Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1(BDXV2/4AB). Momentum hujus areæ ſive huic æqualis (DAqXBDXM2/DEqXAB)
eſt ad momentum differentiæ arearum DET& AbNK,ut
(DAqXBDX2MXm/DEqXAB) ad (APXBDXm/AB), hoc eſt, ut (DAqXBDXM/DEq)
ad 1/2BDXAP,ſive ut (DAq/DEq) in DETad DAP; adeoque ubi
areæ DET& DAPquam minimæ ſunt, in ratione æqualitatis.
Æqualis igitur eſt area quam minima (BDXV2/4AB) differentiæ quam
minimæ arearum DET& AbNK.Unde cum ſpatia in Me­
dio utroque, in principio deſcenſus vel fine aſcenſus ſimul deſcrip­
ta accedunt ad æqualitatem, adeoque tunc ſunt ad invicem ut area
(BDXV2/4AB) & arearum DET& AbNKdifferentia; ob eorum ana­
loga incrementa neceſſe eſt ut in æqualibus quibuſcunque tempo­
ribus ſint ad invicem ut area illa (BDXV2/4AB) & arearum DET&
AbNKdifferentia. que E. D.

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