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version 1.9, 2007/01/09 18:11:59 |
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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 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-->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> | <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>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>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>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> | |
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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 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><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 etiam 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><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 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"> | <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 fiatpercu&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 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 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"> | <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><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"/>; 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> | <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 eiu&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="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 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, 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 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"> | <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 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><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 eiu&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 eiu&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 <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"> | <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;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"> | <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 moueatur 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 eiu&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>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="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"/> 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"/> 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 <expan abbr="eũdem">eundem</expan> 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"/>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 <expan abbr="eãdem">eandem</expan> 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;cilicet 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, 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;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><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"/>Hinc reiicies Galileum,<emph.end type="italics"/> qui in dialogis hæc &longs;emper &longs;uppo&longs;uit, &longs;ed nun­<lb/>quam probauit, nec probare vnquam potuit; hoc etiam &longs;upponunt <lb/>multi Galilei &longs;ectatores, qui cen&longs;ent impetum nunquam de&longs;trui ni&longs;i à <lb/>re&longs;i&longs;tentia medij; &longs;ed quæro ab illis quodnam medium de&longs;truat partem <lb/>impetus in motu mixto; nec enim linea motus mixti adæquat duas alias <lb/>ex quibus qua&longs;i re&longs;ultat; certè hoc non potc&longs;t explicari cum infinitis fetè <lb/>aliis, ni&longs;i dicatur impetum de&longs;trui ab alio impetu, eo modo quo &longs;æpè <lb/>diximus, hoc e&longs;t ne &longs;it fru&longs;trà; igitur impetus violentus de&longs;truitur ab in­<lb/>nato, non tamen innatus à violento, vt &longs;æpiùs inculcauimus. </s></p><p type="main"> | <s><emph type="italics"/>Hinc reiicies Galileum,<emph.end type="italics"/> qui in dialogis hæc &longs;emper &longs;uppo&longs;uit, &longs;ed nun­<lb/>quam probauit, nec probare vnquam potuit; hoc etiam &longs;upponunt <lb/>multi Galilei &longs;ectatores, qui cen&longs;ent impetum nunquam de&longs;trui ni&longs;i à <lb/>re&longs;i&longs;tentia medij; &longs;ed quæro ab illis quodnam medium de&longs;truat partem <lb/>impetus in motu mixto; nec enim linea motus mixti adæquat duas alias <lb/>ex quibus qua&longs;i re&longs;ultat; certè hoc non pote&longs;t explicari cum infinitis fetè <lb/>aliis, ni&longs;i dicatur impetum de&longs;trui ab alio impetu, eo modo quo &longs;æpè <lb/>diximus, hoc e&longs;t ne &longs;it fru&longs;trà; igitur impetus violentus de&longs;truitur ab in­<lb/>nato, non tamen innatus à violento, vt &longs;æpiùs inculcauimus. </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>Re&longs;p, me aliquando fui&longs;&longs;e in ea &longs;ententiâ, vt reuerâ exi&longs;timarem de­<lb/>cre&longs;cere impetum violentum in iactu perpendiculari deor&longs;um; cum <lb/>etiam exi&longs;timarem decre&longs;cere vim ictus; &longs;ed re melius con&longs;iderata, cum <lb/>nunquam id experiri potuerim; nam &longs;emper fentio vim ictus maiorem, <pb xlink:href="026/01/207.jpg" pagenum="175"/>cum deorfum mobile proiicitur, quàm cum &longs;ua &longs;ponte ex eadem altitu­<lb/>dine de&longs;cendit; certè ni fallor cum ratio demon&longs;tratiua pro hac &longs;en­<lb/>tentia faciat, non dubitaui ampliùs priorem &longs;ententiam immutare. </s></p><p type="main"> | <s>Re&longs;p, me aliquando fui&longs;&longs;e in ea &longs;ententiâ, vt reuerâ exi&longs;timarem de­<lb/>cre&longs;cere impetum violentum in iactu perpendiculari deor&longs;um; cum <lb/>etiam exi&longs;timarem decre&longs;cere vim ictus; &longs;ed re melius con&longs;iderata, cum <lb/>nunquam id experiri potuerim; nam &longs;emper fentio vim ictus maiorem, <pb xlink:href="026/01/207.jpg" pagenum="175"/>cum deorfum mobile proiicitur, quàm cum &longs;ua &longs;ponte ex eadem altitu­<lb/>dine de&longs;cendit; certè ni fallor cum ratio demon&longs;tratiua pro hac &longs;en­<lb/>tentia faciat, non dubitaui ampliùs priorem &longs;ententiam immutare. </s></p><p type="main"> |
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| <s>Porrò ratio, quæ pro hac &longs;ententia facit, remque ip&longs;am euincit, talis <lb/>e&longs;t; certum e&longs;t impetum violentum de&longs;trui à naturali aliquando in ma­<lb/>iori, aliquando in minori proportione, vt con&longs;tat ex dictis; illa autem, <lb/>&longs;eu maior, &longs;eu minor proportio aliam regulam non habet præter illam <lb/>quam toties inculcauimus, id e&longs;t impetum de&longs;trui pro rata, id e&longs;t qua <lb/>propo rtione e&longs;t fru&longs;trà, id e&longs;t qua proportione e&longs;t minor motus co, qui <lb/>e&longs;&longs;et ab vtroque impetu &longs;i ad <expan abbr="eãdem">eandem</expan> lineam vterque determinatus e&longs;&longs;et <lb/>atqui cum proiicitur mobile deor&longs;um, vterque impetus ad <expan abbr="eãdem">eandem</expan> li­<lb/>ne am e&longs;t determinatus; igitur nihil motus dec&longs;t per Th.138.l.1. igitur <lb/>nihil impetus e&longs;t fru&longs;trà; igitur nihil impetus illius de&longs;truitur. </s></p><p type="main"> | <s>Porrò ratio, quæ pro hac &longs;ententia facit, remque ip&longs;am euincit, talis <lb/>e&longs;t; certum e&longs;t impetum violentum de&longs;trui à naturali aliquando in ma­<lb/>iori, aliquando in minori proportione, vt con&longs;tat ex dictis; illa autem, <lb/>&longs;eu maior, &longs;eu minor proportio aliam regulam non habet præter illam <lb/>quam toties inculcauimus, id e&longs;t impetum de&longs;trui pro rata, id e&longs;t qua <lb/>propo rtione e&longs;t fru&longs;trà, id e&longs;t qua proportione e&longs;t minor motus co, qui <lb/>e&longs;&longs;et ab vtroque impetu &longs;i ad <expan abbr="eãdem">eandem</expan> lineam vterque determinatus e&longs;&longs;et <lb/>atqui cum proiicitur mobile deor&longs;um, vterque impetus ad <expan abbr="eãdem">eandem</expan> li­<lb/>ne am e&longs;t determinatus; igitur nihil motus dee&longs;t per Th.138.l.1. igitur <lb/>nihil impetus e&longs;t fru&longs;trà; igitur nihil impetus illius de&longs;truitur. </s></p><p type="main"> |
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| <s>Quod dictum e&longs;&longs;e velim non con&longs;iderata medij re&longs;i&longs;tentiâ, quæ certè <lb/>aliquid impetus de&longs;truit, quod tamen in&longs;en&longs;ibile e&longs;t in medio libero, pu­<lb/>tà in aëre; &longs;i enim in&longs;en&longs;ibilis e&longs;t hæc re&longs;i&longs;tentia in motu naturali; dum <lb/>mobile &longs;it eius &longs;oliditatis, quæ &longs;uperet facilè vim aëris; certè etiam in­<lb/>&longs;en&longs;ibilis e&longs;t in motu proiectorum, præ&longs;ertim in mediocri &longs;patio, e&longs;t <lb/>enim par vtrobique ratio. </s></p><p type="main"> | <s>Quod dictum e&longs;&longs;e velim non con&longs;iderata medij re&longs;i&longs;tentiâ, quæ certè <lb/>aliquid impetus de&longs;truit, quod tamen in&longs;en&longs;ibile e&longs;t in medio libero, pu­<lb/>tà in aëre; &longs;i enim in&longs;en&longs;ibilis e&longs;t hæc re&longs;i&longs;tentia in motu naturali; dum <lb/>mobile &longs;it eius &longs;oliditatis, quæ &longs;uperet facilè vim aëris; certè etiam in­<lb/>&longs;en&longs;ibilis e&longs;t in motu proiectorum, præ&longs;ertim in mediocri &longs;patio, e&longs;t <lb/>enim par vtrobique ratio. </s></p><p type="main"> |
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| <s>Duodecimò, maior e&longs;t ictus, &longs;i initio de&longs;cen&longs;us fu&longs;tis AB tantillùm <lb/>retrò inclinet, vt GH; quia B ab H in B plùs temporis ponit, quàm à <lb/>Q, vt patet; igitur diutiùs potentia manet applicata; igitur maiorem <lb/>impetum producit; igitur maior e&longs;t ictus; debet autem in eo &longs;itu e&longs;&longs;e, <lb/>in quo motus A in G ita temperetur cum motu B in H, vt eodem mo­<lb/>mento vtrumque feriat planum AB; &longs;i enim vel A attingat antè B, vel <lb/>B antè A, minor e&longs;t ictus, vt con&longs;tat; quia totus motus &longs;imul non im­<lb/>peditur; pote&longs;t autem cogno&longs;ci ille &longs;itus vel illa inclinatio cognita pro­<lb/>portione motus circularis circa D, & circa A; immò ni&longs;i retineatur <lb/>DA; haud dubiè A tanget &longs;olum AB ex G, antequam B de&longs;cendat in B <lb/>ex H; igitur attemperandus e&longs;t motus fu&longs;tis DA; præterea pondus in <lb/>de&longs;cen&longs;u auget ictum, deinde B de&longs;cendit deor&longs;um motu orbis & motu <lb/>centri: præterea B pote&longs;t in a&longs;cen&longs;u maiorem arcum &longs;ui orbis decurre­<lb/>re, quàm in de&longs;cen&longs;u, vel æqualem: denique maior e&longs;t ictus quando po­<lb/>tentia toto ni&longs;u cuitente &longs;u&longs;tis AB plùs temporis ante ictum in &longs;uo mo­<lb/>tu in&longs;umit. </s></p><p type="main"> | <s>Duodecimò, maior e&longs;t ictus, &longs;i initio de&longs;cen&longs;us fu&longs;tis AB tantillùm <lb/>retrò inclinet, vt GH; quia B ab H in B plùs temporis ponit, quàm à <lb/>Q, vt patet; igitur diutiùs potentia manet applicata; igitur maiorem <lb/>impetum producit; igitur maior e&longs;t ictus; debet autem in eo &longs;itu e&longs;&longs;e, <lb/>in quo motus A in G ita temperetur cum motu B in H, vt eodem mo­<lb/>mento vtrumque feriat planum AB; &longs;i enim vel A attingat antè B, vel <lb/>B antè A, minor e&longs;t ictus, vt con&longs;tat; quia totus motus &longs;imul non im­<lb/>peditur; pote&longs;t autem cogno&longs;ci ille &longs;itus vel illa inclinatio cognita pro­<lb/>portione motus circularis circa D, & circa A; immò ni&longs;i retineatur <lb/>DA; haud dubiè A tanget &longs;olum AB ex G, antequam B de&longs;cendat in B <lb/>ex H; igitur attemperandus e&longs;t motus fu&longs;tis DA; præterea pondus in <lb/>de&longs;cen&longs;u auget ictum, deinde B de&longs;cendit deor&longs;um motu orbis & motu <lb/>centri: præterea B pote&longs;t in a&longs;cen&longs;u maiorem arcum &longs;ui orbis decurre­<lb/>re, quàm in de&longs;cen&longs;u, vel æqualem: denique maior e&longs;t ictus quando po­<lb/>tentia toto ni&longs;u cuitente &longs;u&longs;tis AB plùs temporis ante ictum in &longs;uo mo­<lb/>tu in&longs;umit. </s></p><p type="main"> |
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| <s>Decimotertiò, e&longs;t etiam aliud flagelli genus pluribus catenulis ferreis <lb/>in&longs;tructi, ex quibus &longs;ingulis &longs;inguli ferrei globi aliquando &longs;piculis, & <lb/>clauis armati pendent, quorum graui&longs;&longs;imus e&longs;t ictus propter rationes <lb/>prædictas; præ&longs;ertim cùm catenula, &longs;eu funiculus, faciliùs adduci, & in­<lb/>flecti po&longs;&longs;it, quàm extremus ille fu&longs;tis, de quo &longs;uprà; neque dec&longs;t ar­<lb/>tificium; quo quis hoc armorum genere vtens etiam contra plures &longs;e&longs;e <lb/>tueri po&longs;&longs;it. </s></p><p type="main"> | <s>Decimotertiò, e&longs;t etiam aliud flagelli genus pluribus catenulis ferreis <lb/>in&longs;tructi, ex quibus &longs;ingulis &longs;inguli ferrei globi aliquando &longs;piculis, & <lb/>clauis armati pendent, quorum graui&longs;&longs;imus e&longs;t ictus propter rationes <lb/>prædictas; præ&longs;ertim cùm catenula, &longs;eu funiculus, faciliùs adduci, & in­<lb/>flecti po&longs;&longs;it, quàm extremus ille fu&longs;tis, de quo &longs;uprà; neque dee&longs;t ar­<lb/>tificium; quo quis hoc armorum genere vtens etiam contra plures &longs;e&longs;e <lb/>tueri po&longs;&longs;it. </s></p><p type="main"> |
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| <s>Decimoquartò, denique vulgare e&longs;t phœnomenum illud funiculi, &longs;en <lb/>flagelli, quo &longs;cilicet inirio remouetur manubrij extremitas, mox &longs;tatim <lb/>adducitur, ex qua productione, & adductione per vndantem funem <lb/>propagatur impetus v&longs;que ad eiu&longs;dem extremitatem nodo vt plurimùm <lb/>ad&longs;trictam. </s> | <s>Decimoquartò, denique vulgare e&longs;t phœnomenum illud funiculi, &longs;en <lb/>flagelli, quo &longs;cilicet inirio remouetur manubrij extremitas, mox &longs;tatim <lb/>adducitur, ex qua productione, & adductione per vndantem funem <lb/>propagatur impetus v&longs;que ad eiu&longs;dem extremitatem nodo vt plurimùm <lb/>ad&longs;trictam. </s> |
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