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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 84, page id 1041163592:0118
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PFTTLOSOPHTA NATDRALIS
LE MIMIA XXIV.
Si rectae tres tangant quamcunque Conisectionem, quarum duae pa
rallelae sint ac dentur positione; dico quod Sectionis semidia-
meter hisce duabus parallela, sit media proportionalis inter ha-
rum sermenia, punctis contactuum e tangenti tertiae inter-
jecta.
SunEo AF, G BP2-
rallelae dux Conilee
tionem AD B Ean
gentesin Ae B; L.V
recta certia Conitee.
cionem tansens in L
et OccurrenS prioribus
cansentibus in le G;
scque C. D Cemidiame-
ter Ligurae tangenti
bus parallela
quod AF, C D, B
fune continue proporcioaus.
Nam s diametri conjugatae AB, DM tangenti FG OcCUrran
in F: e TI, leque mutuo secent in C, ec compleatur parallelogram-
inUm TKC L; erie, ex natura Sectionum Conicarum, ut L.C 2d
CA ita C A ad C L, _ ita dirisim F C =C A ad C A - CF, Ceu
E A ad AL, e compoMItC F. A ad F. A + AL TCU F. L UE F. C 2d
F.C + C A Ceu FB; adeoque (ob similitudinem trianzulorum P. AF,
EL B FCHI EBG) AF 1d L. TUE CFF 2d BC. FA icidem.
ex natura Sectionum Conicarum, L. Y (Ccu C) 2d CD ut CD ad
CFT; aeque, adeO CX aQUO PeRTUrbaTC,  F ad CD ut C D ad BC.
d. F. D
Corol. 2. Ilinc A tangentes dux FG, P Q cansentibus parallelis
AF, BC OCCurranE in F e G, P e Q. seque mutuo secent in O;
erit (ex aequo perturbace) AF ad B a uE A P ad B C, e divisim
Ut F P ad G ∞ atque adco uE FO adO.
Corol. 2. Unde etiam rectae duxe PC, F  per puncta P ec C
F ex _ ductae concurrent ad rectam AC. B per centrum Figurx &
puncta contactuum A, B tranleuncem.
LEMI
L
DE MOTD
EORPOKVM