Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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& qualitates Phyſicas, ſed quantitates & proportiones Mathema
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ticas in hoc Tractatu expendens, ut in Definitionibus explicui. </
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<
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>In
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Matheſi inveſtigandæ ſunt virium quantitates & rationes illæ, quæ
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ex conditionibus quibuſcunque poſitis conſequentur: deinde, ubi
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in Phyſicam deſcenditur, conferendæ ſunt hæ rationes cum Phæ
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nomenis, ut innoteſcat quænam virium conditiones ſingulis cor
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porum attractivorum generibus competant. </
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<
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>Et tum demum de vi
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rium ſpeciebus, cauſis & rationibus Phyſicis tutius diſputare lice
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bit. </
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<
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>Videamus igitur quibus viribus corpora Sphærica, ex particu
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lis modo jam expoſito attractivis conſtantia, debeant in ſe mutuo
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agere, & quales motus inde conſequantur. </
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LIBER
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PRIMUS.</
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SECTIO XII.
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De Corporum Sphæriccrum Viribus attractivis.
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PROPOSITIO LXX. THEOREMA XXX.
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Si ad Sphæricæ ſuperficiei puncta ſingula tendant vires æquales cen
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tripetæ decreſcentes in duplicata ratione diſtantiarum a punctis:
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dico quod corpuſculum intra ſuperficiem conſtitutum his viri
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bus nullam in partem attrahitur.
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<
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HIKL
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ſuperficies illa Sphæri
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ca, &
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P
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corpuſculum intus conſtitu
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tum. </
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<
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P
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agantur ad hanc ſuper
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ficiem lineæ duæ
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HK, IL,
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arcus
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quam minimos
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HI, KL
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intercipi
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entes; &, ob triangula
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HPI, LPK
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(per Corol. </
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<
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>3. Lem. </
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<
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>VII) ſimilia, arcus
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illi erunt diſtantiis
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HP, LP
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pro
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portionales; & ſuperficiei Sphæricæ
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particulæ quævis ad
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HI
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&
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KL,
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rec
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tis per punctum
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P
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tranſeuntibus un
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dique terminatæ, erunt in duplicata
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illa ratione. </
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<
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>Ergo vires harum particularum in corpus
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P
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exercitæ
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ſunt inter ſe æquales. </
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<
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>Sunt enim ut particulæ directe & quadrata
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diſtantiarum inverſe. </
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<
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>Et hæ duæ rationes componunt rationem </
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