026/01/160.jpg" pagenum="128"/>nam DF & FN &longs;unt duplæ MH & & HQ igitur dupla vi motrice opus <lb/>e&longs;t; &longs;ed vires cubi AF &longs;unt ad vires cubi GI, vt 8. ad 1. partes verò aëris, <lb/>quas impellit AF, &longs;unt ad partes aëris, quas impellit GI, vt 4.ad 1. igitur <lb/>&longs;i partes aëris mouerentur æquali motu cum ip&longs;is cubis, à quibus mo­<lb/>uentur; certè maior moueretur motu velociori; vt autem moueantur par­<lb/>tes DF duplò velociore motu, quàm partes MH; debent vires, quæ mo­<lb/>nent DF, e&longs;&longs;e in ratione dupla ad illas, quæ mouent MH, id e&longs;t eo tem­<lb/>pore, quo vires vt 8.mouebunt mobile vt 4. motu vt 2. vires vt 1.moue­<lb/>bunt mobile vt 1. motu vt 1. licèt enim &longs;uperficies aëris EF moueatur <lb/>deor&longs;um; attamen ab alio aëere inferiore ita repertitur, vt &longs;ur&longs;um ver&longs;us <lb/>FN repellatur. </s></p><p type="main"> |
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| <s>Equidem tota &longs;uperficies aëris DF, cum pluribus partibus con&longs;tet, <lb/>non pote&longs;t &longs;imul tran&longs;ire in FN; quia pars D antequam perueniat ad F <lb/>tran&longs;it per medium DF; igitur &longs;ucce&longs;&longs;iuè permea ad illud &longs;patium DF, <lb/>quo tempore quie&longs;ceret globus AF, quod ridiculum e&longs;t. </s></p><p type="main"> | <s>Equidem tota &longs;uperficies aëris DF, cum pluribus partibus con&longs;tet, <lb/>non pote&longs;t &longs;imul tran&longs;ire in FN; quia pars D antequam perueniat ad F <lb/>tran&longs;it per medium DF; igitur &longs;ucce&longs;&longs;iuè permea ad illud &longs;patium DF, <lb/>quo tempore quie&longs;ceret globus AF, quod ridiculum e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 112.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 112.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Duo cubi eiu&longs;de<emph.end type="italics"/>m <emph type="italics"/>materiæ, & diuer&longs;æ grauitatis æquali motu per &longs;e de&longs;­<lb/>cendunt<emph.end type="italics"/>; probatur, quia licèt &longs;it maior proportio actiuitatis minus ad <lb/>&longs;uam re&longs;i&longs;tentiam, quàm alterius; illud tamen compen&longs;atur; eóque par­<lb/>tes aëris velociùs moueri debeant inxta rationem laterum, vt patet ex <lb/>dictis; vnde nece&longs;&longs;ariò &longs;equitur motus æqualis in vtroque cubo; igitur <lb/>licèt maioris cubi vires habeant maiorem proportionem ad molem, <lb/>quæ præcipuum illius motus retardat; tum tamen aër, qui re&longs;i&longs;tit maiori <lb/>cubo debeat amoueri, vt dictum e&longs;t velociore motu quam aër, qui re&longs;i­<lb/>&longs;tit minori, &longs;itque eadem proportio re&longs;i&longs;tentiæ ratione motus minoris <lb/>ad maiorem, quæ e&longs;t ratione molis maioris ad minorem; certè ratio <lb/>compo&longs;ita vtriu&longs;què erit eadem in vtroque cubo; igitur æquè velociter <lb/>vterque de&longs;cendet: hinc &longs;atís facilè &longs;oluitur ratio Galilci, quam multi <lb/>parum cauti pro demon&longs;tratione venditarunt, ad aliam verò rationem, <lb/>quam ex minuto puluere ducere videtur, etiam facilè re&longs;ponderi pote&longs;t; <lb/>ideo corpu&longs;cula illa diu fluitare in aëre, tùm quòd minimo ferè tenuis <lb/>auræ flatu agitentur; &longs;ic pulueris nubes medius ventus agit; quis enim <lb/>ne&longs;cit aëris partes agitari perpetuò; immò & aquæ inter &longs;e mi&longs;ceri; igi­<lb/>tur ab agitationis veluti impre&longs;&longs;ione fluitant illa corpu&longs;cula, cum mini­<lb/>musferèimpetus extrin&longs;ecus illa commouere po&longs;&longs;it; tùm etiam quòd à <lb/>filamentis illis, quibus partes aëris implicantur facilè detineantur; ana­<lb/>logiam habes in lapillo, qui ab araneæ tela intercipitur. </s></p><pb xlink:href="026/01/161.jpg" pagenum="129"/><p type="main"> | <s><emph type="italics"/>Duo cubi eiu&longs;de<emph.end type="italics"/>m <emph type="italics"/>materiæ, & diuer&longs;æ grauitatis æquali motu per &longs;e de&longs;­<lb/>cendunt<emph.end type="italics"/>; probatur, quia licèt &longs;it maior proportio actiuitatis minus ad <lb/>&longs;uam re&longs;i&longs;tentiam, quàm alterius; illud tamen compen&longs;atur; eóque par­<lb/>tes aëris velociùs moueri debeant iuxta rationem laterum, vt patet ex <lb/>dictis; vnde nece&longs;&longs;ariò &longs;equitur motus æqualis in vtroque cubo; igitur <lb/>licèt maioris cubi vires habeant maiorem proportionem ad molem, <lb/>quæ præcipuum illius motus retardat; tum tamen aër, qui re&longs;i&longs;tit maiori <lb/>cubo debeat amoueri, vt dictum e&longs;t velociore motu quam aër, qui re&longs;i­<lb/>&longs;tit minori, &longs;itque eadem proportio re&longs;i&longs;tentiæ ratione motus minoris <lb/>ad maiorem, quæ e&longs;t ratione molis maioris ad minorem; certè ratio <lb/>compo&longs;ita vtriu&longs;què erit eadem in vtroque cubo; igitur æquè velociter <lb/>vterque de&longs;cendet: hinc &longs;atís facilè &longs;oluitur ratio Galilei, quam multi <lb/>parum cauti pro demon&longs;tratione venditarunt, ad aliam verò rationem, <lb/>quam ex minuto puluere ducere videtur, etiam facilè re&longs;ponderi pote&longs;t; <lb/>ideo corpu&longs;cula illa diu fluitare in aëre, tùm quòd minimo ferè tenuis <lb/>auræ flatu agitentur; &longs;ic pulueris nubes medius ventus agit; quis enim <lb/>ne&longs;cit aëris partes agitari perpetuò; immò & aquæ inter &longs;e mi&longs;ceri; igi­<lb/>tur ab agitationis veluti impre&longs;&longs;ione fluitant illa corpu&longs;cula, cum mini­<lb/>mus ferè impetus extrin&longs;ecus illa commouere po&longs;&longs;it; tùm etiam quòd à <lb/>filamentis illis, quibus partes aëris implicantur facilè detineantur; ana­<lb/>logiam habes in lapillo, qui ab araneæ tela intercipitur. </s></p><pb xlink:href="026/01/161.jpg" pagenum="129"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 113.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 113.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Duo globi eiu&longs;dem materiæ, & diuer&longs;æ diametri de&longs;cendunt etiam æquali <lb/>motu propter eamdem rationem<emph.end type="italics"/>; immò e&longs;t perfectior æqualitas in globis, <lb/>quàm in cubis; quia perfectior fit circuitio, vt con&longs;ideranti patebit; <lb/>hinc globus eiu&longs;dem materiæ, & grauitatis cum cubo de&longs;cendit velociùs <lb/>quia &longs;cilicet aër in de&longs;cen&longs;u globi faciliùs agitur retrò, vt con&longs;tat. </s></p><p type="main"> | <s><emph type="italics"/>Duo globi eiu&longs;dem materiæ, & diuer&longs;æ diametri de&longs;cendunt etiam æquali <lb/>motu propter <expan abbr="eãdem">eandem</expan> rationem<emph.end type="italics"/>; immò e&longs;t perfectior æqualitas in globis, <lb/>quàm in cubis; quia perfectior fit circuitio, vt con&longs;ideranti patebit; <lb/>hinc globus eiu&longs;dem materiæ, & grauitatis cum cubo de&longs;cendit velociùs <lb/>quia &longs;cilicet aër in de&longs;cen&longs;u globi faciliùs agitur retrò, vt con&longs;tat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 114.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 114.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Corpus vtrimque in mucronem de&longs;inens faciliùs adhuc de&longs;cendit, <lb/>quâm globus eiu&longs;dem materiæ<emph.end type="italics"/>; ratio e&longs;t; quia breuiore circuitu partes re­<lb/>trocunt; quippe tunc maxima e&longs;t facilitas in pellendo aëre, qui e&longs;t à fron­<lb/>te mobilis, cum velociùs moueri non debet ip&longs;o mobili; atqui hoc ip­<lb/>&longs;um e&longs;t quod accidit mobili vtrimque aucto; nam linea curua DBA, <lb/>quam percurrit de&longs;criptum mebile, non e&longs;t multò longior; at verò in <lb/>quadrato &longs;uperiori AF maiori e&longs;t duplò; in circulo quidem minor dia­<lb/>meter &longs;emiperipheriæ, &longs;ed non duplò. </s></p><p type="main"> | <s><emph type="italics"/>Corpus vtrimque in mucronem de&longs;inens faciliùs adhuc de&longs;cendit, <lb/>quâm globus eiu&longs;dem materiæ<emph.end type="italics"/>; ratio e&longs;t; quia breuiore circuitu partes re­<lb/>troeunt; quippe tunc maxima e&longs;t facilitas in pellendo aëre, qui e&longs;t à fron­<lb/>te mobilis, cum velociùs moueri non debet ip&longs;o mobili; atqui hoc ip­<lb/>&longs;um e&longs;t quod accidit mobili vtrimque aucto; nam linea curua DBA, <lb/>quam percurrit de&longs;criptum mobile, non e&longs;t multò longior; at verò in <lb/>quadrato &longs;uperiori AF maiori e&longs;t duplò; in circulo quidem minor dia­<lb/>meter &longs;emiperipheriæ, &longs;ed non duplò. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 115.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 115.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Porrò ob&longs;cruabis omne <lb/>corpus difficiliùs pelli per lineam perpendicularem quàm per obliquam; <lb/>hinc globus pellit tantùm vnicum punctum perpendiculariter; idem di­<lb/>co de cono; cylindrus verò vnam lineam, cubus integrum planum. </s></p><p type="main"> | <s>Porrò ob&longs;eruabis omne <lb/>corpus difficiliùs pelli per lineam perpendicularem quàm per obliquam; <lb/>hinc globus pellit tantùm vnicum punctum perpendiculariter; idem di­<lb/>co de cono; cylindrus verò vnam lineam, cubus integrum planum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 116.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 116.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 119.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 119.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Globi otiam inæquales diuer&longs;æ materiæ inæqualiter de&longs;cendunt<emph.end type="italics"/>; quod de­<lb/>mon&longs;tro; quia globi ciu&longs;dem materiæ inæqualiter de&longs;cendunt per Th. <!-- REMOVE S--><lb/>113. &longs;ed duo globi æquales diuer&longs;æ materiæ de&longs;cendunt inæqualiter per <lb/>Th.118. igitur, & inæquales; quod dico de globis', dicatur de cubis, & <lb/>aliis figuris &longs;imilibus. </s> | <s><emph type="italics"/>Globi otiam inæquales diuer&longs;æ materiæ inæqualiter de&longs;cendunt<emph.end type="italics"/>; quod de­<lb/>mon&longs;tro; quia globi eiu&longs;dem materiæ inæqualiter de&longs;cendunt per Th. <!-- REMOVE S--><lb/>113. &longs;ed duo globi æquales diuer&longs;æ materiæ de&longs;cendunt inæqualiter per <lb/>Th.118. igitur, & inæquales; quod dico de globis', dicatur de cubis, & <lb/>aliis figuris &longs;imilibus. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 122.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 122.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Globi æquales diuer&longs;æ materiæ,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->ligneus, & plumbeus de&longs;cendunt <lb/>mæqualiter iuxta proportionem grauitatis, & re&longs;i&longs;tentiæ medij compa­<lb/>ratæ cum vtroque, v.g. <!-- REMOVE S-->plumbo detrahitur (1/4800); ligno verò (8/300) v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>grauitas ligni &longs;it ad grauitatem aëris vt 300.ad 1. & plumbi vt 4800. ad <lb/>1. &longs;it enim altitudo 33. pedum 4. digit. </s> | <s><emph type="italics"/>Globi æquales diuer&longs;æ materiæ,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->ligneus, & plumbeus de&longs;cendunt <lb/>inæqualiter iuxta proportionem grauitatis, & re&longs;i&longs;tentiæ medij compa­<lb/>ratæ cum vtroque, v.g. <!-- REMOVE S-->plumbo detrahitur (1/4800); ligno verò (8/300) v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i <lb/>grauitas ligni &longs;it ad grauitatem aëris vt 300.ad 1. & plumbi vt 4800. ad <lb/>1. &longs;it enim altitudo 33. pedum 4. digit. </s> |
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| <s>reducantur in digitos erunt 400. <lb/>in lineas 4800. igitur detrahetur vna linea &longs;patij plumbeo globo; ligneo­<lb/>verò vnus digitus cum 4. lineis; &longs;ed quis hoc ob&longs;eruet? </s></p><p type="main"> | <s>reducantur in digitos erunt 400. <lb/>in lineas 4800. igitur detrahetur vna linea &longs;patij plumbeo globo; ligneo <lb/>verò vnus digitus cum 4. lineis; &longs;ed quis hoc ob&longs;eruet? </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 123.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 123.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ex his con&longs;tat quid dicendum &longs;it de motu corporum grauium in <lb/>medio, &longs;iue &longs;int eiu&longs;dem maieriæ, & &longs;imilis figuræ, maioris vel minoris, <lb/>vel æqualis; tunc enim de&longs;cendunt æqualiter contra Galileum, &longs;iue <lb/>&longs;int diuer&longs;æ materiæ, & &longs;imilis figuræ, æqualis, vel inæqualis, <pb xlink:href="026/01/163.jpg" pagenum="131"/>tunc enim de&longs;cendunt inæqualiter, &longs;iue diuer&longs;æ materiæ & diuer&longs;æ fi­<lb/>guræ; tunc enim de&longs;cendunt modò æqualiter, modò inæqualiter; æquali­<lb/>ter certè, cum figura compen&longs;at materiam; cum verò non compen&longs;at, <lb/>inæqualiter pro rata; denique &longs;i comparentur duo corpora cum diuer&longs;is <lb/>mediis; primo inuenienda e&longs;t proportio motuum vtriu&longs;que in eodem <lb/>tùm &longs;ingulorum in diuer&longs;is mediis, vt &longs;uprà dictum e&longs;t. </s></p><p type="main"> | <s>Ex his con&longs;tat quid dicendum &longs;it de motu corporum grauium in <lb/>medio, &longs;iue &longs;int eiu&longs;dem materiæ, & &longs;imilis figuræ, maioris vel minoris, <lb/>vel æqualis; tunc enim de&longs;cendunt æqualiter contra Galileum, &longs;iue <lb/>&longs;int diuer&longs;æ materiæ, & &longs;imilis figuræ, æqualis, vel inæqualis, <pb xlink:href="026/01/163.jpg" pagenum="131"/>tunc enim de&longs;cendunt inæqualiter, &longs;iue diuer&longs;æ materiæ & diuer&longs;æ fi­<lb/>guræ; tunc enim de&longs;cendunt modò æqualiter, modò inæqualiter; æquali­<lb/>ter certè, cum figura compen&longs;at materiam; cum verò non compen&longs;at, <lb/>inæqualiter pro rata; denique &longs;i comparentur duo corpora cum diuer&longs;is <lb/>mediis; primo inuenienda e&longs;t proportio motuum vtriu&longs;que in eodem <lb/>tùm &longs;ingulorum in diuer&longs;is mediis, vt &longs;uprà dictum e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 124.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 124.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 130.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 130.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si cre&longs;cit re&longs;i&longs;tentia in eadem ratione in qua cre&longs;cunt vires, non mutatur <lb/>progre&longs;&longs;io effectuum.<emph.end type="italics"/> v.g. <!-- REMOVE S-->primo in&longs;tanti impetus &longs;it vt 1.&longs;itque 1.&longs;patium, <lb/>in quo e&longs;t re&longs;i&longs;tentia, vt 1. Secundo in&longs;tanti &longs;it impetus vt 2. re&longs;i&longs;tentia in <lb/>2. &longs;patiis vt 2. haud dubiè &longs;i vno in&longs;tanti vnus gradus impetus &longs;uperat <lb/>re&longs;i&longs;tentiam vt 1. dum percurrit 1.&longs;patium; certè 2. gradus impetus vno <lb/>in&longs;tanti &longs;uperabunt re&longs;i&longs;tentiam vt 2. dum con&longs;icit mobile 2. &longs;patia; at­<lb/>que ita deinceps. </s> | <s><emph type="italics"/>Si cre&longs;cit re&longs;i&longs;tentia in eadem ratione in qua cre&longs;cunt vires, non mutatur <lb/>progre&longs;&longs;io effectuum.<emph.end type="italics"/> v.g. <!-- REMOVE S-->primo in&longs;tanti impetus &longs;it vt 1.&longs;itque 1.&longs;patium, <lb/>in quo e&longs;t re&longs;i&longs;tentia, vt 1. Secundo in&longs;tanti &longs;it impetus vt 2. re&longs;i&longs;tentia in <lb/>2. &longs;patiis vt 2. haud dubiè &longs;i vno in&longs;tanti vnus gradus impetus &longs;uperat <lb/>re&longs;i&longs;tentiam vt 1. dum percurrit 1.&longs;patium; certè 2. gradus impetus vno <lb/>in&longs;tanti &longs;uperabunt re&longs;i&longs;tentiam vt 2. dum conficit mobile 2. &longs;patia; at­<lb/>que ita deinceps. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="italics"/>MOtus violentus e&longs;t, quo corpus graue mouetur &longs;ursùm per li­<lb/>neam verticalem à principio extrin&longs;eco mediatè, vel immediatè vt <lb/>plurimùm.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>MOtus violentus e&longs;t, quo corpus graue mouetur &longs;ursùm per li­<lb/>neam verticalem à principio extrin&longs;eco mediatè, vel immediatè vt <lb/>plurimùm.<emph.end type="italics"/></s></p><p type="main"> |
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| <s>Dixi à principio extrin&longs;eco, &longs;iue cunjuncto, vt cum manu attollo &longs;ur­<lb/>&longs;um corpus graue, &longs;iue non conjuncto, vt cum quis proiicit lapidem &longs;ur­<lb/>sùm, &longs;iue &longs;it verum principium effectiuum, vt cum impetus, quem poten­<lb/>tia motrix producit in manu, producit alium in mobili; &longs;iue non &longs;it <lb/>principium effectiuum, &longs;ed tantùm determinans, vt cum mobilc quod <lb/>cadit deor&longs;um, &longs;ur&longs;um deinde repercutitur; nec enim corpus repercu­<lb/>tiens producit impetum nouum, vt dicemus cum de motu re&longs;lexo; quin <lb/>potiùs producti partem de&longs;truit per accidens, & quidquid illius &longs;upere&longs;t, <lb/>ad nouam lineam determinat; quod quomodo fiat fusè &longs;uo loco expli­<lb/>cabimus, igitur licèt corpus reflectens &longs;it tantùm principium nouæ de­<lb/>terminationis, non verò alicuius impetus producti, dici pote&longs;t princi­<lb/>pium huius motus violenti. </s></p><p type="main"> | <s>Dixi à principio extrin&longs;eco, &longs;iue cunjuncto, vt cum manu attollo &longs;ur­<lb/>&longs;um corpus graue, &longs;iue non conjuncto, vt cum quis proiicit lapidem &longs;ur­<lb/>sùm, &longs;iue &longs;it verum principium effectiuum, vt cum impetus, quem poten­<lb/>tia motrix producit in manu, producit alium in mobili; &longs;iue non &longs;it <lb/>principium effectiuum, &longs;ed tantùm determinans, vt cum mobile quod <lb/>cadit deor&longs;um, &longs;ur&longs;um deinde repercutitur; nec enim corpus repercu­<lb/>tiens producit impetum nouum, vt dicemus cum de motu reflexo; quin <lb/>potiùs producti partem de&longs;truit per accidens, & quidquid illius &longs;upere&longs;t, <lb/>ad nouam lineam determinat; quod quomodo fiat fusè &longs;uo loco expli­<lb/>cabimus, igitur licèt corpus reflectens &longs;it tantùm principium nouæ de­<lb/>terminationis, non verò alicuius impetus producti, dici pote&longs;t princi­<lb/>pium huius motus violenti. </s></p><p type="main"> |
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| <s>Dixi vt plurimùm, nam &longs;i terra ducto per centrum foramine e&longs;&longs;et <lb/>peruia, haud dubiè lapis demi&longs;&longs;us versùs centrum iret motu naturaliter <pb xlink:href="026/01/166.jpg" pagenum="134"/>accelerato, tùm deinde propter impetus acqui&longs;iti vim, à centro versùs <lb/>oppo&longs;itum circumferentiæ punctum iret, motu certè violento, qui ta­<lb/>men ab extrin&longs;eco non e&longs;&longs;et. </s></p><p type="main"> | <s>Dixi vt plurimùm, nam &longs;i terra ducto per centrum foramine e&longs;&longs;et <lb/>peruia, haud dubiè lapis demi&longs;&longs;us versùs centrum iret motu naturaliter <pb xlink:href="026/01/166.jpg" pagenum="134"/>accelerato, tùm deinde propter impetus acqui&longs;iti vim, à centro versùs <lb/>oppo&longs;itum circumferentiæ punctum iret, motu certè violento, qui ta­<lb/>men ab extrin&longs;eco non e&longs;&longs;et. </s></p><p type="main"> |
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| <s>1. nam reuera non &longs;emper mo­<lb/>uetur. </s></p><p type="main"> | <s>1. nam reuera non &longs;emper mo­<lb/>uetur. </s></p><p type="main"> |
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| <s>Diceret fortè alius excitari quædam corpu&longs;cula, à quibus mouetur <lb/>corpus graue &longs;ursùm; &longs;ed contrà; nam vel &longs;unt in ip&longs;o mobili illa cor­<lb/>pu&longs;cula, vel extra mobile; &longs;i primum; igitur hic motus &longs;emper crit ab <lb/>extrin&longs;eco mediatè, cum ab extrin&longs;eco excitentur; &longs;ed hoc &longs;ufficit ad <lb/>hoc; vt motus dicatur violentus per def. </s> | <s>Diceret fortè alius excitari quædam corpu&longs;cula, à quibus mouetur <lb/>corpus graue &longs;ursùm; &longs;ed contrà; nam vel &longs;unt in ip&longs;o mobili illa cor­<lb/>pu&longs;cula, vel extra mobile; &longs;i primum; igitur hic motus &longs;emper erit ab <lb/>extrin&longs;eco mediatè, cum ab extrin&longs;eco excitentur; &longs;ed hoc &longs;ufficit ad <lb/>hoc; vt motus dicatur violentus per def. </s> |
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| <s>1. &longs;i verò &longs;unt extra mobile; <lb/>igitur motus ille e&longs;t &longs;emper ab extrin&longs;eco, idque duplici nomine. </s></p><p type="main"> | <s>1. &longs;i verò &longs;unt extra mobile; <lb/>igitur motus ille e&longs;t &longs;emper ab extrin&longs;eco, idque duplici nomine. </s></p><p type="main"> |
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| <s><lb/>quæ porrò fabulæ, quæ commenta, quæ &longs;omnia excogitari po&longs;&longs;unt, quæ <lb/>non vile&longs;cant &longs;i cum his comparentur. </s></p><p type="main"> | <s><lb/>quæ porrò fabulæ, quæ commenta, quæ &longs;omnia excogitari po&longs;&longs;unt, quæ <lb/>non vile&longs;cant &longs;i cum his comparentur. </s></p><p type="main"> |
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| <s>Illa quoqne corpu&longs;cula excitata leuiora &longs;unt, quàm vt aliquod præfe­<lb/>rant rationis momentum; cum mera &longs;int philo&longs;ophiæ ludibria. </s></p><p type="main"> | <s>Illa quoque corpu&longs;cula excitata leuiora &longs;unt, quàm vt aliquod præfe­<lb/>rant rationis momentum; cum mera &longs;int philo&longs;ophiæ ludibria. </s></p><p type="main"> |
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| <s>Denique illa hypothe&longs;is de terræ motu nullis demon&longs;trationibus fir­<lb/>mata e&longs;t, vt videbimus &longs;uo loco. </s></p><p type="main"> | <s>Denique illa hypothe&longs;is de terræ motu nullis demon&longs;trationibus fir­<lb/>mata e&longs;t, vt videbimus &longs;uo loco. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Motus violentus habet caufam<emph.end type="italics"/>; quia de nouo e&longs;t, & tandem de&longs;init per <lb/>hypoth. </s> | <s><emph type="italics"/>Motus violentus habet cau&longs;am<emph.end type="italics"/>; quia de nouo e&longs;t, & tandem de&longs;init per <lb/>hypoth. </s> |
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| <s>1. igitur habet cau&longs;am per Ax.8.l.1. </s></p><p type="main"> | <s>1. igitur habet cau&longs;am per Ax.8.l.1. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Vt &longs;it motus violentus debent produci plures partes impetus violenti <lb/>quàm &longs;int partes impetus naturalis<emph.end type="italics"/>; Probatur, quia &longs;i e&longs;&longs;ent plures natura­<lb/>lis deorsùm, quàm &longs;int vielenti &longs;ur&longs;um, corpus tenderet deor&longs;um; &longs;ed <lb/>tardiùs per Th.134.l.1. & &longs;i tot e&longs;&longs;ent vnius, quot alterius, mobile ip&longs;um <lb/>non moueretur per Th.133.l.1. </s></p><p type="main"> | <s><emph type="italics"/>Vt &longs;it motus violentus debent produci plures partes impetus violenti <lb/>quàm &longs;int partes impetus naturalis<emph.end type="italics"/>; Probatur, quia &longs;i e&longs;&longs;ent plures natura­<lb/>lis deorsùm, quàm &longs;int violenti &longs;ur&longs;um, corpus tenderet deor&longs;um; &longs;ed <lb/>tardiùs per Th.134.l.1. & &longs;i tot e&longs;&longs;ent vnius, quot alterius, mobile ip&longs;um <lb/>non moueretur per Th.133.l.1. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Tertiò, globus &longs;ursùm projectus <lb/>a&longs;cendit, & deinde de&longs;cendit æquali tempore; igitur &longs;altem &longs;ingulis in­<lb/>&longs;tantibus de&longs;truitur vnus gradus impetus violenti æqualis primo gradui <lb/>innato; atqui aër non pote&longs;t vno in&longs;tanti de&longs;truere impetum æqualem <lb/>primo innato; alioqui non intenderetur motus naturalis. </s> | <s>Tertiò, globus &longs;ursùm projectus <lb/>a&longs;cendit, & deinde de&longs;cendit æquali tempore; igitur &longs;altem &longs;ingulis in­<lb/>&longs;tantibus de&longs;truitur vnus gradus impetus violenti æqualis primo gradui <lb/>innato; atqui aër non pote&longs;t vno in&longs;tanti de&longs;truere impetum æqualem <lb/>primo innato; alioqui non intenderetur motus naturalis. </s> |
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| <s>Quartò, & hæc <lb/>e&longs;t ratio à priori, quotie&longs;cumque &longs;unt in eodem mobili duo impetus ad <lb/>oppo&longs;itas lineas determinati, pugnant pro rata, vt demon&longs;trauimus l.1. <lb/>Th. 149. 150. 152. & in toto Schol. <!-- REMOVE S-->& multis aliis pa&longs;&longs;im; atqui con&longs;er­<lb/>natur &longs;emper impetus naturalis innatus per Sch. <!-- REMOVE S-->Th.152.n.6.l.1.per Th. <!-- REMOVE S--><lb/>9. & Schol.Th.14. & Th.73.l.2. </s> | <s>Quartò, & hæc <lb/>e&longs;t ratio à priori, quotie&longs;cumque &longs;unt in eodem mobili duo impetus ad <lb/>oppo&longs;itas lineas determinati, pugnant pro rata, vt demon&longs;trauimus l.1. <lb/>Th. 149. 150. 152. & in toto Schol. <!-- REMOVE S-->& multis aliis pa&longs;&longs;im; atqui con&longs;er­<lb/>uatur &longs;emper impetus naturalis innatus per Sch. <!-- REMOVE S-->Th.152.n.6.l.1.per Th. <!-- REMOVE S--><lb/>9. & Schol.Th.14. & Th.73.l.2. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 21.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Illa cau&longs;a non e&longs;t eutitas corporis mobilis, vel ip&longs;a grauitas, di&longs;tincta &longs;cili­<lb/>cet ab impetu muato&longs;i quæ e&longs;t de quæ alias,<emph.end type="italics"/> probatur, quia non e&longs;&longs;et potior <lb/>ratiocur vno in&longs;tanti de&longs;truerentur duo gradus impetus, quàm 3. 4. 5. <lb/>quippe grauitas exigeret de&longs;tructionem omnium: præterea omnis impe­<lb/>tus de&longs;truitur ne &longs;it fru&longs;trà per Schol, Th.152. & Th.162.l.1. denique &longs;i <pb xlink:href="026/01/171.jpg" pagenum="139"/>ade&longs;t contrarius impetus de&longs;tructiuus eo modo, quo explicuimus l. <!-- REMOVE S-->1. non <lb/>e&longs;t ponenda alia cau&longs;a de&longs;tructiua. </s> | <s><emph type="italics"/>Illa cau&longs;a non e&longs;t entitas corporis mobilis, vel ip&longs;a grauitas, di&longs;tincta &longs;cili­<lb/>cet ab impetu muato&longs;i quæ e&longs;t de quæ alias,<emph.end type="italics"/> probatur, quia non e&longs;&longs;et potior <lb/>ratiocur vno in&longs;tanti de&longs;truerentur duo gradus impetus, quàm 3. 4. 5. <lb/>quippe grauitas exigeret de&longs;tructionem omnium: præterea omnis impe­<lb/>tus de&longs;truitur ne &longs;it fru&longs;trà per Schol, Th.152. & Th.162.l.1. denique &longs;i <pb xlink:href="026/01/171.jpg" pagenum="139"/>ade&longs;t contrarius impetus de&longs;tructiuus eo modo, quo explicuimus l. <!-- REMOVE S-->1. non <lb/>e&longs;t ponenda alia cau&longs;a de&longs;tructiua. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>certè cum impetus innatus pugnet cum vio­<lb/>lento pro rata; nec &longs;it potior ratio cur maiorem portionem quàm mino­<lb/>rem de&longs;truat, æqualem certè de&longs;truit, itemque &longs;ecundo in&longs;tanti æqua­<lb/>lem, item tertio, quarto; igitur in eadem proportione decre&longs;cit violentus, <lb/>&longs;eu retardatur, in qua naturalis acceleratur. </s></p><pb xlink:href="026/01/172.jpg" pagenum="140"/><p type="main"> | <s>certè cum impetus innatus pugnet cum vio­<lb/>lento pro rata; nec &longs;it potior ratio cur maiorem portionem quàm mino­<lb/>rem de&longs;truat, æqualem certè de&longs;truit, itemque &longs;ecundo in&longs;tanti æqua­<lb/>lem, item tertio, quarto; igitur in eadem proportione decre&longs;cit violentus, <lb/>&longs;eu retardatur, in qua naturalis acceleratur. </s></p><pb xlink:href="026/01/172.jpg" pagenum="140"/><p type="main"> |
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| <s>Hinc inuertenda e&longs;t progre&longs;&longs;ionis linca; quippe linea AE repræ&longs;en­<lb/>tat nobis progre&longs;&longs;ionem motus accelerati, quæ fit in in&longs;tantibus, & li­<lb/>nea FK progre&longs;&longs;ionem motus, quæ fit in partibus temporis &longs;en&longs;ibilibus; <lb/>in illa primo in&longs;tanti decurritur primum &longs;patium AB, &longs;ecundo tempore <lb/>æquali BC, tertio CD, quarto DE: in hac vero prima parte acquiritur <lb/>&longs;patium FG &longs;ecunda æquali primæ GH, tertia HI, quarta IK; igitur &longs;i ac­<lb/>cipiatur linea AE, progrediendo ab A ver&longs;us E, vel linea FK progre­<lb/>diendo ab F ver&longs;us K habebitur progre&longs;&longs;io motus naturaliter acceletati; <lb/>&longs;i verò accipiatur EA, vel KF, progrediendo &longs;cilicet ab E ver&longs;us A, vel à <lb/>K ver&longs;us F, erit progre&longs;&longs;io motus violenti naturaliter retardati; vt con­<lb/>&longs;tat ex præcedèatibus Theorematis; & quemadmodum progre&longs;&longs;io acce­<lb/>lerationis in in&longs;tantibus finitis fit iuxta &longs;eriem i&longs;torum numerorum 1.2. <lb/>3.4. in partibus verò temporis &longs;en&longs;ibilibus iuxta &longs;eriem i&longs;torum 1.3.5.7. <lb/>ita fit omninò progre&longs;&longs;io retardationis in in&longs;tantibus iuxta hos nume­<lb/>ros 4.3.2.1. in partibus temperis &longs;en&longs;ibilibus iuxta hos 7.5. 3. 1. <!-- KEEP S--></s></p><p type="main"> | <s>Hinc inuertenda e&longs;t progre&longs;&longs;ionis linea; quippe linea AE repræ&longs;en­<lb/>tat nobis progre&longs;&longs;ionem motus accelerati, quæ fit in in&longs;tantibus, & li­<lb/>nea FK progre&longs;&longs;ionem motus, quæ fit in partibus temporis &longs;en&longs;ibilibus; <lb/>in illa primo in&longs;tanti decurritur primum &longs;patium AB, &longs;ecundo tempore <lb/>æquali BC, tertio CD, quarto DE: in hac vero prima parte acquiritur <lb/>&longs;patium FG &longs;ecunda æquali primæ GH, tertia HI, quarta IK; igitur &longs;i ac­<lb/>cipiatur linea AE, progrediendo ab A ver&longs;us E, vel linea FK progre­<lb/>diendo ab F ver&longs;us K habebitur progre&longs;&longs;io motus naturaliter accelerati; <lb/>&longs;i verò accipiatur EA, vel KF, progrediendo &longs;cilicet ab E ver&longs;us A, vel à <lb/>K ver&longs;us F, erit progre&longs;&longs;io motus violenti naturaliter retardati; vt con­<lb/>&longs;tat ex præcedèntibus Theorematis; & quemadmodum progre&longs;&longs;io acce­<lb/>lerationis in in&longs;tantibus finitis fit iuxta &longs;eriem i&longs;torum numerorum 1.2. <lb/>3.4. in partibus verò temporis &longs;en&longs;ibilibus iuxta &longs;eriem i&longs;torum 1.3.5.7. <lb/>ita fit omninò progre&longs;&longs;io retardationis in in&longs;tantibus iuxta hos nume­<lb/>ros 4.3.2.1. in partibus temporis &longs;en&longs;ibilibus iuxta hos 7.5. 3. 1. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 28.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 29.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si accipiantur &longs;patia æqualiain hac progre&longs;&longs;ione retardationis, e&longs;t inuer&longs;a <lb/>illius, quàm tribuimus &longs;uprà acceberationi, a&longs;&longs;umptis &longs;cilicet &longs;patiis æqualibus; <lb/>tiem &longs;i accipiantur &longs;patia æqualia prime &longs;patie quod decurritur prime in&longs;tan­<lb/>ti metus naturalis, tum &longs;i accipiantur &longs;patia æqualia date &longs;patie quod in par­<lb/>te temporis &longs;en&longs;ibili percurritur<emph.end type="italics"/>; quippe quemadmodum in progre&longs;&longs;ione <lb/>accelerationis decre&longs;cunt tempora; &longs;ic in progre&longs;&longs;ione retardationis <lb/>cre&longs;cunt, a&longs;&longs;umptis &longs;cilicet &longs;patiis æqualibus; quare ne iam dicta hic re­<lb/>petam, con&longs;ule quæ diximus lib.2. de hac progre&longs;&longs;ione. </s></p><p type="main"> | <s><emph type="italics"/>Si accipiantur &longs;patia æqualia in hac progre&longs;&longs;ione retardationis, e&longs;t inuer&longs;a <lb/>illius, quàm tribuimus &longs;uprà accelerationi, a&longs;&longs;umptis &longs;cilicet &longs;patiis æqualibus; <lb/>tum &longs;i accipiantur &longs;patia æqualia prime &longs;patie quod decurritur prime in&longs;tan­<lb/>ti metus naturalis, tum &longs;i accipiantur &longs;patia æqualia date &longs;patie quod in par­<lb/>te temporis &longs;en&longs;ibili percurritur<emph.end type="italics"/>; quippe quemadmodum in progre&longs;&longs;ione <lb/>accelerationis decre&longs;cunt tempora; &longs;ic in progre&longs;&longs;ione retardationis <lb/>cre&longs;cunt, a&longs;&longs;umptis &longs;cilicet &longs;patiis æqualibus; quare ne iam dicta hic re­<lb/>petam, con&longs;ule quæ diximus lib.2. de hac progre&longs;&longs;ione. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 30.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc instantia initio huius metus &longs;unt minora &longs;icut initio met menatur alis <lb/>&longs;unt maiora; & &longs;ub finem in motu violente &longs;unt maiora, in naturali &longs;unt mi­<lb/>nora<emph.end type="italics"/>; quia &longs;cilicet hic acceleratur, ille retardatur: igitur velo­<lb/>catas accelerati cre&longs;cit; igitur &longs;i accipiantur &longs;patia æqualia, decre&longs;cit tem­<lb/>pus; at verò velocitas retardati decre&longs;cit, igitur a&longs;&longs;umptis &longs;patiis æquali­<lb/>bus, cre&longs;cit tempus; igitur &longs;i accipiatur &longs;patium, quod percurritur primo <lb/>in&longs;tanti huius motus, & deinde alia huic æqualia; haud dubiè, cum &longs;e­<lb/>cundo in&longs;tanti motus &longs;it tardior, &longs;itque a&longs;&longs;umptum æquale &longs;patium; haud <lb/>dubiè inquam in&longs;tans &longs;ecundum erit maius primo, & tertium &longs;ecundo, <lb/>atque ita deinceps. </s></p><pb xlink:href="026/01/173.jpg" pagenum="141"/><p type="main"> | <s><emph type="italics"/>Hinc instantia initio huius metus &longs;unt minora &longs;icut initio motus naturalis <lb/>&longs;unt maiora; & &longs;ub finem in motu violente &longs;unt maiora, in naturali &longs;unt mi­<lb/>nora<emph.end type="italics"/>; quia &longs;cilicet hic acceleratur, ille retardatur: igitur velo­<lb/>citas accelerati cre&longs;cit; igitur &longs;i accipiantur &longs;patia æqualia, decre&longs;cit tem­<lb/>pus; at verò velocitas retardati decre&longs;cit, igitur a&longs;&longs;umptis &longs;patiis æquali­<lb/>bus, cre&longs;cit tempus; igitur &longs;i accipiatur &longs;patium, quod percurritur primo <lb/>in&longs;tanti huius motus, & deinde alia huic æqualia; haud dubiè, cum &longs;e­<lb/>cundo in&longs;tanti motus &longs;it tardior, &longs;itque a&longs;&longs;umptum æquale &longs;patium; haud <lb/>dubiè inquam in&longs;tans &longs;ecundum erit maius primo, & tertium &longs;ecundo, <lb/>atque ita deinceps. </s></p><pb xlink:href="026/01/173.jpg" pagenum="141"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 31.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Re&longs;pondeo negando; quia primo in&longs;tanti, quo <lb/>e&longs;t impetus, non e&longs;t motus per Th.34.l.1. <!-- KEEP S--></s></p><p type="main"> | <s>Re&longs;pondeo negando; quia primo in&longs;tanti, quo <lb/>e&longs;t impetus, non e&longs;t motus per Th.34.l.1. <!-- KEEP S--></s></p><p type="main"> |
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| <s>Dices, igitur impetus ille e&longs;t fru&longs;trà, quia nullus effectus, &longs;eu motus <lb/>ex eo &longs;equitur; Re&longs;pondeo negando; nam omnes gradus impetus qui ci­<lb/>dem parti mobilis in&longs;unt, communi qua&longs;i actione, vel exigentia indi­<lb/>ui&longs;ibiliter exigunt motum. </s></p><p type="main"> | <s>Dices, igitur impetus ille e&longs;t fru&longs;trà, quia nullus effectus, &longs;eu motus <lb/>ex eo &longs;equitur; Re&longs;pondeo negando; nam omnes gradus impetus qui ei­<lb/>dem parti mobilis in&longs;unt, communi qua&longs;i actione, vel exigentia indi­<lb/>ui&longs;ibiliter exigunt motum. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 32.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 33.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 33.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc redditur optima ratio, cur tot producantur potiùs quàm plures, quæ <lb/>alioquin minimè afferri pote&longs;t<emph.end type="italics"/>; immò, ni&longs;i hoc e&longs;&longs;et, nulla e&longs;&longs;et huiu&longs;modi <lb/>naturalis retardatio; nam producantut, &longs;i fieri pote&longs;t, omnes æquales, &longs;int­<lb/>que v.g.20. nunquid po&longs;&longs;unt e&longs;&longs;e 40. perfectionis &longs;ubduplæ, vel 10. du­<lb/>plæ, vel 5. quadruplæ &c. </s> | <s><emph type="italics"/>Hinc redditur optima ratio, cur tot producantur potiùs quàm plures, quæ <lb/>alioquin minimè afferri pote&longs;t<emph.end type="italics"/>; immò, ni&longs;i hoc e&longs;&longs;et, nulla e&longs;&longs;et huiu&longs;modi <lb/>naturalis retardatio; nam producantur, &longs;i fieri pote&longs;t, omnes æquales, &longs;int­<lb/>que v.g.20. nunquid po&longs;&longs;unt e&longs;&longs;e 40. perfectionis &longs;ubduplæ, vel 10. du­<lb/>plæ, vel 5. quadruplæ &c. </s> |
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| <s>cur autem potiùs vnum dices quàm aliud? </s> | <s>cur autem potiùs vnum dices quàm aliud? </s> |
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| <s><emph type="italics"/>Hinc &longs;unt inæquales in eâdem proportione, in quæ in&longs;tantia &longs;unt inæqualia<emph.end type="italics"/><lb/>v. </s> | <s><emph type="italics"/>Hinc &longs;unt inæquales in eâdem proportione, in quæ in&longs;tantia &longs;unt inæqualia<emph.end type="italics"/><lb/>v. </s> |
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| <s>g. <!-- REMOVE S-->quà proportione primum in&longs;tans e&longs;t minus &longs;ecundo, & &longs;ecundum <lb/>tertio, ita ille gradus impetus, qui de&longs;truitur primo in&longs;tanti, e&longs;t minor <lb/>vel imperfectior co, qui de&longs;truitur &longs;ecundo, & qui de&longs;truitur &longs;ecundo <lb/>imperfectior co, qui de&longs;truitut tertio, atque ita deinceps. </s> | <s>g. <!-- REMOVE S-->quà proportione primum in&longs;tans e&longs;t minus &longs;ecundo, & &longs;ecundum <lb/>tertio, ita ille gradus impetus, qui de&longs;truitur primo in&longs;tanti, e&longs;t minor <lb/>vel imperfectior co, qui de&longs;truitur &longs;ecundo, & qui de&longs;truitur &longs;ecundo <lb/>imperfectior co, qui de&longs;truitur tertio, atque ita deinceps. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 35.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc perfecti&longs;&longs;imus omnium gruduum ille e&longs;t qui de&longs;truitur vltimo in&longs;tan­<lb/>ti, de quo infrá<emph.end type="italics"/>; quod &longs;equitur ex dictis nece&longs;&longs;ariò: vtrùm verò ille &longs;it æ­<lb/>qualis omninò in perfectione impetui naturali innato, dicemus <lb/>infrà. </s></p><p type="main"> | <s><emph type="italics"/>Hinc perfecti&longs;&longs;imus omnium graduum ille e&longs;t qui de&longs;truitur vltimo in&longs;tan­<lb/>ti, de quo infrá<emph.end type="italics"/>; quod &longs;equitur ex dictis nece&longs;&longs;ariò: vtrùm verò ille &longs;it æ­<lb/>qualis omninò in perfectione impetui naturali innato, dicemus <lb/>infrà. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Hic ob&longs;eruabis mirabilem &longs;anæ naturæ prouidentiam, quæ motus <lb/>omnes cum ip&longs;o naturali ita compo&longs;uit, vt &longs;it veluti regula omnium mo­<lb/>taum, &longs;itque vnum qua&longs;i principium perfectionis totius impetus; tùm in <pb xlink:href="026/01/174.jpg" pagenum="142"/>motu naturali, in cuius progre&longs;&longs;ione producitur &longs;emper imperfectior, <lb/>tùm in violento, in cuius progre&longs;&longs;ione de&longs;truitur &longs;emper perfectior; <lb/>producitur imperfectior ab eadem cau&longs;a in minoribus temporibus, & <lb/>de&longs;truitur perfectior ab eadem cau&longs;a in maioribus temporibus; & cum <lb/>impetus innatus &longs;it cau&longs;a de&longs;tructiua impetus violenti, habet inæqualem <lb/>proportionem cum &longs;uo effectu pro temporibus inæqualibus; & cum <lb/>idem impetus innatus &longs;it qua&longs;i principium crementi, vel accelerationis, <lb/>&longs;icut e&longs;t principium retardationis; certè pro inæqualitate temporum e&longs;t <lb/>diuer&longs;a proportio crementorum; quo nihil clarius in hac materia meo <lb/>iudicio dici pote&longs;t. </s></p><p type="main"> | <s>Hic ob&longs;eruabis mirabilem &longs;anæ naturæ prouidentiam, quæ motus <lb/>omnes cum ip&longs;o naturali ita compo&longs;uit, vt &longs;it veluti regula omnium mo­<lb/>tuum, &longs;itque vnum qua&longs;i principium perfectionis totius impetus; tùm in <pb xlink:href="026/01/174.jpg" pagenum="142"/>motu naturali, in cuius progre&longs;&longs;ione producitur &longs;emper imperfectior, <lb/>tùm in violento, in cuius progre&longs;&longs;ione de&longs;truitur &longs;emper perfectior; <lb/>producitur imperfectior ab eadem cau&longs;a in minoribus temporibus, & <lb/>de&longs;truitur perfectior ab eadem cau&longs;a in maioribus temporibus; & cum <lb/>impetus innatus &longs;it cau&longs;a de&longs;tructiua impetus violenti, habet inæqualem <lb/>proportionem cum &longs;uo effectu pro temporibus inæqualibus; & cum <lb/>idem impetus innatus &longs;it qua&longs;i principium crementi, vel accelerationis, <lb/>&longs;icut e&longs;t principium retardationis; certè pro inæqualitate temporum e&longs;t <lb/>diuer&longs;a proportio crementorum; quo nihil clarius in hac materia meo <lb/>iudicio dici pote&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 36.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc finis motus naturalis omninò conuenit cum principio motus violenti; <lb/>& finis huius cum principio illius<emph.end type="italics"/>; quæcumque tandem progre&longs;&longs;io accipia­<lb/>tur; &longs;iue temporum æqualium in &longs;patiis inæquaiibus; &longs;iue &longs;patio­<lb/>rum æqualium in temporibus inæqualibus, &longs;iue a&longs;&longs;umantur in&longs;tan­<lb/>tia in progre&longs;&longs;ione arithmetica &longs;implici iuxta hos numeros 1.2.3.4. &longs;iue <lb/>a&longs;&longs;umantur temporis partes &longs;en&longs;ibiles in progre&longs;&longs;ione Galilei iuxta hos <lb/>numeros 1.3.5.7. quæ omnia ex dictis nece&longs;&longs;ariò con&longs;equuntur. </s></p><p type="main"> | <s><emph type="italics"/>Hinc finis motus naturalis omninò conuenit cum principio motus violenti; <lb/>& finis huius cum principio illius<emph.end type="italics"/>; quæcumque tandem progre&longs;&longs;io accipia­<lb/>tur; &longs;iue temporum æqualium in &longs;patiis inæqualibus; &longs;iue &longs;patio­<lb/>rum æqualium in temporibus inæqualibus, &longs;iue a&longs;&longs;umantur in&longs;tan­<lb/>tia in progre&longs;&longs;ione arithmetica &longs;implici iuxta hos numeros 1.2.3.4. &longs;iue <lb/>a&longs;&longs;umantur temporis partes &longs;en&longs;ibiles in progre&longs;&longs;ione Galilei iuxta hos <lb/>numeros 1.3.5.7. quæ omnia ex dictis nece&longs;&longs;ariò con&longs;equuntur. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 37.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Nec modò conuenit principium vnius cum alterius fine, & vici&longs;&longs;im, &longs;ed <lb/>etiam aliæ partes motus in di&longs;tantiis æqualibus<emph.end type="italics"/> &longs;it enim linea AG, quam <lb/>percurrit mobile demi&longs;&longs;um ex puncto A deor&longs;um motu naturaliter ac­<lb/>celerato, & moueatur per 6. in&longs;tantia, &longs;eu 6. tempora æqualia: Primo <lb/>in&longs;tanti, quo percurtit &longs;patium AB; haud dubiè, quando perueuit ad pun­<lb/>ctum G, habet 7. gradus impetus æquales, quia ante motum AB habebat <lb/>innatum; &longs;ed in motu illo fluunt 6. tempora æqualia, vt dictum e&longs;t; igitur <lb/>6. acquirit gradus impetus, quorum quidem vltimò acqui&longs;itus nullum <lb/>adhuc habuit motum; &longs;ed haud dubiè haberet, &longs;i vlteriùs hic motus pro­<lb/>pagaretur: his po&longs;itis imprimantur mobili in O 7.gradus impetus æqua­<lb/>les prioribus &longs;ursùm motu violento, per lineam OH; certè primo in&longs;tan­<lb/>ti motus, &longs;eu tempore æquali prioribus percurret ON, id e&longs;t 6. &longs;patiola; <lb/>quia licèt &longs;int 7.gradus; attamen impetus innatus corporis grauis detra­<lb/>hit vnum &longs;patium, &longs;imulque de&longs;truit vnum gradum, &longs;ecundo tempore <lb/>percurret NM 5. tertio ML 4. quarto LK 3. quinto KI 2. &longs;exto IH 1. <lb/>igitur primum violenti ON re&longs;pondet vltimo naturali FG &longs;eu &longs;ecun­<lb/>dum illius quinto huius, tertium illius quarto huius, quartum tertio, <lb/>quintum &longs;ecundo &longs;extum primo, & vici&longs;&longs;im; idem pror&longs;us in progre&longs;&longs;ione <lb/>Galilei accidit, a&longs;&longs;umptis &longs;cilicet partibus temporis &longs;en&longs;ibilibus. </s></p><p type="main"> | <s><emph type="italics"/>Nec modò conuenit principium vnius cum alterius fine, & vici&longs;&longs;im, &longs;ed <lb/>etiam aliæ partes motus in di&longs;tantiis æqualibus<emph.end type="italics"/> &longs;it enim linea AG, quam <lb/>percurrit mobile demi&longs;&longs;um ex puncto A deor&longs;um motu naturaliter ac­<lb/>celerato, & moueatur per 6. in&longs;tantia, &longs;eu 6. tempora æqualia: Primo <lb/>in&longs;tanti, quo percurrit &longs;patium AB; haud dubiè, quando peruenit ad pun­<lb/>ctum G, habet 7. gradus impetus æquales, quia ante motum AB habebat <lb/>innatum; &longs;ed in motu illo fluunt 6. tempora æqualia, vt dictum e&longs;t; igitur <lb/>6. acquirit gradus impetus, quorum quidem vltimò acqui&longs;itus nullum <lb/>adhuc habuit motum; &longs;ed haud dubiè haberet, &longs;i vlteriùs hic motus pro­<lb/>pagaretur: his po&longs;itis imprimantur mobili in O 7.gradus impetus æqua­<lb/>les prioribus &longs;ursùm motu violento, per lineam OH; certè primo in&longs;tan­<lb/>ti motus, &longs;eu tempore æquali prioribus percurret ON, id e&longs;t 6. &longs;patiola; <lb/>quia licèt &longs;int 7.gradus; attamen impetus innatus corporis grauis detra­<lb/>hit vnum &longs;patium, &longs;imulque de&longs;truit vnum gradum, &longs;ecundo tempore <lb/>percurret NM 5. tertio ML 4. quarto LK 3. quinto KI 2. &longs;exto IH 1. <lb/>igitur primum violenti ON re&longs;pondet vltimo naturali FG &longs;eu &longs;ecun­<lb/>dum illius quinto huius, tertium illius quarto huius, quartum tertio, <lb/>quintum &longs;ecundo &longs;extum primo, & vici&longs;&longs;im; idem pror&longs;us in progre&longs;&longs;ione <lb/>Galilei accidit, a&longs;&longs;umptis &longs;cilicet partibus temporis &longs;en&longs;ibilibus. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 38.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 40.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc, vt &longs;patia vtroque motu diner&longs;a &longs;unt æqualia, ita tempora quibus de­<lb/>curruntur &longs;unt æqualia,<emph.end type="italics"/> & impetus acqui&longs;itus in fine naturalis cum in­<lb/>nato e&longs;t æqualis impetui producta in principio violenti. </s></p><p type="main"> | <s><emph type="italics"/>Hinc, vt &longs;patia vtroque motu diuer&longs;a &longs;unt æqualia, ita tempora quibus de­<lb/>curruntur &longs;unt æqualia,<emph.end type="italics"/> & impetus acqui&longs;itus in fine naturalis cum in­<lb/>nato e&longs;t æqualis impetui producta in principio violenti. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 41.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Sed hîc duo obiici po&longs;&longs;unt, <lb/>primò &longs;agittam per lineam verticalem vibratam po&longs;ui&longs;&longs;e tantùm in a&longs;­<lb/>cen&longs;u 3. &longs;ecunda, in de&longs;cen&longs;u verò 5. vt &longs;æpiùs ob&longs;eruatum e&longs;t, te&longs;te Mer­<lb/>&longs;enno; &longs;ecundò, &longs;i eodem tempore corpus graue &longs;ursùm proiectum motu <lb/>violento a&longs;cenderet, quo deinde de&longs;cendit, in fine de&longs;cen&longs;us æqualis <lb/>e&longs;&longs;et ictus, &longs;eu percu&longs;&longs;io vtriu&longs;que; cum tamen illa &longs;it maior, quæ infli­<lb/>gitur motu violento, vt con&longs;tat multis experimentis. </s></p><p type="main"> | <s>Sed hîc duo obiici po&longs;&longs;unt, <lb/>primò &longs;agittam per lineam verticalem vibratam po&longs;ui&longs;&longs;e tantùm in a&longs;­<lb/>cen&longs;u 3. &longs;ecunda, in de&longs;cen&longs;u verò 5. vt &longs;æpiùs ob&longs;eruatum e&longs;t, te&longs;te Mer­<lb/>&longs;enno; &longs;ecundò, &longs;i eodem tempore corpus graue &longs;ursùm proiectum motu <lb/>violento a&longs;cenderet, quo deinde de&longs;cendit, in fine de&longs;cen&longs;us æqualis <lb/>e&longs;&longs;et ictus, &longs;eu percu&longs;&longs;io vtriu&longs;que; cum tamen illa &longs;it maior, quæ infli­<lb/>gitur motu violento, vt con&longs;tat multis experimentis. </s></p><p type="main"> |
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| <s>Re&longs;pondeo ad primum etiam te&longs;te Mer&longs;enno globum ferreum trium <lb/>aut 4. librarum &longs;ur&longs;um explo&longs;um è breuiore tormento &longs;ed latiore, æqua­<lb/>le tempus in a&longs;cen&longs;u, & in de&longs;cen&longs;u in&longs;ump&longs;i&longs;&longs;e; quod reuerâ &longs;ecùs acci­<lb/>dit &longs;agittæ, cuius differentia a&longs;cen&longs;us, & de&longs;cen&longs;us &longs;en&longs;u etiam percipi <lb/>pote&longs;t; tùm quia lignea materia multò leuior e&longs;t ferro, tùm quia leui&longs;&longs;i­<lb/>mæ illæ pennæ, quibus in&longs;truitur, motum retardant in de&longs;cen&longs;u; quod <lb/>maximè confirmatur ex eo quod pluma facilè anhelitu &longs;ur&longs;um pellatur <lb/>&longs;atis veloci motu, quæ deinde tardi&longs;&longs;imo &longs;ua &longs;ponte de&longs;cendit: præterea <lb/>mucro ferreus, quo &longs;agitta armatur, &longs;emper præire debet, cuius rei ratio­<lb/>nem afferemus infrà; igitur cum in a&longs;cen&longs;u præeat, vt præeat in de&longs;cen­<lb/>&longs;u, altera extremitas &longs;emicirculum &longs;uo motu facere debet, qui certè ad <lb/>naturalem motum pertinet, alteta tamen extremitas, quæ mouetur mo­<lb/>motu contrario alterius motum retardat; ad &longs;ecundam obiectionem <lb/>re&longs;pondebo Th.44. </s></p><p type="main"> | <s>Re&longs;pondeo ad primum etiam te&longs;te Mer&longs;enno globum ferreum trium <lb/>aut 4. librarum &longs;ur&longs;um explo&longs;um è breuiore tormento &longs;ed latiore, æqua­<lb/>le tempus in a&longs;cen&longs;u, & in de&longs;cen&longs;u in&longs;ump&longs;i&longs;&longs;e; quod reuerâ &longs;ecùs acci­<lb/>dit &longs;agittæ, cuius differentia a&longs;cen&longs;us, & de&longs;cen&longs;us &longs;en&longs;u etiam percipi <lb/>pote&longs;t; tùm quia lignea materia multò leuior e&longs;t ferro, tùm quia leui&longs;&longs;i­<lb/>mæ illæ pennæ, quibus in&longs;truitur, motum retardant in de&longs;cen&longs;u; quod <lb/>maximè confirmatur ex eo quod pluma facilè anhelitu &longs;ur&longs;um pellatur <lb/>&longs;atis veloci motu, quæ deinde tardi&longs;&longs;imo &longs;ua &longs;ponte de&longs;cendit: præterea <lb/>mucro ferreus, quo &longs;agitta armatur, &longs;emper præire debet, cuius rei ratio­<lb/>nem afferemus infrà; igitur cum in a&longs;cen&longs;u præeat, vt præeat in de&longs;cen­<lb/>&longs;u, altera extremitas &longs;emicirculum &longs;uo motu facere debet, qui certè ad <lb/>naturalem motum pertinet, altera tamen extremitas, quæ mouetur mo­<lb/>tu contrario alterius motum retardat; ad &longs;ecundam obiectionem <lb/>re&longs;pondebo Th.44. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 42.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 44.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Eadem e&longs;t ratio &longs;eu proportio ictuum, & percu&longs;&longs;ionum, quæ integrorum <lb/>&longs;patiorum quæ &longs;cilicet toto motu percurruntur in a&longs;cen&longs;u & de&longs;cen&longs;u,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->corpus graue cadens ex data altitudine 48 pedum æqualem ictum infli­<lb/>git in fine de&longs;cen&longs;us, & in principio a&longs;cen&longs;us, quo &longs;cilicet ad eamdem <lb/>altitudinem a&longs;cenderet; probatur, quia æqualis acquiritur impetus in <lb/>de&longs;cen&longs;u alteri, qui de&longs;truitur in a&longs;cen&longs;u, a&longs;&longs;umptis dumtaxat &longs;patiis illis <lb/>æqualibus; igitur æqualis e&longs;t in fine de&longs;cen&longs;us, in quo e&longs;t totus acqui&longs;i­<lb/>tus, atque in principio a&longs;cen&longs;us, in quo nullus e&longs;t de&longs;tructus: ad id verò, <lb/>quod dicebatur &longs;uprà de &longs;agitta, cuius ictus maior e&longs;t initio a&longs;cen&longs;us, <lb/>quàm in fine de&longs;cen&longs;us non diffiteor; quia materia &longs;agittæ, tùm lignea <lb/>tùm plumea motum &longs;atis &longs;uperque retardat, vt differentia ictuum &longs;en&longs;u <lb/>ip&longs;o percipi po&longs;&longs;it; quæ tamen nulla perciperetur in a&longs;cen&longs;u de&longs;cen&longs;u­<lb/>que globi ferrei. </s> | <s><emph type="italics"/>Eadem e&longs;t ratio &longs;eu proportio ictuum, & percu&longs;&longs;ionum, quæ integrorum <lb/>&longs;patiorum quæ &longs;cilicet toto motu percurruntur in a&longs;cen&longs;u & de&longs;cen&longs;u,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->corpus graue cadens ex data altitudine 48 pedum æqualem ictum infli­<lb/>git in fine de&longs;cen&longs;us, & in principio a&longs;cen&longs;us, quo &longs;cilicet ad <expan abbr="eãdem">eandem</expan> <lb/>altitudinem a&longs;cenderet; probatur, quia æqualis acquiritur impetus in <lb/>de&longs;cen&longs;u alteri, qui de&longs;truitur in a&longs;cen&longs;u, a&longs;&longs;umptis dumtaxat &longs;patiis illis <lb/>æqualibus; igitur æqualis e&longs;t in fine de&longs;cen&longs;us, in quo e&longs;t totus acqui&longs;i­<lb/>tus, atque in principio a&longs;cen&longs;us, in quo nullus e&longs;t de&longs;tructus: ad id verò, <lb/>quod dicebatur &longs;uprà de &longs;agitta, cuius ictus maior e&longs;t initio a&longs;cen&longs;us, <lb/>quàm in fine de&longs;cen&longs;us non diffiteor; quia materia &longs;agittæ, tùm lignea <lb/>tùm plumea motum &longs;atis &longs;uperque retardat, vt differentia ictuum &longs;en&longs;u <lb/>ip&longs;o percipi po&longs;&longs;it; quæ tamen nulla perciperetur in a&longs;cen&longs;u de&longs;cen&longs;u­<lb/>que globi ferrei. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Diceret fortè aliquis cadentem globum ex alti&longs;&longs;imæ turris apice de­<lb/>clinare à perpendiculari antequam terram feriat, vt con&longs;tat ex multis <lb/>experimentis; igitur præualet tandem re&longs;i&longs;tentia aëris: &longs;ed re&longs;pondeo id <lb/>rantùm accidere propter currentem illac aëris tractum; alioquin non <lb/>e&longs;&longs;et potiùs ratio, cur in vnam partem declinaret, quàm in aliam. </s></p><p type="main"> | <s>Diceret fortè aliquis cadentem globum ex alti&longs;&longs;imæ turris apice de­<lb/>clinare à perpendiculari antequam terram feriat, vt con&longs;tat ex multis <lb/>experimentis; igitur præualet tandem re&longs;i&longs;tentia aëris: &longs;ed re&longs;pondeo id <lb/>tantùm accidere propter currentem illac aëris tractum; alioquin non <lb/>e&longs;&longs;et potiùs ratio, cur in vnam partem declinaret, quàm in aliam. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theoroma<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theoroma<emph.end type="italics"/> 46.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 48.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc cognitis viribus, quibus corpus graue proijcitur ad datam altitudi­<lb/>nem, cogno&longs;ci po&longs;&longs;unt vires, quibus ad aliam quamcumque proijciatur<emph.end type="italics"/>; v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->proiiciatur corpus graue ad altitudinem 48. pedum; vires &longs;unt iis æqua­<lb/>les, quas acquirit in de&longs;cen&longs;u ciu&longs;dem altitudinis 48. pedum; &longs;it alia di­<lb/>&longs;tantia 100. pedum; haud dubiè vires nece&longs;&longs;ariæ ad motum hunc violen­<lb/>tum &longs;unt æquales iis, quas acquireret in de&longs;cen&longs;u 100. pedum per Th. <!-- REMOVE S--><lb/>40. atqui ita &longs;e habent vires acqui&longs;itæ in de&longs;cen&longs;u 48. pedum ad vires <lb/>acqui&longs;itas in de&longs;cen&longs;u 100. vt v.g. <!-- REMOVE S-->48. ad v.g. <!-- REMOVE S-->100. id e&longs;t ferè vt 7. <lb/>ad 10. </s> | <s><emph type="italics"/>Hinc cognitis viribus, quibus corpus graue proijcitur ad datam altitudi­<lb/>nem, cogno&longs;ci po&longs;&longs;unt vires, quibus ad aliam quamcumque proijciatur<emph.end type="italics"/>; v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->proiiciatur corpus graue ad altitudinem 48. pedum; vires &longs;unt iis æqua­<lb/>les, quas acquirit in de&longs;cen&longs;u eiu&longs;dem altitudinis 48. pedum; &longs;it alia di­<lb/>&longs;tantia 100. pedum; haud dubiè vires nece&longs;&longs;ariæ ad motum hunc violen­<lb/>tum &longs;unt æquales iis, quas acquireret in de&longs;cen&longs;u 100. pedum per Th. <!-- REMOVE S--><lb/>40. atqui ita &longs;e habent vires acqui&longs;itæ in de&longs;cen&longs;u 48. pedum ad vires <lb/>acqui&longs;itas in de&longs;cen&longs;u 100. vt v.g. <!-- REMOVE S-->48. ad v.g. <!-- REMOVE S-->100. id e&longs;t ferè vt 7. <lb/>ad 10. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 51.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Ex his &longs;atis facilè comparari po&longs;&longs;unt rationes pereu&longs;&longs;ionis,<emph.end type="italics"/> quæ infliguntur <pb xlink:href="026/01/178.jpg" pagenum="146"/>tùm ex ca&longs;u corporis grauis cadentis, tùm ex vi mallei impacti, tùm ex <lb/>impetu corporis projecti, tùm ex grauitatione corporis grauis incum­<lb/>bentis, quæ omnia hîc fu&longs;iùs e&longs;&longs;ent tractanda, ni&longs;i locum proprium infrà <lb/>&longs;ibi vendicarent. </s></p><p type="main"> | <s><emph type="italics"/>Ex his &longs;atis facilè comparari po&longs;&longs;unt rationes percu&longs;&longs;ionis,<emph.end type="italics"/> quæ infliguntur <pb xlink:href="026/01/178.jpg" pagenum="146"/>tùm ex ca&longs;u corporis grauis cadentis, tùm ex vi mallei impacti, tùm ex <lb/>impetu corporis projecti, tùm ex grauitatione corporis grauis incum­<lb/>bentis, quæ omnia hîc fu&longs;iùs e&longs;&longs;ent tractanda, ni&longs;i locum proprium infrà <lb/>&longs;ibi vendicarent. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 52.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Ad motum violentum non concurrit impetus innatus,<emph.end type="italics"/> probatur, quia im­<lb/>petus ad lineas oppo&longs;itas ex diametro determinati ad communem li­<lb/>neam determinari non po&longs;&longs;unt, cur enim potiùs dextror&longs;um quam &longs;ini­<lb/>ctror&longs;um? </s> | <s><emph type="italics"/>Ad motum violentum non concurrit impetus innatus,<emph.end type="italics"/> probatur, quia im­<lb/>petus ad lineas oppo&longs;itas ex diametro determinati ad communem li­<lb/>neam determinari non po&longs;&longs;unt, cur enim potiùs dextror&longs;um quam &longs;ini­<lb/>stror&longs;um? </s> |
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| <s>igitur non concurrunt ad communem motum, ni&longs;i dicatur <lb/>impetus innatus veleo nomine concurrere ad violentum, quod eius li­<lb/>neam &longs;ingulis temporibus qua&longs;i ca&longs;tiget, vltróque, vel vlteriùs currentem <lb/>contineat. </s></p><p type="main"> | <s>igitur non concurrunt ad communem motum, ni&longs;i dicatur <lb/>impetus innatus valeo nomine concurrere ad violentum, quod eius li­<lb/>neam &longs;ingulis temporibus qua&longs;i ca&longs;tiget, vltróque, vel vlteriùs currentem <lb/>contineat. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 53.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 58.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Impetus violentus producitur minor, quàm produceretur vno dunt ax at gra­<lb/>du aquali ip&longs;i impetui innato<emph.end type="italics"/>; quippe &longs;icut de&longs;truit &longs;ingulis in&longs;tantibu: <lb/>æqualibus vnum gradum; quia pugnat pro rata; ita pror&longs;us impedit, ne <pb xlink:href="026/01/179.jpg" pagenum="147"/>producatur vnus gradus &longs;ibi æqualis primo in&longs;tanti; cur enim duo po­<lb/>tiùs, quàm tres? </s></p><p type="main"> | <s><emph type="italics"/>Impetus violentus producitur minor, quàm produceretur vno dumtaxat gra­<lb/>du aquali ip&longs;i impetui innato<emph.end type="italics"/>; quippe &longs;icut de&longs;truit &longs;ingulis in&longs;tantibus <lb/>æqualibus vnum gradum; quia pugnat pro rata; ita pror&longs;us impedit, ne <pb xlink:href="026/01/179.jpg" pagenum="147"/>producatur vnus gradus &longs;ibi æqualis primo in&longs;tanti; cur enim duo po­<lb/>tiùs, quàm tres? </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 59.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 61.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc corpus quod non grauitat, facilè proijcitur, vel impellitur<emph.end type="italics"/>: &longs;ic na­<lb/>uis aquis innatans, nubes in aëre libratæ; halitus, atque adeo ip&longs;æ partes <lb/>aquæ, quas perexiguus lapillus in orbes penè innumeros agit, ne quid <lb/>dicam de partibus aëris, quæ tam citò & procul mouentur, vt con&longs;tat in <lb/>&longs;ono, motu &longs;cilicet ferè æquabili. </s></p><p type="main"> | <s><emph type="italics"/>Hinc corpus quod non grauitat, facilè proijcitur, vel impellitur<emph.end type="italics"/>: &longs;ic na­<lb/>uis aquis innatans, nubes in aëre liberatæ; halitus, atque adeo ip&longs;æ partes <lb/>aquæ, quas perexiguus lapillus in orbes penè innumeros agit, ne quid <lb/>dicam de partibus aëris, quæ tam citò & procul mouentur, vt con&longs;tat in <lb/>&longs;ono, motu &longs;cilicet ferè æquabili. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 62.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 64.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Concurrunt omnes illæ, quæ in&longs;unt eidem parti &longs;eu puncto mobilis commun <lb/>qua&longs;i actione vel exigentia<emph.end type="italics"/>; patet ex dictis de impetu, quia concurrunt ad <lb/>velocitatem, quæ e&longs;t indiui&longs;ibilis actu. </s></p><p type="main"> | <s><emph type="italics"/>Concurrunt omnes illæ, quæ in&longs;unt eidem parti &longs;eu puncto mobilis <expan abbr="commun">communes</expan> <lb/>qua&longs;i actione vel exigentia<emph.end type="italics"/>; patet ex dictis de impetu, quia concurrunt ad <lb/>velocitatem, quæ e&longs;t indiui&longs;ibilis actu. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 65.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 66.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc ille gradus motus quinon ponitur &longs;ecundo instanti respondet gradus <lb/>im petus qui destruitur<emph.end type="italics"/>; cum vterque habeat eamdem men&longs;uram, &longs;cilicet <lb/>im petum innatum. </s></p><pb xlink:href="026/01/180.jpg" pagenum="148"/><p type="main"> | <s><emph type="italics"/>Hinc ille gradus motus qui non ponitur &longs;ecundo instanti respondet gradus <lb/>impetus qui destruitur<emph.end type="italics"/>; cum vterque habeat <expan abbr="eãdem">eandem</expan> men&longs;uram, &longs;cilicet <lb/>impetum innatum. </s></p><pb xlink:href="026/01/180.jpg" pagenum="148"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 67.<emph.end type="center"/></s></p><p type="main"> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s>Vnde cum effectus qui ponitur &longs;ecundo in&longs;tanti non re&longs;pondeat per­<lb/>fectioni cau&longs;æ totius propter impedimentum, aliquis gradus cau&longs;æ e&longs;&longs;et <lb/>fru&longs;trà; igitur eodem in&longs;tanti &longs;ecundo de&longs;trui debet, alioqui ni&longs;i de&longs;true­<lb/>retur &longs;ingulis in&longs;tantibus poneretur effectus non re&longs;pondens per&longs;ectioni <lb/>cau&longs;æ; immò numquam de&longs;trueretur totus motus violentus, vt con&longs;tat; <lb/>itaque primo in&longs;tanti omnes gradus impetus qui &longs;unt exigunt motum <lb/>pro &longs;ecundo ne aliquis eo in&longs;tanti &longs;it &longs;ru&longs;trà &longs;i non exigeret, & &longs;ecundo <lb/>in&longs;tanti aliquis gradus impetus de&longs;truitur, ne &longs;it fru&longs;trà codem in&longs;tanti <lb/>&longs;ecundo, cum &longs;cilicet non &longs;int tot gradus motus, quot &longs;unt gradus impe­<lb/>tus; atque ita deinceps tertio in&longs;tanti de&longs;truitur vnus gradus, vt iam &longs;u­<lb/>prà dictum e&longs;t. </s></p><p type="main"> | <s>Vnde cum effectus qui ponitur &longs;ecundo in&longs;tanti non re&longs;pondeat per­<lb/>fectioni cau&longs;æ totius propter impedimentum, aliquis gradus cau&longs;æ e&longs;&longs;et <lb/>fru&longs;trà; igitur eodem in&longs;tanti &longs;ecundo de&longs;trui debet, alioqui ni&longs;i de&longs;true­<lb/>retur &longs;ingulis in&longs;tantibus poneretur effectus non re&longs;pondens perfectioni <lb/>cau&longs;æ; immò numquam de&longs;trueretur totus motus violentus, vt con&longs;tat; <lb/>itaque primo in&longs;tanti omnes gradus impetus qui &longs;unt exigunt motum <lb/>pro &longs;ecundo ne aliquis eo in&longs;tanti &longs;it fru&longs;trà &longs;i non exigeret, & &longs;ecundo <lb/>in&longs;tanti aliquis gradus impetus de&longs;truitur, ne &longs;it fru&longs;trà codem in&longs;tanti <lb/>&longs;ecundo, cum &longs;cilicet non &longs;int tot gradus motus, quot &longs;unt gradus impe­<lb/>tus; atque ita deinceps tertio in&longs;tanti de&longs;truitur vnus gradus, vt iam &longs;u­<lb/>prà dictum e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 68.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Ideo de&longs;truitur potiùs vnus gradus impetus quàm alius &longs;ecundo in&longs;tanti, <lb/>tertioque, &c. </s> | <s><emph type="italics"/>Ideo de&longs;truitur potiùs vnus gradus impetus quàm alius &longs;ecundo in&longs;tanti, <lb/>tertioque, &c. </s> |
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| <s>quia talis e&longs;t per&longs;ectionis<emph.end type="italics"/>; hoc iam &longs;uprà explicatum e&longs;t; quia <lb/>cum motus initio &longs;it velocior, in&longs;tantia &longs;unt minora, igitur minùs im­<lb/>petus in &longs;ingulis de&longs;truitur, pater ex dictis. </s></p><p type="main"> | <s>quia talis e&longs;t perfectionis<emph.end type="italics"/>; hoc iam &longs;uprà explicatum e&longs;t; quia <lb/>cum motus initio &longs;it velocior, in&longs;tantia &longs;unt minora, igitur minùs im­<lb/>petus in &longs;ingulis de&longs;truitur, pater ex dictis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 69.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Ille gradus impetus qui de&longs;truitur &longs;ecundo in&longs;tanti non concurrit ad motuns <lb/>tertij in&longs;tantis<emph.end type="italics"/>; quia non pote&longs;t concurrere ad motum ni&longs;i exigendo; at­<lb/>qui exigere tantùm pote&longs;t, quando e&longs;t; quod enim non e&longs;t non exigit, <lb/>&longs;ed motus tertij in&longs;tantis exigitur &longs;ecundo; &longs;ic enim tota res motus pro­<lb/>cedit vt impetus primo in&longs;tanti exigat motum pro &longs;ecundo; & &longs;ecundo <lb/>pro tertio; & tertio pro quarto, atque ita deinceps; igitur impetus ille <lb/>qui de&longs;tru&longs;tur; &longs;ecundo in&longs;tanti non exigit motum pro tertio, & qui de­<lb/>&longs;truitur tertio non exigit pro quarto, atque ita deinceps. </s></p><p type="main"> | <s><emph type="italics"/>Ille gradus impetus qui de&longs;truitur &longs;ecundo in&longs;tanti non concurrit ad motum <lb/>tertij in&longs;tantis<emph.end type="italics"/>; quia non pote&longs;t concurrere ad motum ni&longs;i exigendo; at­<lb/>qui exigere tantùm pote&longs;t, quando e&longs;t; quod enim non e&longs;t non exigit, <lb/>&longs;ed motus tertij in&longs;tantis exigitur &longs;ecundo; &longs;ic enim tota res motus pro­<lb/>cedit vt impetus primo in&longs;tanti exigat motum pro &longs;ecundo; & &longs;ecundo <lb/>pro tertio; & tertio pro quarto, atque ita deinceps; igitur impetus ille <lb/>qui de&longs;truitur; &longs;ecundo in&longs;tanti non exigit motum pro tertio, & qui de­<lb/>&longs;truitur tertio non exigit pro quarto, atque ita deinceps. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 70.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 76.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Igitur in&longs;tanti quietis nullus e&longs;&longs;et ampliùs impetus violantus<emph.end type="italics"/>; cum enim <lb/>&longs;ingulis in&longs;tantibus de&longs;truatur vnus gradus, v. <!-- REMOVE S-->g in&longs;tanti illo, quod &longs;e­<lb/>quitur po&longs;t in&longs;tans æqualitatis, de&longs;truitur ille gradus, qui &longs;upere&longs;t; nec <lb/>pote&longs;t vel plùs, vel minùs de&longs;trui; pugnant enim pro rata; quod certè <lb/>cuiquam fortè paradoxor videbitur, &longs;cilicet nullum tune e&longs;&longs;e motum <lb/>propter pugnam, cum tamen nulla e&longs;t amplius pugna. </s> | <s><emph type="italics"/>Igitur in&longs;tanti quietis nullus e&longs;&longs;et ampliùs impetus violentus<emph.end type="italics"/>; cum enim <lb/>&longs;ingulis in&longs;tantibus de&longs;truatur vnus gradus, v. <!-- REMOVE S-->g in&longs;tanti illo, quod &longs;e­<lb/>quitur po&longs;t in&longs;tans æqualitatis, de&longs;truitur ille gradus, qui &longs;upere&longs;t; nec <lb/>pote&longs;t vel plùs, vel minùs de&longs;trui; pugnant enim pro rata; quod certè <lb/>cuiquam fortè paradoxor videbitur, &longs;cilicet nullum tune e&longs;&longs;e motum <lb/>propter pugnam, cum tamen nulla e&longs;t amplius pugna. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 78.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Quies illa non fit propter æliquam reflexionem, vt aliqui dicunt<emph.end type="italics"/>; quia nul­<lb/>la pror&longs;us e&longs;t reflexio, vbi nullum e&longs;t reflectens; atqui nullum e&longs;t refle­<lb/>ctens, vt patet, quia nullum e&longs;t corpus impediens motus propagationem; <lb/>licèt enim medium impediat, non tamen per modum reflectentis pro­<lb/>priè; immo vt dicemus infrà in puncto reflexionis nulla datur quies; &longs;ed <lb/>motus reflexus &longs;ibi vendicat librum &longs;ingularem. </s></p><p type="main"> | <s><emph type="italics"/>Quies illa non fit propter aliquam reflexionem, vt aliqui dicunt<emph.end type="italics"/>; quia nul­<lb/>la pror&longs;us e&longs;t reflexio, vbi nullum e&longs;t reflectens; atqui nullum e&longs;t refle­<lb/>ctens, vt patet, quia nullum e&longs;t corpus impediens motus propagationem; <lb/>licèt enim medium impediat, non tamen per modum reflectentis pro­<lb/>priè; immo vt dicemus infrà in puncto reflexionis nulla datur quies; &longs;ed <lb/>motus reflexus &longs;ibi vendicat librum &longs;ingularem. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 79.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 80.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc reiicies aliquos æpud Galileum, qui volunt ideo motum naturalem <lb/>accelerari, quia &longs;en&longs;im de&longs;truitur impetus violentus antè impre&longs;&longs;us,<emph.end type="italics"/> quod pe­<lb/>nitus ridiculum e&longs;t; quia lapis deci&longs;us è rupe etiam motu naturaliter <lb/>accelerato deor&longs;um cadit, licèt eò nunquam motu violento euectus <lb/>fuerit. </s></p><p type="main"> | <s><emph type="italics"/>Hinc reiicies aliquos apud Galileum, qui volunt ideo motum naturalem <lb/>accelerari, quia &longs;en&longs;im de&longs;truitur impetus violentus antè impre&longs;&longs;us,<emph.end type="italics"/> quod pe­<lb/>nitus ridiculum e&longs;t; quia lapis deci&longs;us è rupe etiam motu naturaliter <lb/>accelerato deor&longs;um cadit, licèt eò nunquam motu violento euectus <lb/>fuerit. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis hanc hypothe&longs;im gradus impetus violenti æqualis perfe­<lb/>ctionis cum innato e&longs;&longs;e fal&longs;am. </s> | <s>Ob&longs;eruabis hanc hypothe&longs;im gradus impetus violenti æqualis perfe­<lb/>ctionis cum innato e&longs;&longs;e fal&longs;am. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 81.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Corpus quod non grauitat proiicitur &longs;ur&longs;um motu æquabili per &longs;e<emph.end type="italics"/>; patet, quia <lb/>nihil e&longs;t quod de&longs;truat ip&longs;um impetum; igitur &longs;emper moueretur, ni&longs;i <lb/>per accideens ab ip&longs;o medio eius motus retardaretur; vnde dixi <emph type="italics"/>per &longs;e,<emph.end type="italics"/><lb/>cum ratione medij retardetur; immò quò leuius e&longs;t, faciliùs à medio re­<lb/>tinetur, vide Th.61. </s></p><p type="main"> | <s><emph type="italics"/>Corpus quod non grauitat proiicitur &longs;ur&longs;um motu æquabili per &longs;e<emph.end type="italics"/>; patet, quia <lb/>nihil e&longs;t quod de&longs;truat ip&longs;um impetum; igitur &longs;emper moueretur, ni&longs;i <lb/>per accidens ab ip&longs;o medio eius motus retardaretur; vnde dixi <emph type="italics"/>per &longs;e,<emph.end type="italics"/><lb/>cum ratione medij retardetur; immò quò leuius e&longs;t, faciliùs à medio re­<lb/>tinetur, vide Th.61. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 82.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Motus violentus non tendit ad quietem per omnes tarditatis gradus, vt <lb/>pa&longs;&longs;im a&longs;&longs;erit Galileus<emph.end type="italics"/>; Primò, quia non &longs;unt infinita in&longs;tantia, &longs;ed retarda­<lb/>tur tantùm &longs;ingulis in&longs;tantibus; Secundò in medio den&longs;iore minùs du­<lb/>rat; igitur non tran&longs;it per tot gradus tarditatis; præterea in plano incli­<lb/>nato &longs;ur&longs;um în minore proportione retardatur motus, quod etiam in <lb/>plano horizontali certi&longs;&longs;imum e&longs;t; quorum omnium rationes &longs;uo loco <lb/>videbimus. </s></p><p type="main"> | <s><emph type="italics"/>Motus violentus non tendit ad quietem per omnes tarditatis gradus, vt <lb/>pa&longs;&longs;im a&longs;&longs;erit Galileus<emph.end type="italics"/>; Primò, quia non &longs;unt infinita in&longs;tantia, &longs;ed retarda­<lb/>tur tantùm &longs;ingulis in&longs;tantibus; Secundò in medio den&longs;iore minùs du­<lb/>rat; igitur non tran&longs;it per tot gradus tarditatis; præterea in plano incli­<lb/>nato &longs;ur&longs;um în minore proportione retardatur motus, quod etiam in <lb/>plano horizontali certi&longs;&longs;imum e&longs;t; quorum omnium rationes &longs;uo loco <lb/>videbimus. </s></p><p type="main"> |
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| <s>Nec e&longs;t quod aliqui dicant infinito tribui non po&longs;&longs;e hæc prædicata <lb/>æqualitatis vel inæqualitatis, quod fal&longs;um e&longs;t, loquamur de infinito actu; <lb/>&longs;i enim e&longs;&longs;et numerus infinitus hominum, nunquid verum e&longs;&longs;et dicere <lb/>numerum oculorum e&longs;&longs;e maiorem numero hominum; nec e&longs;t quod ali­<lb/>qui confugiant ad di&longs;iunctiones; nos rem i&longs;tam &longs;uo loco fusè tractabi­<lb/>mus & demon&longs;trabimus, ni fallor, cum Ari&longs;totele, fieri non pò&longs;&longs;e vt &longs;it <lb/>aliquod creatum infinitum actu; licèt vltrò concedamus plura e&longs;&longs;e infi­<lb/>nita potentiâ; & verò certum e&longs;t infinito potentiâ non ine&longs;&longs;e huiu&longs;inodi <lb/>prædicata æqualitatis, vel inæqualitatis. </s></p><p type="main"> | <s>Nec e&longs;t quod aliqui dicant infinito tribui non po&longs;&longs;e hæc prædicata <lb/>æqualitatis vel inæqualitatis, quod fal&longs;um e&longs;t, loquamur de infinito actu; <lb/>&longs;i enim e&longs;&longs;et numerus infinitus hominum, nunquid verum e&longs;&longs;et dicere <lb/>numerum oculorum e&longs;&longs;e maiorem numero hominum; nec e&longs;t quod ali­<lb/>qui confugiant ad di&longs;iunctiones; nos rem i&longs;tam &longs;uo loco fusè tractabi­<lb/>mus & demon&longs;trabimus, ni fallor, cum Ari&longs;totele, fieri non pò&longs;&longs;e vt &longs;it <lb/>aliquod creatum infinitum actu; licèt vltrò concedamus plura e&longs;&longs;e infi­<lb/>nita potentiâ; & verò certum e&longs;t infinito potentiâ non ine&longs;&longs;e huiu&longs;modi <lb/>prædicata æqualitatis, vel inæqualitatis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 84.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Ob&longs;eruabis primò &longs;i aliquando accidat, vt aliqui volunt ictum, qui <lb/>&longs;tatim initio motus violenti infligitur, non e&longs;&longs;e maximum, &longs;ed minorem <lb/>eo, qui po&longs;t aliquod confectum &longs;patium infligitur; quod probant in pila <lb/>ex fi&longs;tula ænea &longs;ur&longs;um emi&longs;&longs;a, quæ <expan abbr="moior&etilde;">moiorem</expan> ictum infligit in data di&longs;tantia, <lb/>quod &longs;anè &longs;i verum e&longs;t, hæc vnica e&longs;t, &longs;eu ratio, &longs;eu cau&longs;a, quòd &longs;cilicet &longs;ur­<lb/>&longs;um pila pellatur ab igne, qui ab ore fi&longs;tulæ erumpens per aliquod &longs;pa­<lb/>tium à tergo vrget; igni enim innatum e&longs;t &longs;ur&longs;um euolare. </s></p><p type="main"> | <s>Ob&longs;eruabis primò &longs;i aliquando accidat, vt aliqui volunt ictum, qui <lb/>&longs;tatim initio motus violenti infligitur, non e&longs;&longs;e maximum, &longs;ed minorem <lb/>eo, qui po&longs;t aliquod confectum &longs;patium infligitur; quod probant in pila <lb/>ex fi&longs;tula ænea &longs;ur&longs;um emi&longs;&longs;a, quæ <expan abbr="moior&etilde;">maiorem</expan> ictum infligit in data di&longs;tantia, <lb/>quod &longs;anè &longs;i verum e&longs;t, hæc vnica e&longs;t, &longs;eu ratio, &longs;eu cau&longs;a, quòd &longs;cilicet &longs;ur­<lb/>&longs;um pila pellatur ab igne, qui ab ore fi&longs;tulæ erumpens per aliquod &longs;pa­<lb/>tium à tergo vrget; igni enim innatum e&longs;t &longs;ur&longs;um euolare. </s></p><p type="main"> |
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| <s>Ob&longs;eruabis &longs;ecundò, vix po&longs;&longs;e manu mobile &longs;ur&longs;um rectà proiici, quia <lb/>&longs;cilicet manus extremitas motu mixto mouetur ex duobus vel pluribus <lb/>circularibus, de quo infrà. </s></p><p type="main"> | <s>Ob&longs;eruabis &longs;ecundò, vix po&longs;&longs;e manu mobile &longs;ur&longs;um rectà proiici, quia <lb/>&longs;cilicet manus extremitas motu mixto mouetur ex duobus vel pluribus <lb/>circularibus, de quo infrà. </s></p><p type="main"> |
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| <s>Ob&longs;erua tertiò, non tantùm propter grauitationem con&longs;eruari impe­<lb/>rum naturalem innatum, &longs;ed etiam vt motui violento re&longs;i&longs;tat; at verò <lb/>non re&longs;i&longs;teret, ni&longs;i grauitaret. </s></p><p type="main"> | <s>Ob&longs;erua tertiò, non tantùm propter grauitationem con&longs;eruari impe­<lb/>tum naturalem innatum, &longs;ed etiam vt motui violento re&longs;i&longs;tat; at verò <lb/>non re&longs;i&longs;teret, ni&longs;i grauitaret. </s></p><p type="main"> |
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| <s>Ob&longs;erua quartò, reciprocas rationes motus naturalis & violenti; in <lb/>quibus mirabile pror&longs;us fuit naturæ in&longs;titutum, cum idem in vtroque il­<lb/>larum &longs;it principium. </s></p><p type="main"> | <s>Ob&longs;erua quartò, reciprocas rationes motus naturalis & violenti; in <lb/>quibus mirabile pror&longs;us fuit naturæ in&longs;titutum, cum idem in vtroque il­<lb/>larum &longs;it principium. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>DE MOTV MIXTO EX <lb/>duobus, vel pluribus rectis.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>DE MOTV MIXTO EX <lb/>duobus, vel pluribus rectis.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>MOTVM mixtum eum e&longs;&longs;e non dico, qui <lb/>ex pluribus aliis motibus componatur; <lb/>&longs;eu mi&longs;ceatur; nec enim plures motus <lb/>&longs;imul e&longs;&longs;e po&longs;&longs;unt in eodem mobili; cùm <lb/>tantùm e&longs;&longs;e po&longs;&longs;it vno dumtaxat in&longs;tan­<lb/>ti vnica migratio ex loco in locum; nec plura loca <lb/>naturali virtute &longs;imul acquiri po&longs;&longs;unt; Igitur nec &longs;i­<lb/>mul e&longs;&longs;e duo motus; Itaque motus mixtus &longs;implex <lb/>e&longs;t, &longs;i con&longs;ideretur ratio, & linea motus; mixtus verò <lb/>dicitur, quod ex pluribus re&longs;ultet, qui reuerâ non <lb/>&longs;unt, &longs;ed cùm e&longs;&longs;e po&longs;&longs;int, qua&longs;i confluunt in tertium <lb/>motum communi &longs;umptu qua&longs;i de vtroque partici­<lb/>pantem, quod totum fit propter diuer&longs;os impetus, <lb/>vel eumdem ad diuer&longs;as lineas determinatum, vt fusè <lb/>explicabimus infrà: Porrò in hoc Libro explicamus <lb/>tantùm motum mixtum, qui re&longs;ultat ex pluribus re­<lb/>ctis, vt titulus ip&longs;e præfert. <lb/><gap desc="hr tag"/></s></p><p type="main"> | <s>MOTVM mixtum eum e&longs;&longs;e non dico, qui <lb/>ex pluribus aliis motibus componatur; <lb/>&longs;eu mi&longs;ceatur; nec enim plures motus <lb/>&longs;imul e&longs;&longs;e po&longs;&longs;unt in eodem mobili; cùm <lb/>tantùm e&longs;&longs;e po&longs;&longs;it vno dumtaxat in&longs;tan­<lb/>ti vnica migratio ex loco in locum; nec plura loca <lb/>naturali virtute &longs;imul acquiri po&longs;&longs;unt; Igitur nec &longs;i­<lb/>mul e&longs;&longs;e duo motus; Itaque motus mixtus &longs;implex <lb/>e&longs;t, &longs;i con&longs;ideretur ratio, & linea motus; mixtus verò <lb/>dicitur, quod ex pluribus re&longs;ultet, qui reuerâ non <lb/>&longs;unt, &longs;ed cùm e&longs;&longs;e po&longs;&longs;int, qua&longs;i confluunt in tertium <lb/>motum communi &longs;umptu qua&longs;i de vtroque partici­<lb/>pantem, quod totum fit propter diuer&longs;os impetus, <lb/>vel <expan abbr="eũdem">eundem</expan> ad diuer&longs;as lineas determinatum, vt fusè <lb/>explicabimus infrà: Porrò in hoc Libro explicamus <lb/>tantùm motum mixtum, qui re&longs;ultat ex pluribus re­<lb/>ctis, vt titulus ip&longs;e præfert. <lb/><gap desc="hr tag"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>DEFINITIO 1.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>DEFINITIO 1.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>MOtus mixtus e&longs;t, qui &longs;equitur ex multiplici impetu ad eamdem, vel di­<lb/>uer&longs;as lineas determinato, vel eodem ad diuer&longs;as<emph.end type="italics"/>; hæc definitio cla­<lb/>ra e&longs;t; ob&longs;eruabis tantùm ad motum mixtum &longs;ufficere duplicem impe-<pb xlink:href="026/01/186.jpg" pagenum="154"/>tum ad eamdem lineam determinatam, deor&longs;um, v.g. <!-- REMOVE S-->in mobili proiecto; <lb/>nec enim e&longs;t motus purè naturalis, nec etiam violentus, vt con&longs;tat; igi­<lb/>tur mixtus. </s> | <s><emph type="italics"/>MOtus mixtus e&longs;t, qui &longs;equitur ex multiplici impetu ad <expan abbr="eãdem">eandem</expan>, vel di­<lb/>uer&longs;as lineas determinato, vel eodem ad diuer&longs;as<emph.end type="italics"/>; hæc definitio cla­<lb/>ra e&longs;t; ob&longs;eruabis tantùm ad motum mixtum &longs;ufficere duplicem impe-<pb xlink:href="026/01/186.jpg" pagenum="154"/>tum ad <expan abbr="eãdem">eandem</expan> lineam determinatam, deor&longs;um, v.g. <!-- REMOVE S-->in mobili proiecto; <lb/>nec enim e&longs;t motus purè naturalis, nec etiam violentus, vt con&longs;tat; igi­<lb/>tur mixtus. </s> |
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| <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Ille impetus qui cum alio ad eumdem motum concurrit, concurrit etiam pro <lb/>rata<emph.end type="italics"/>; hoc etiam &longs;uprà demon&longs;tratum e&longs;t, e&longs;t enim cau&longs;a nece&longs;&longs;aria, igitur <lb/>quantum pote&longs;t concurrit, igitur pro rata &longs;uæ virtutis. </s></p><p type="main"> | <s><emph type="italics"/>Ille impetus qui cum alio ad <expan abbr="eũdem">eundem</expan> motum concurrit, concurrit etiam pro <lb/>rata<emph.end type="italics"/>; hoc etiam &longs;uprà demon&longs;tratum e&longs;t, e&longs;t enim cau&longs;a nece&longs;&longs;aria, igitur <lb/>quantum pote&longs;t concurrit, igitur pro rata &longs;uæ virtutis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Axioma<emph.end type="italics"/> 4.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Licèt &longs;int plures impetus in eodem mobili, non &longs;unt tamen plures &longs;imul li­<lb/>ueæ motus<emph.end type="italics"/>; ne mobile &longs;it &longs;imul in pluribus locis. </s></p><p type="main"> | <s><emph type="italics"/>Licèt &longs;int plures impetus in eodem mobili, non &longs;unt tamen plures &longs;imul li­<lb/>neæ motus<emph.end type="italics"/>; ne mobile &longs;it &longs;imul in pluribus locis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Po&longs;tulatum<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Po&longs;tulatum<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Licedt a&longs;&longs;ismere quamlibet coniugætionem motuum,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->vel duorum æ­<lb/>quabilium, vel alterius æquabilis, & alterius retardati, vel alterius æqua­<lb/>bilis, & alterius accelerati, vel alterius reterdati, & alterius accelera­<lb/>ti, &c. </s> | <s><emph type="italics"/>Liceat a&longs;&longs;umere quamlibet coniugationem motuum,<emph.end type="italics"/> v. <!-- REMOVE S-->g. <!-- REMOVE S-->vel duorum æ­<lb/>quabilium, vel alterius æquabilis, & alterius retardati, vel alterius æqua­<lb/>bilis, & alterius accelerati, vel alterius retardati, & alterius accelera­<lb/>ti, &c. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Motus mixtus ex duobus æquabilibus æquælibus e&longs;t rectus<emph.end type="italics"/>; &longs;it enim mo-<pb xlink:href="026/01/187.jpg" pagenum="155"/>bile in A, &longs;itque impetus per AB, & alter æqualis per AD, motus mixtus <lb/>fiet per AE, a&longs;&longs;umpra fcilicet DE æquali, & parallela AB, quod probatur <lb/>per Th.137.l.1. <!-- KEEP S--></s></p><p type="main"> | <s><emph type="italics"/>Motus mixtus ex duobus æquabilibus æqualibus e&longs;t rectus<emph.end type="italics"/>; &longs;it enim mo-<pb xlink:href="026/01/187.jpg" pagenum="155"/>bile in A, &longs;itque impetus per AB, & alter æqualis per AD, motus mixtus <lb/>fiet per AE, a&longs;&longs;umpta &longs;cilicet DE æquali, & parallela AB, quod probatur <lb/>per Th.137.l.1. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 2.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Linea AE e&longs;t diagonalis quadrati, quotie&longs;cumque vterque impetus e&longs;t æ­<lb/>qualis, & liueæ determinationum decu&longs;&longs;antur ad angulos rectos<emph.end type="italics"/>; probatur per <lb/>idem Th.137. <!-- KEEP S--></s></p><p type="main"> | <s><emph type="italics"/>Linea AE e&longs;t diagonalis quadrati, quotie&longs;cumque vterque impetus e&longs;t æ­<lb/>qualis, & lineæ determinationum decu&longs;&longs;antur ad angulos rectos<emph.end type="italics"/>; probatur per <lb/>idem Th.137. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 3.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 5.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Linea AF e&longs;t diagonalis rectanguli, quotie&longs;cunqne lineæ deterninationum <lb/>decu&longs;&longs;antur ad angulos rectos<emph.end type="italics"/>; probatur per idem Th.137. <!-- KEEP S--></s></p><p type="main"> | <s><emph type="italics"/>Linea AF e&longs;t diagonalis rectanguli, quotie&longs;cunque lineæ determinationum <lb/>decu&longs;&longs;antur ad angulos rectos<emph.end type="italics"/>; probatur per idem Th.137. <!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 6.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Hinc de&longs;truitur aliquid impetus per Th.<emph.end type="italics"/>141. & 142.<emph type="italics"/>l.<emph.end type="italics"/>1. idque pro rata <lb/>ne aliquid &longs;it fru&longs;trà per Ax.2. & &longs;æpè iam probatnm e&longs;t. </s></p><p type="main"> | <s><emph type="italics"/>Hinc de&longs;truitur aliquid impetus per Th.<emph.end type="italics"/>141. & 142.<emph type="italics"/>l.<emph.end type="italics"/>1. idque pro rata <lb/>ne aliquid &longs;it fru&longs;trà per Ax.2. & &longs;æpè iam probatum e&longs;t. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 7.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 8.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Aliquando impetus qui remanet in motu mixto est rationalis<emph.end type="italics"/>; id e&longs;t habet <lb/>proportionem ad vtrumque, quæ appellari pote&longs;t, aliquando ad neutrum, <lb/><expan abbr="aliquãdo">aliquando</expan> ad alterutrum; ad vtrumque v.g. <!-- REMOVE S-->&longs;i alter impetuum &longs;it 8.alter 6. <lb/>haud dubiè linea motus mixti erit 10. ad neuttum vt in diagonali qua­<lb/>drati, & in multis aliis; ad alterum denique v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i alter &longs;it &longs;ubduplus la­<lb/>teris æquilateri; alter verò eiu&longs;dem perpendicularis; nam diagonalis, &longs;eu <lb/>linea motus mixti erit latus ip&longs;um æquilateri. </s> | <s><emph type="italics"/>Aliquando impetus qui remanet in motu mixto est rationalis<emph.end type="italics"/>; id e&longs;t habet <lb/>proportionem ad vtrumque, quæ appellari pote&longs;t, aliquando ad neutrum, <lb/><expan abbr="aliquãdo">aliquando</expan> ad alterutrum; ad vtrumque v.g. <!-- REMOVE S-->&longs;i alter impetuum &longs;it 8.alter 6. <lb/>haud dubiè linea motus mixti erit 10. ad neutrum vt in diagonali qua­<lb/>drati, & in multis aliis; ad alterum denique v. <!-- REMOVE S-->g. <!-- REMOVE S-->&longs;i alter &longs;it &longs;ubduplus la­<lb/>teris æquilateri; alter verò eiu&longs;dem perpendicularis; nam diagonalis, &longs;eu <lb/>linea motus mixti erit latus ip&longs;um æquilateri. </s> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 10.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si lineæ determinationum decu&longs;&longs;entur ad angulum acutum, & &longs;int æqua­<lb/>les impetus, linea motus mixti erit diaganalis Rhombi<emph.end type="italics"/>; quæ certè eò longior <lb/>erit, quò angulus erit acutior per Th. 139. l.1. porrò e&longs;t &longs;emper maior <lb/>lateribus &longs;eor&longs;im &longs;umptis. </s></p><p type="main"> | <s><emph type="italics"/>Si lineæ determinationum decu&longs;&longs;entur ad angulum acutum, & &longs;int æqua­<lb/>les impetus, linea motus mixti erit diagonalis Rhombi<emph.end type="italics"/>; quæ certè eò longior <lb/>erit, quò angulus erit acutior per Th. 139. l.1. porrò e&longs;t &longs;emper maior <lb/>lateribus &longs;eor&longs;im &longs;umptis. </s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Scholium.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 12.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Cum alter impetus in motu mixto est maior, linea motus mixti accedit <lb/>propiits ad lineam maioris; hoc est facit angulum acutiorem cum illa<emph.end type="italics"/>; v.g. <!-- REMOVE S-->in <lb/>eadem figura &longs;it linea impetus maioris AC, & minoris AD, linea motus <lb/>mixti e&longs;t diagonalis AF, quæ accedit propiùs ad AC, quàm ad AD, id e&longs;t <lb/>facit angulum acutiorem cum AC, vt patet ex dictis. </s> | <s><emph type="italics"/>Cum alter impetus in motu mixto est maior, linea motus mixti accedit <lb/>proprius ad lineam maioris; hoc est facit angulum acutiorem cum illa<emph.end type="italics"/>; v.g. <!-- REMOVE S-->in <lb/>eadem figura &longs;it linea impetus maioris AC, & minoris AD, linea motus <lb/>mixti e&longs;t diagonalis AF, quæ accedit propiùs ad AC, quàm ad AD, id e&longs;t <lb/>facit angulum acutiorem cum AC, vt patet ex dictis. </s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main"> | <s><emph type="center"/><emph type="italics"/>Theorema<emph.end type="italics"/> 13.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Cum verò impetus &longs;unt &aeli |
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