Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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tranſgredi, neque prius attingere quam quantitates diminuuntur in
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infinitum. </
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>Res clarius intelligetur in infinite magnis. </
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>Si quantitates
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duæ quarum data eſt differentia auges ntur in infinitum, dabitur
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harum ultima ratio, nimirum ratio æqualitatis, nec tamen ideo da
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buntur quantitates ultimæ ſeu maximæ quarum iſta eſt ratio. </
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>Igitur
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in ſequentibus, ſiquando facili rerum conceptui conſulens dixero
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quantitates quam minimas, vel evaneſcentes, vel ultimas; cave in
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telligas quantitates magnitudine determinatas, ſed cogita ſemper
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diminuendas ſine limite. </
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DE MOTU
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CORPORUM</
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SECTIO II.
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De Inventione Virium Centripetarum.
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PROPOSITIO I. THEOREMA I.
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Areas, quas corpora in gyros acta radiis ad immobile centrum virium
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ductis deſcribunt, & in planis immobilibus conſiſtere, & eſſe tem
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poribus proportionales.
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>Dividatur tempus in partes æquales, & prima temporis parte de
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ſcribat corpus vi inſita rectam
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AB.
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Idem ſecunda temporis parte, ſi
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nil impediret, recta
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pergeret ad
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c,
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(per
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Leg. </
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>1.) deſcribens
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lineam
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Bc
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æqualem
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ipſi
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AB
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; adeo ut ra
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diis
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AS, BS, cS
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ad
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centrum actis, con
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fectæ forent æqua
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les areæ
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ASB, BSc.
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Verum ubi corpus
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venit ad
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B,
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agat vis
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centripeta impul
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ſu unico ſed mag
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no, efficiatque ut
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corpus de recta
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Bc
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declinet & pergat
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in recta
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BC.
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Ipſi
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BS
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parallela agatur
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cC,
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occurens
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BC
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in
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C
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; & completa ſecunda
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temporis parte, corpus (per Legum Corol. </
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<
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>1.) reperietur in
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C,
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in </
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