Philosophiae naturalis principia mathematica . atum quodvis tempus verfabitur, tum de-niq; velocitas corporis in loco illojg.; & contra. Q. Prop. XLVIL Theor. XV. Poftto quod vk centripeta proportionalk fit diftanti^ corpork a cen-tro i corpora omvia in plams quibufcunq\ revolventia defcribentILUipfesy &> revohttiones temponbus dequalibus peragent \ qu<eq\moventitr in lineis re&k ultro citroq\ difcurrendo, fingulas eundi &redeundi periodos iifdem temporibus abfolvent,Nam ftantibus quae in fuperiore Propofitione \ vis S^quacor- pus QJ\x\ plano quovis PQK revolvens trahitur verfus cen
Philosophiae naturalis principia mathematica . atum quodvis tempus verfabitur, tum de-niq; velocitas corporis in loco illojg.; & contra. Q. Prop. XLVIL Theor. XV. Poftto quod vk centripeta proportionalk fit diftanti^ corpork a cen-tro i corpora omvia in plams quibufcunq\ revolventia defcribentILUipfesy &> revohttiones temponbus dequalibus peragent \ qu<eq\moventitr in lineis re&k ultro citroq\ difcurrendo, fingulas eundi &redeundi periodos iifdem temporibus abfolvent,Nam ftantibus quae in fuperiore Propofitione \ vis S^quacor- pus QJ\x\ plano quovis PQK revolvens trahitur verfus centrum S eft ut diftantia SQ; V atq^ adeo ob proporti-onaIesSF& SQ, TV& CQ, vis TV quacorpus trahitur verfuspunclum C in Orbisplano datum , eft utd iftantia C Q^ Viresigitur, quibus corporain plano P QK ver-fantia trahuntur ver-fus pun&um C,funt proratione diftantiarumaequales viribus quibus corpora undiquaq; trahuntur verfus centrum S; Sc proptereacorpora movebuntur iifdexn temporibus in iifdem figuris in plano quo-. [ H7 ]quovis FQR circa pun&um C, atq; in fpatiis liberis circa cen-trum 51, adeoq^ ( per Corol. i. Prop. X. & Corol. 2. ^ternporibus femper sequalibus, vel defcribent Ellip-fes in plano illo circa centrum C, vel periodos movendi ultro ci-troq; in lineis re&is per centrum C in plano illo du&is, comple-bunt. (X. E. D. Scholium. His affines funt afcenfus ac defcenfus corporum in fuperficie-bus curvis. Concipe lineas curvas in plano defcribi, dein circaaxes quofvis datos per centrum virium tranfeuntes revolvi, & earevolutione {uperfieies curvas defcribere \ tum corpora ita moveriut eorum centra in his fuperficiebus perpetuo reperiantur. Sicorpora illa oblique afcendendo & defcendendo currant ultro ci-troq; peragentur eorum motus in planis per axem tranfeuntibus,atqj adeo in lineis curvis quarum revolutione curvae ill& fuperfi-cies genitae funt. Iftis igitur in cafibus fufficit motum in his lineiscurvis confiderare. Prop. XLVIII. Theor. XVI. Si rot
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