Newton, Isaac - Philosophia naturalis principia mathematica

Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1Gv; & GvPad Qv quad.ut PCquead CDq; & (per Corol. 2.
Lem. VII.) Qv quad.ad Qx quad.punctis Q& P coeuntibus fit
ratio æqualitatis; & Qx quad.ſeu Qv quad.eſt ad QTq,ut EPq,
ad PFq,id eſt ut CAq,ad PFq,ſive (per Lem. XII.) ut CDq,
ad CBq:& conjunctis his omnibus rationibus LXQRfit ad
QTqueut ACXLXPCqXCDqſeu 2CBqXPCqXCDqad
PCXGvXCDqXCB quad.ſive ut 2PCad Gv.Sed punctis
P& Q coeuntibus æquantur 2PC& Gv.Ergo & his propor
tionalia LXQR& QTqueæquantur. Ducantur hæc æqualia in
(SPq/QR). & fiet LXSPqueæquale (SPqXQTq/QR). Ergo (per Corol. I

22[Figure 22]
& 5 Prop. VI.) vis centripeta reciproce eſt ut LXSPq,id eſt
reciproce in ratione duplicata diſtantiæ SP. que E. I.

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