Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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SECTIO VII.
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De Motu Fluidorum & Reſiſtentia Projectilium.
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PROPOSITIO XXXII. THEOREMA XXVI.
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DE MOTU
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CORPORUM</
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Si Corporum Syſtemata duo ſimilia ex æquali particularum numero
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conſtent, & particulæ correſpondentes ſimiles ſint & propor
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tionales, ſingulæ in uno Syſtemate ſingulis in altero, & ſimiliter
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ſitæ inter ſe, ac datam habeant rationem denſitatis ad invicem,
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& inter ſe temporibus proportionalibus ſimiliter moveri inci
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piant, (eæ inter ſe quæ in uno ſunt Syſtemate & eæ inter ſe quæ
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ſunt in altero) & ſi non tangant ſe mutuo quæ in eodem ſunt
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Syſtemate, niſi in momentis reflexionum, neque attrahant vel fu
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gent ſe mutuo, niſi viribus acceleratricibus quæ ſint ut particu
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larum correſpondentium diametri inverſe & quadrata velocita.
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tum directe: dico quod Syſtematum particulæ illæ pergent inter
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ſe temporibus proportionalibus ſimiliter moveri.
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>Corpora ſimilia & ſimiliter ſita temporibus proportionalibus in
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ter ſe ſimiliter moveri dico, quorum ſitus ad invicem in fine tem
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porum illorum ſemper ſunt ſimiles: puta ſi particulæ unius Syſte
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matis cum alterius particulis correſpondentibus conferantur. </
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>Un
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de tempora erunt proportionalia, in quibus ſimiles & proportiona
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les Figurarum ſimilium partes a particulis correſpondentibus de
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ſcribuntur. </
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>Igitur ſi duo ſint ejuſmodi Syſtemata, particulæ cor
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reſpondentes, ob ſimilitudinem incæptorum motuum, pergent ſi
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militer moveri uſQ.E.D.nec ſibi mutuo occurrant. </
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>Nam ſi nullis
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agitantur viribus, progredientur uniformiter in lineis rectis per mo
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tus Leg. 1. Si viribus aliquibus ſe mutuo agitant, & vires illæ ſint
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ut particularum correſpondentium diametri inverſe & quadrata ve
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locitatum directe; quoniam particularum ſitus ſunt ſimiles & vires
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proportionales, vires totæ quibus particulæ correſpondentes agi
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tantur, ex viribus ſingulis agitantibus (per Legum Corollarium </
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