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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 41, page id 1041163592:0075
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O
di
D
t
PRTNOTDTA MATHDMILAL LOL
Nam perpendicula a cenero S
in tansentCS PF, Q T demissa (per
COrOl. F. PFOD. P.) LunE reciPTOCCS
ue relocitates corporis in punctis
PXV; adeoqueper constructio.
nem ut perpendicula AP, B 9 di-
recte, id est ut perpendicula a pun-
eto D in tangentes demissa. IIn-
de Facile colligitur quod puncta
S,D, T, Cunt inuna recta. FF simili
arsumento puncta S, F, V Cunceti-
am in una recta; ex propterea centrum S’in concurlu rectarum TD, V P.
vertatur. d. F. D.
PROPOSITIO VI THEOREMA V.
Si corpus in spatio non resistente circa centrum immobile in Orbe quocun.
querev olvatur. arcum quemvis jamjam nascentem tempore quam
minimo describat, C facitta arcus duci intellicatur quae chordam bi-
secet, e producta transeat per centrum virium: erit vis centripeta
in medio arcus, ut saritta directe es tempus bis in verse.
Nam Pagieta dato rempore est uE vis (per Corol. 4PrOD. 1,) _ augen-
do tempus in ratione quaris, ob auctum arcum in eadem ratione la-
sicca augetur in ratione illa duplicata (per C. OrOl. 2 ec 3, L CM. ZF,) ad
eoque estut ris semel ec tempus bis. Subducatur duplicata ratio tempo-
ris uerinque, ee het risur lagitra directe ec tempus bis inverle. Q. F.D.
Idem Facile demonstratur etiam per Corol. 4 LCm. X.
Corol. T. Si corpusFprerolvendo
circacenerum sdelcribat lincam
curvam AF O. tangat vero recta
Z F R curram illam in puncto
quorisP, Sc ad tangentem ab alio
quoris Currae puncto  agatur
R distantia SF parallela, ac
demitratur QT perpendicularis
ad distanciam illam SF: vis cen-
cripeta crit reciproce ut solidum
P quad. X Q F quad. Ei mocto solidi illius ea semper Lumatur quan-
eR
cicas, quae ulrimo sit ubi cOCunt puncta P et . Nam _ R aequalis
o
PRTMOS