Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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corpus alterum
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T,
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erunt areæ illæ temporibus quamproxime pro
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portionales. </
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DE MOTU
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CORPORUM</
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Corol.
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4. Si corpus
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L
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radio ad alterum corpus
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T
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ducto deſcri
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bit areas quæ, cum temporibus collatæ, ſunt valde inæquales; &
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corpus illud alterum
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T
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vel quieſcit vel movetur uniformiter in di
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rectum: actio vis centripetæ ad corpus illud alterum
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T
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tendentis,
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vel nulla eſt, vel miſcetur & componitur cum actionibus admodum
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potentibus aliarum virium: Viſque tota ex omnibus, ſi plures ſunt
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vires, compoſita, ad aliud (ſive immobile ſive mobile) centrum
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dirigitur. </
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>Idem obtinet, ubi corpus alterum motu quocunque mo
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vetur; ſi modo vis centripeta ſumatur, quæ reſtat poſt ſubductio
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nem vis totius in corpus illud alterum
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T
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agentis. </
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Scholium.
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<
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>Quoniam æquabilis arearum deſcriptio Index eſt Centri, quod
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vis illa reſpicit qua corpus maxime afficitur, quaque retrahitur a mo
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tu rectilineo & in orbita ſua retinetur: quidni uſurpemus in ſequen
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tibus æquabilem arearum deſcriptionem, ut Indicem Centri circum
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quod motus omnis circularis in ſpatiis liberis peragitur? </
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PROPOSITIO IV. THEOREMA IV.
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Corporum, quæ diverſos circulos æquabili motu deſcribunt, vires cen
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tripetas ad centra eorundem circulorum tendere; & eſſe inter ſe,
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ut ſunt arcuum ſimul deſcriptorum quadrata applicata ad circulo
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rum radios.
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<
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>Tendunt hæ vires ad centra circulorum per Prop.II. & Corol. </
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>II.
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Prop. </
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>1; & ſunt inter ſe ut arcuum æqualibus temporibus quam miNI
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mis deſcriptorum ſinus verſi per Corol. </
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>IV. Prop. </
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>I; hoc eſt, ut qua
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drata arcuum eorundem ad diametros circulorum applicata per
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Lem. </
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>VII: & propterea, cum hi arcus ſint ut arcus temporibus
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quibuſvis æqualibus deſcripti, & diametri ſint ut eorum radii; vi
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res erunt ut arcuum quorumvis ſimul deſcriptorum quadrata ap
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plicata ad radios circulorum.
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Q.E.D.
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Corol.
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1. Igitur, cum arcus illi ſint ut velocitates corporum, vi
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res centripetæ ſunt ut velocitatum quadrata applicata ad radios
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circulorum: hoc eſt, ut cum Geometris loquar, vires ſunt in ra
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tione compoſita ex duplicata ratione velocitatum directe & ratione
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ſimplici radiorum inverſe. </
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