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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 57, page id 1041163592:0091
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10
et
det
PRINOIPTA MATHEMATICA.
De loco F, secundum lincam P R, CXCAE COrpUIS F, cum data velo
F. 1B E1
citate, ex mox inde, cogente vi centripera, dellectac illud in Coni. lutos
sectionem P 9. TIanc isitur recta P R tanget in P. Tansatitidem
recta aliqua pr Orbitam pg in p, dc si ab S ad eas tang entes demieti
incelligantur perpendicula, erit (per Corol. L. PFOP. ZVT.) latuS re
ctum principale Conilectionis ad latus rectum principale Orbicx, in
ratione composica ex duplicata ratione perpendiculorum ec dupli
cata ratione relocitatum, aeque adco datur. Sic istud L. Da-
cur praeterea Conise-
ctionis umbilicus S.
anguli RPS com-
plementum ad du-
05 rectos AaL anC
IuS RF II, ec dabi
cur politione linca
P FC in qua umbilicus
alter TY IOCaEUT. DC-
misso ad F FI PerDen-
diculo SX, crisi intelligatur semiaxis conjugatus BC, e crie
5P9. = 2R PHL + F FIg. =SII9. = 4 C TI9. = 4 BIIg -= 4 B,C 9
dF + F HL: quad. = F XSF + F H = S F 9. + 2S F
LXSF F F H. Addantur uerobique 2 H F I -5 P
= L. XSF + F A _E ACE L XSV F Y 1 = 25 PH + 2Y
(en 5~ + PHI, ad F HI, uE 2S F + 2R F adL. Onde datur FF
cam lonsitudine quam positione. Nimirum s ca corporis in 
velocitas, uc lacus rectum L. minus Fuerit quam 25F + 2R F
Jacebic F FI ad eandem parrem cangeneis F R cum linea FS,
adeoque figura cric Ellipsis, et ex datis umbilicis S, TI, ec aXC
principali SP L P HI, dabitur: Sin tanta sic corporis relocitas ue
lacus rectum L. aequale Fuerit 25F = 2 R P, longicudo F FL inA-
nita erie, _E PrODEerCa Roura erit ParabOla aZem habCnS SFL par2I-
lelum linexe P K, ex inde dabitur. Ouod si corpus majori adhuc
cum velocitare de loco suo P exeat, capienda erie lonsitudo P I
ad alteram parrem rangentis, adeoque tansente inter umbilicos per-
gente, sigura erit IIyperbola axem habens principalem aequalem dit-
ferentix linearum SZ _c P FI, e inde dabitur. 9. L. I.
Corol. T. Flinc in omni Conilectione ex dato verrice principali D.
latere recto L, exumbilico s, dacur umbilicus alter FY capiendo D LL
2d DS uE est lacus rectum ad difterentiam inter latus rectum de
+DS. Nlamprovoreio SP + P II ad, P IL ut 2SP + 2 RL P ad L.3
I1