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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 72, page id 1041163592:0106
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2
PHILOSOPMTLLE NATDRALIS
De MOTD CorOl. T. FIInC (I aGaEuT BC SCCanS P Q in r, ec in F Z capiatUE
Gonronon p, in ratione ad Fr quam Habet P T ad F R: Crit Bt tanGCnS
Conicae sectionis ad punctum B. Nam concipe punctum D coirc
cum puncto B ita ut, chorda B D cranelcente, BT tangens cra-
dat; e CD ac B F coincident cum C B e BF.
Corol. 2. EF vice verta AI
BF Ec tangens, ec ad quod-
vis Coniexe sectionis punc-
tum D conveniant B D.
CD; CrIt P R ad PT ut
UE Fr ad P F. EE CONEra,
SI SIE Z R ad F Z UE Fr ad
PF: convenient B D, CD
ad Conicae Sectionis punc-
um aliquod D.
Corol. 3. Conica sectio
non secat Conicam sectio-
nem in punctis pluribus quam quatuor. Nam, si teri potest, trans-
eane dux Conicae sectiones per quinque puncta L, B, C3 P3O; ca-
que secet recta B D in punctis D, d ec iplam P  secet recta C a
in F. ErSO D R cA ad P F uc P e 2d PZ; unde P R d P esibi
inricem aequantur, contra Flypochesi.
L F M NI A XXI.
Si rectae duae mobiles es infinitae BHI, CMI per data puncta B, C, ceu
polos duetae, concursu suo M describant tertiam positione da
tam rectam WNI; e aliae duae infinitae rectae BD, CD cum
prioribus duabus ad puncta illa data B, C datos anculos
MIBD, MCD efficientes ducantur; dico quod hae duae BD,
CD concursu suo D describent sectionem Conicam per puncta
B, C transeuntem. Ft vice versa, si rectae BD, CD concur (u
suo D describant Sectionem Conicam per data puncta B, C, A
transeuntem, es sit ansulus DBM semper aequalis ansulo dato
ABC, angulusque DCM semper aequalis anculo dato ACB:
punctum MI contincet rectam positione datam.
Nam
ou