Philosophiæ Naturalis Principia Mathematica

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Philosophiæ Naturalis Principia Mathematica
Isaac Newton
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Ent en,m fpatium illud ad fpatium L defSnZ^l motus totus fub initio ad motus iUius partem amiffanu ^ Lem e 237 } Lemma. L Quantitates differentiis fuk froportionaks^ funt continue proportiona^ les.
Sic A ad ^-B ut B ad Z^-C & C ad C-D &c. & dividen- do fiec ^ ad J5 ut B ad C & C ad D &c. CÌ,E. D.
Prop. IL Theor. IL Si cor pori refiflitur iu ratione ^velocitatisi é^ fola ^i infita per Medi^ am ft ni il are moveatur^ fumamjir antew tempora ccqualia : ^velocita-- tes in principiis fmgìdorum tempon
...im jiwt in progrejfione Geome- trica ^ C^ fpatia fmgulis temporibus de/cripta funt ut 'veloci- tates, Cas. I. Divìdatur tempus in particiilas aequales, & fi ipfis partìcularum initiis agat vis refijftcntiis iinpui fu unico, qax fit ut veJocitas, crit decrementum vclocitatis fingulis temporis particu- lis ut eadcm vclocitas. Sunt ergo vclocitates difFerentiis fuispro- portionalcs, & propterca ( per Lem. I. Lib. IL ) continue pro- portionalcs. Proinde fi ex aquali particularum numero compo- nantur tempora quxlibet sequalia, erunt velocitates ipffs tempo- rum initiis, ut termini in progreffione continua, qui per faltum capiuntur, omiilb paffim asquali terminorum intermediorum nu- mero.

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