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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 109, page id 1041163592:0143
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PRINOIPIA MATHIEMATICA.
Cas. 2. Jam E Figura D F. SC irculus eAt rel Hxperbola, bisece.
cur ejus transversa diameter AS in O, dc CriE
S0 dimidium laceris recti. EE quoniam cA
TC 2d TD ut C c 2d D d _ TD ad FS uE
CD ad ST; CFIE CX aequo F C ad Y S ut
CDXCC ad SPZ D d. Scdper Corol. T. ProP.
XXXIXI CA TC ad FS ut AC 2d AO, DUTa SI
in coitu punctorum D, a capianeur lincarum
rationesultimae. Freo AC cA 2d (AO PCu) SR
UE CD X CC ad S Y X D d. POTTO COrPOTIS
descendentis velocitas in C est ad velocitarem
corporis Circulum intervallo SC circa cen-
trum S describentis in subduplicata rationc
AC ad (AO vel) SR (pEF PFOD. ZXXILI.) RF
haec relocitas ad velocitatem corporis descri.
bentis Circulum OFk in subduplicata ratione
SK ad SC Per COr. 6. Prop. 1V, ec Cx aequo velo.
citas prima ad ulcimam, hoc est lincola Cc 2d
arcum Xk in subduplicata rarione AC ad SC
id est in ratione AC adC D. Onare CAC D XCC
aequale AC X KK, dE PrOpterca AC ad SR uE
ACZ RR2dSYY D d, indeq; SR XRh aequa-
IC SYZD du _ ZSRX KK aequalC = SYX D d
id est area KSk aqualis arexe SD d. Singulis
isitur temporis particulis generantur arearum
duarum particulae RSs, ec SD d, quae, si mag-
nitudo carum minuatur ex numerus auseatur in infinitum, racio-
nem obcinene aequalitatis, et proprerea (per Corollarium Lem.
atis IV) areae coca simul genicae sunt semper aequales. . F.. D.
Cas. 2. Ouod si Figura D F S ParabOla (E, invenietur eNC UE s
PTa C D XCC 2dSYX D a uE FC ad ZS, hoc est ut 2 ad r, 2d-
eoque = CD X Cc aequale ese : SPX Dd. Sed corporis caden-
eis velocitas in C aequalis est velocitati qua C irculus interrallo ZSC
umtormiter deseribi posit (per Prop. XXXLV) LFhaec velocitas ad ve-
locitatem qua Circulus radio SR describi poMic, hoc elt, lincola
Cc adarcum RLR (per C orOI. 6. PFOD. LV) eAt in subduplicata ratione
SRad 2SC, id est, in ratione SR ad = C. D. Duare clt ZSR X KK
aequale +C D XC∞, adcoque aequale 2SPX D dhoc est, arca R Se
aequalis areae S D d, UE TUPrA. d. Li. D.
109
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