Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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vi centripeta
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TV
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qua corpus
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Q
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in ſpatio libero circa centrum
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datum
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C
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revolvitur, datur per Prop. </
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PQR
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quam corpus deſcribit, tum locus
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Q
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in quo corpus ad datum quod
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vis tempus verſabitur, tum denique velocitas corporis in loco illo
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Q
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; & contra.
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E. I.
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LIBER
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PRIMUS.</
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PROPOSITIO XLVII. THEOREMA XV.
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Poſito quod Vis centripeta proportionalis ſit diſtantiæ corporis a
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centro; corpora omnia in planis quibuſcunque revolventia de
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ſcribent Ellipſes, & revolutiones Temporibus æqualibus peragent;
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quæque moventur in lineis rectis, ultro citroQ.E.D.ſcurrendo,
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ſingulas eundi & redeundi periodos iiſdem Temporibus abſol
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vent.
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<
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>Nam, ſtantibus quæ
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in ſuperiore Propoſitio
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ne, vis
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SV
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qua corpus
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Q
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in plano quovis
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PQR
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revolvens trahitur ver
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ſus centrum
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S
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eſt ut di
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ſtantia
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atque adeo
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ob proportionales
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SV
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&
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SQ, TV
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&
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CQ,
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vis
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TV
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qua corpus trahi
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tur verſus punctum
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C
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in Orbis plano datum,
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eſt ut diſtantia
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C Q.
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Vi
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res igitur, quibus cor
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pora in plano
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PQR
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verſantia trahuntur ver
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ſus punctum
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C,
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ſunt pro
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ratione diſtantiarum æquales viribus quibus corpora undiquaque
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trahuntur verſus centrum
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S
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; & propterea corpora movebuntur iiſ
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dem Temporibus, in iiſdem Figuris, in plano quovis
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PQR
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circa
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punctum
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C,
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atQ.E.I. ſpatiis liberis circa centrum
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S
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; adeoque (per
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Corol. </
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>2. Prop. </
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<
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>X, & Corol. </
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<
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<
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>XXXVIII) Temporibus ſemper </
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