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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 51, page id 1041163592:0085
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acta malccatia
Inveniatur vis quae cendic ab s Pervola centro C. Prodibithaec
distantiae C. P proxortionalis. Inde vero (per C orol. 3PrOD. VIT.)
vis ad umbilicum Scendens crie ue
reCIPTOCE UE SF9. 2. F. I.
D F. Cub
5F hoc eAt, ob datam P F.,
Eodem modo demonstratur quod corpus, hac vi centripeca in
centritusam versa, morebitur in EIyperbola conjugata.
L E M M A XII.
Latus rectum Parabolae ad verticem quemvis pertimens, est quadru
plum distantiae verticis illius ab umbilico firurae. Patet ex C Onicis.
L E MM A XIV.
Perpendiculum quod ab umbilico Parabolae ad tansentem ejus demitti
tur, medium est proportionale inter distantias umbilici a puncto con
ractus e a verrice principali ficura.
Sic enim AQ F Parabola, S umbilicus ejus,  vertex principa-
lis P punctum
contactus, PO
ordinacim ap.
plicata ad dia-
metrum prin-
cipalem, F NI
cansens dia-
metro princi
Palioccurrens
in M, _
linca De
AN e OF, ec inde triangulum S_ N rectangulum M 2d A e
limile criangulis aequalibus SElL VILL.
et SNV ad d A.
Lut60 L 8 Cl de d2l3
Corol. 2. FSg. CA ad S Ng. UE F SadS
Corol. 2. F.F ob datam S A, cA SNg. ut PS.
Idem aliter.
dicularis ab umbilico in tangentem. Jungatur AN, de ob aequales
MS ec S F, MN e NF, M A et AO, Parallelae crune rectae
D
eximve
Drol.