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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 249, page id 1041163592:0283
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IIIHIII
PRINCIPTA MATTTEMATICA.
243
Nam relocitatis decrementum P Q, in data temporis particula LIven
factum, est uc summa relictentix AP g F 2B A F e Gravitatis SECVNDUS.
AB9 -B D9, id cAt, ut B F g - B D g. FA autem arCA D YV
ad aream D F Q ut D Fg ad D Pg adeoque, si ad D F demitta-
cur perpendiculum GT, ut GTg Teu GD g = D Fg ad B D9
uEque GD g 2d B F q ec divisim uE D Fg ad B F g - BD9.
Duare cum area D P G AE uE P 4 id eAt, uc B F g - B Dg; eric
area D TV uc datum D Fg. DecreSCIE igIEUF arCA F, D F unifor-
miter linsulis temporis parciculis aequalibus, per subductionem par-
ticularum coridem datarum DTV, dt Propterea tempori propor.
cionalis eAt. d. F. D.
Cas. 3. Sit AF relocitas in descensu corporis, _t AF 9 + 2B AP
resistentia, e BD g - ABg vis graritacis, existente anguio DB A
recto. EF (I CentrO D, vertice
principali B, describatur FTy.
Derbola rectangula B F YY
secans productas D A, D F et
D Q in F; T e V; cxit HIy-
Derbolae hujus (ectOE D F. T vE
cempus deicentus.
Nam velocitacis incremetum
P 9 eique proportionalis arca
DY
eis supra relstentiam, id eAt, ut
BDg -AB9 - 2B AF - AF
(cu BD q =BF g. PC arca
DTV eA ad aream D P Q uE
DF9 ad D P9, adcoque uE
6T9 Icu GD 9 - B Dg 2d
BF g ueque G Dg ad BDq
ex dirisim ut B D q ad B D g - BF9.
Ouare cum area D F0)
sIE uE BD 9 - B F q. CrIE arC2 D TV uc darum BDg. Crescie
IgieUE arC2 P DT unitormiter singulis temporis particulis equali-
bus, per additionem tocidem datarum particularum D T V, ec prop.
cerea cempori descensus proportionalis cAt. Q. F. D.
Corol. Igitur velocitas AP est ad relocitarem quam corpus rem-
DOrC P. DT, in spario non resistente, alcendendo amittere vel de-
Ecendendo acquirere portets ut area crianguli D A F ad aream sC
ctoris centro D, radio D A, angulo AD F descripei; ideoque ex
dato cempore dacur. Nam relocitas, in Medio non resctentes tem-
LK
Pori
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