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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 279, page id 1041163592:0313
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PRINCIPLA MATETEMATICA.
dicatur X, aeque Arex P TO R decrementum RG Er dCCUT, CrIE LIVEN
incrementum arcxe Y ut F IC R -Y
SECONDOS.
Duod si V delignet vim a gravicace oriundam, arcui describendo
CD proportionalem, qua corpus urgetur in D: eE R pro resicten.
Eia POnatUE: erit V -R vis EOTa qua COrpUS urgCtuE in D. F B
icaque incrementum relociatis ut V - R ee particula illa temporis
in qua factum est conjunctim: Scd e velocitas ipsa est ut incre
mentum contemporancum spatii descripei directe et particula ca-
dem temporis inverle. Inde, cum relistentia (per LIypochelin)
SIc ut quadratum relocitaris, incrementum resistentia (per L Cm. LI)
erit ut velocitas ex incrementum velocitaeis conjunctim, id est, uE
momentum spatii ec V =R conjunctim; aeque adeo, si momen-
tum spacii detur, UE V =R; id eA, Si pro vi V scribatur ejus ex-
DOnenS PYO R, d ressentia R exponatur per aliam aliquam are.
am Z uE F TG R = Z.
lGitur arca PTGR per dacorum momentorum subductionem
uniformiter decrescente, crescune area Y in ratione F ICR = Y.
_e area Z in ratione P IG R =Z. RE PRODECrCA (I ArCX V ex 7, (-
mul incipiane ee sub inicio aequales snE, hae per additionem aequa-
lium momentorum pergent esse aequales, et aequalibus itidem mo-
mentis subinde decrescentes simul cranescent. Rc vicisim, S Simul
incipiunt ec simul cranescunt, aequalia habebunt momenta e sem-
Per erunt aequales: id adeo quia s relistentia Z auseatur, reloci-
eas una cum arcu illo Cas qui in ascensu corporis delcribitur, dimi-
nuetur; ex puncto in quo motus omnis una cum resistentia cestat
propius accedente ad punctum C, relistentia cirius eranescet quam
area Y. Ec contrarium eveniet ubi resistentia diminuitur.
Jam vero arca Z incipit desinitque ubi resistentia nuIIa cA, hOC
est, in principio e Ainc motus, ubi arcus C D, CD arcubus CB 8C
Ca aequantur, adeoque ubi recta RCr incidic in rectas F dc CI.
FC arCa Y seu
eoque ubi 
TF F -TG II incipit desinitque ubi nulla CA, 2d-
Aructionem) ubi recta R C incidit in rectas QF _ CT. Proin-
deque arex illae simul incipiune ei simul erane(cunt, es Propterea
Temper sunt sequales. IBitur ares
B LE. F = TC TL aequalis cst
ATeX Z per quam resRentia exPOnitUE, _ propterea est ad aream
PZNM per quam graritas exponitur, ut resistentia ad grarita-
rem. d. L. D.
Corob.