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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 251, page id 1041163592:0285
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PRINCIPTA MATHEMATTCA.
25I
Cas. 2. Sin corpus alcendie, de gravitas HIE ut ABg =BD q LIVEN
linea AC (F1S. C al. 2. PrOP. XIIY) erir 2B9- BD4, et DZ
erit 2d D P g uE D Fg Icu D Bg 2d BF g - B D 9 seu A F 9 +
2BAP + ABg - B D 9, Id CA, ad AR X  + AC X B ICVCR X L.
ldeoque area D TV crit ad aream D F Q uE DBg adCKX L.
Cas. 3. EF codem argumento, s corpus delcendit, et proptecca
Sraritas sIEuEB D g - ABg, e linea C (F18. C aC. 3. PFOP. prXCCd.)
aequecur BDg -AB9
adC R XZ: UE suPra.
erit area DTV ad aream D P Q ut D B9
Cum isitur arex illae semper sint in hac ratione; sI PrO arCa
DTV, qua momentum temporis sibimet ipsi semper aequalc Cx
Donitur, scribatur determinatum quodvis rectangulum, puta
BDXm, erit area D F ∞, id eAt, EB D X P Q; ad B D Xm ut
CK X Z ad BD g. Acque inde AE F Q X BD cub. aequale
2BD XMZCKZZ, _E ATCX ABNVK MOmCnEUm RI. O N Tu-
perius inventum, AF P P ZB D Xm
AB
ARFEFAEUE AFCX DF F mo.
mentum DTV seu B D Zm, ee restabie AP XBD Xm
AB
Est igi.
tur differentia momentorum, id est, momentum disterentix arca-
rum, aequalis 2P ZBD Xm
AB
; de Propterea (ob dacum L DXm
ut velocitas AP, id cst, ue momentum spatii quod corpus alcen-
dendo vel descendendo describit. Ideoque differentia arearuM
ec spatium illud, proportionalibus momentis crescentia vel decre-
Ecencia ex simul incipientia vel simul crancscentia, sunt proportio-
nalia. d. F. D.
Corol. Igitur Si lonsieudo aliqua V sumatur in ca ratione ad du-
Dlum lonsitudinis MI, quae oritur applicando aream D F F ad B D,
quam habet linea D A ad lineam D Fs Spatium quod corpus alcen-
su vel descensu toro in Medio resistente describit, erit ad spatium
quod in Medio non relstente eodem tempore describere pollct,
ut arearum illarum differentia 2c
BDXV
+QB3 ideoque ex dato tem-
Pore dacur. Nam spatium in Medio non resistente est in dupli-
cata ratione temporis, sIrC ut V, ec Ob datas BD et AB, ut
EK
2
B
S2. C. D 413.