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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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1II
PHITLOSOPMLA NATURALIS
PROPOSITIO XXXIH. PROBLEMA XXVII.
eosita cujuscunque reneris vi centripeta, es concessis figurarum
curvilinearum quadraturis, requiritur corporis recta a(cenden-
eis vel descendentis tum Velocitas in locis sinculis, tum Tempus
quo corpus ad locum quemvis perveniet: Et contra.
De loco quoris A in recta AD F C cadat corpus l3 aeque oc
ejus P crigatur semper perpendicularis P. C, vi centripetx in loco
illo ad centrum C cendenti provortio.
nalis: Sitque B FC linea curra quam
punctum C perpecuo tangit. Coinci
dat autem LC ipso mocus initio cum
perpendiculari AB, e crit corporis V c
locitas in loco quovis L. UE arCK CUr-
vilincae ABG F. latus quadratum.
Q. F. T.
In E G CaPIREUE F. M laceri quadr2
Eo arex ABG F reciproce proportio-
nalis, _C AE AL. M linea curra quam
punctum Mperpetuocangit, _c erit Pem-
pus quo corpus cadendo describie li-
neam A F. uE area curvilinca AL. MF.
. F. I.
Fcenim in recta AF capiatur linca
quam minima D P datae longitudinis,
SIEqUC D L F lOcuS linea F MC ubi
corpus verlabatur in D; et si ca sic ris centripeta, uE arCX ABCF F.
latus quadratum sic ut descendentis velocitas, erie arca ipla in du-
plicata ratione relocitatis, id est, s pro velociratibus in D et F
Seribantur V dc V fI, Crit arCa ABF D UEVV, _ arC2 ABC F. ut
YV + 2VI F II, dc dirisim area D FG F. uc 2VL F II, adeoque
DFGF
DF.
 2VI. F I
DF.
id cst, si primae quantiracum nascencium
V
rationes sumancur, longitudo D F ut quaneitas  F adeoque c.
CY
cium ve quancitatis hujus dimidium  F. PA autem tempus quo
COrDUS
DE MOTV
EDAFORVH