Philosophiae naturalis principia mathematica . tum corporis velocitas tum refiftentia Me-dii, ipfo motus initio, per lineam quamvisdatam AC^ elapfo autem tempore aliquopcr lineam indefinitam D C: exponi per aream ABGD^ & fpatium eotempore defcriptum per lineam AD. Namfi area illa per motum pun&i D augeaturuniforraiter ad modum temporis, decrefcetrecla D C in ratione Geometrica ad modum velocitatis, 8c A C ascjualibus temporibus defcriptse decrefcent in eademratione. Prop. III. Prob. I. Corpork^ cui dmn in Medio (imilari reSia afcendit C, & refifrentia Medii initio a
Philosophiae naturalis principia mathematica . tum corporis velocitas tum refiftentia Me-dii, ipfo motus initio, per lineam quamvisdatam AC^ elapfo autem tempore aliquopcr lineam indefinitam D C: exponi per aream ABGD^ & fpatium eotempore defcriptum per lineam AD. Namfi area illa per motum pun&i D augeaturuniforraiter ad modum temporis, decrefcetrecla D C in ratione Geometrica ad modum velocitatis, 8c A C ascjualibus temporibus defcriptse decrefcent in eademratione. Prop. III. Prob. I. Corpork^ cui dmn in Medio (imilari reSia afcendit C, & refifrentia Medii initio af- cenfus per reclangulum B D fumptum ad contrarias par- tes. Afymptotis reclangu- lis AC, CHj per pundtum B defcribatur Hyperbola fecans perpendicula D £, dem G0-gi 8z corpus afcendendo, tetfh pore DGgd, defcribet VpatiumEGge, tempore DGBA fpati- um. [>3P ]um afcenfus totius E G JB, tempore AB1G1D fpatium defcen-fus BFnG, atq; tempore iDiGig-id fpatium defcenfnsiGF^eig: & velocitates corporis ( refiftentiae Medii propor-tionales ) in horumtemporum periodis erunt ABED, ABed,nulla, ABFiD^ ABieid refpeelive; atq; maxima vclocitas,quam corpns defcendendo potefi acquirere, erit B C. Refolvatur enim reclaneulum AH in rechnoula innumeraA^ Kly Lm, M#, &c. quae fint ut incrementa velocitatumaequalibus totidem temporibus fa&a; & erunt nihil, A\, Al,A /#, A /7, &c. ut velocitates tota*, atq; adeo ( per Hypothefin )ut refiftentia Medii finguloium tem-porum aequalium. Fiat ACad AK vel ABHC adABhJi, ut vis gravitatisad refiftentiam in princi-pio temporis fecundi, deq;vi gravitatis fubducanturrefiftentia, & manebuntABHC, KkHC, LIHC, Nn HC, &c. ut vircs abfoluts quibus corpus in principio fingu-lornni temporum urgetur, atq; adeo ( per motus Legem II. )ut incrementa velocitatum, id eft, ut re&angula^
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