Philosophiae naturalis principia mathematica . arias partes. Afymptotisreftangulis ^C, CH, per punc-tum B defcribatur Hyperbola fecans perpendiculaDEi dem _ G,g; 8z corpus afcendendo , ^ d A ; ^^ c tempore DGgd , defcribet fpatium EGge, tempore T> G B Afpatium ^cenfus totius EGB;. tempore y4B x G % D fpatium de-fcenfus BFz G , atque tempore x © 2 Gx|^i^fpatium-defcenfuszGFzezg: & velocitates corporis Crefirtenriae Medii proportiona-Jes) in horum temporum periodis erunt ^^£2), ABed, nullaABF-lT), ABzezdre(pe&.ive ; atque maxima velocitas , quanicorpus defcendendo poteftacquirere, erit
Philosophiae naturalis principia mathematica . arias partes. Afymptotisreftangulis ^C, CH, per punc-tum B defcribatur Hyperbola fecans perpendiculaDEi dem _ G,g; 8z corpus afcendendo , ^ d A ; ^^ c tempore DGgd , defcribet fpatium EGge, tempore T> G B Afpatium ^cenfus totius EGB;. tempore y4B x G % D fpatium de-fcenfus BFz G , atque tempore x © 2 Gx|^i^fpatium-defcenfuszGFzezg: & velocitates corporis Crefirtenriae Medii proportiona-Jes) in horum temporum periodis erunt ^^£2), ABed, nullaABF-lT), ABzezdre(pe&.ive ; atque maxima velocitas , quanicorpus defcendendo poteftacquirere, erit 5C. Refolvarur enim reftan-gulum A H m redangukinnumera Ak, Kl, Lm, Mn,&c. quas llnt ut incrementavelocitatum aequalibus toti-dem temporibus fadta ; &erunt nihil, /^k, Al, Am, An^&c. utvelocitatestotae, at-que adeo (per Hypothefin)ut refiilentise Medii princi- pio fingulorum temporum aI^lmn ^quaiium. Fiat AC ad AK vd ABHC ^diABkK, ut vis gra-vitatis ad refiltentiam in prmcipio temporis fecundi, deque vi gravf- Dd 3 tatis. ai4 PBILOSOPHI^ NATURALIS D» MoTB tatis fubducantur refiftentiae, & manebunt JBHC, KkHC, LHHCyCmroKvu,J\ln HC, &c. ut vires abfolutae quibus corpus in principio fingulo-rum temporum urgetur , atque adeo (per motus Legem ii) ut in-crementa velocitatum, id elt, utreftangula ^/^, iT/, Z<;», i\/»,&c;& propterea (per Lem. i. Lib, ii.) inprogreilioneGeometrica. Qua-re fi reftae Kk,Ll, Mm, Nn, &c. produftae occurrantHyperbolaem^,r,s,t,&c. erunt&resdJB^K, KqrL,LrsM,MstN,&, adeoque tum temporibus tum viribus gravitatis fempersequalibus analogae. Eit autem area JBcfK {^tr Corol. 5. Lem. vit& Lem. i.)adaream^^^ut iT^ ad4^^feu/fCad i^/^T,hoc eft , ut vis gravitatis ad refiftentiam in medio temporis fimili argumento areisqKL r, r L M s,s MNt,& ad areas qklr, rlms,smnt, &c. ut vires gravi-i:atis ad refiftentias in me-dio temporis fecundi, ter-,tii,quarti, &c, Proindecum areae aequales BAKq,qKLr, rLMs, sMNt,&
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