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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 105, page id 1041163592:0139
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PRINCIDTA MATHEMALICA
DF C, TIO
NII
De Corporum ascensu  Descensu Rectilineo.
PROPOSITTO ZZXIL PROBLEMA XXIV
Posito quod Vis centripeta sit reciproce proportionalis quadrato di
stantiae locorum a centro, Spatia definire quae corpus recta cadendo
datis temporibus describit.
Cas. T. Si Corpus non cadit perpendieu.
lariter describet id, per Corol. L. PFOD. ZILI.
Sectionem aliquam Conicam cujus umbili-
cus congruit cum centro virium. Siet Sec.
tio illa Conica AR P B e umbilicus ejus S
Et primo si Figura FIlipsS eAt, super hu-
jus axc majore AB describatur Semicirculus
AD B, ec per corpus decidens transcat rec.
ta D F C perpendicularis ad axem; actisque
DS, FS CriE arca ASD arCA ASP aE
que adeo etiam tempori provortionalis. Ma
nente azc AB minuatur perpetuo latitudo
Ellipscos, ee semper manebit arca AS D
tempori proportionalis. Minuatur lacitude
illa in infinicum: ec, Orbe AP B jam coin-
cidente cum aXC AB ex umbilico S cum
axis termino B, delcendet corpus in recta
AC. _ area AB D eradet tempOrI prO-
portionalis. Dabitur itaque Spatium 
quod corpus de loco  perpendiculariter
cadendo tempore dato describit, si modo tempori provorriona-
lis capiatur area AB D, e a puncto D ad rectam AB demit.
catur perpendicularis DC. 8. F.. I.
.....
ommmum
as.
L IBKR
P RI AIV 50