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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 85, page id 1041163592:0119
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PRTNOIPLA MATHEMATICA.
L E MM A XZV.
Si paralleloerammi latera quatuor infinite producta tansant Sectio-
nem quamcunque Conicam, e ab scindantur ad tangentem quamvis
quintam; sumantur autem laterum quorum vis duorum contermi-
norum abscissae terminatae ad angulos oppositos paralleloerammi:
dico quod abscissa alterutra sit ad latus illud a quo est abscissa, ut
parslateris alterius contermini inter punctum contactus.  latus
tertium, est ad abscissarum alteram.
Cangane parallelogrammi MIL LK latera quatuIOF M L, LK, KC L.3
MI sectionem Conicam in A, BC
hraeclatera in F, Q, II
_c L; TUmanEur auTem
lacerum NV, KI ab-
SCINX M F, XL Q, vel
IaECTUI KT, MF ab-
SCiNa XL FI, MF: di-
Co quod sIE MF. 2d
ML UE BR ad R Q:
e KII ad KL. uE
AM ad MIF. Nam
per Corollarium (c
t
cundum Lemmatis superioris, est NI F. ad F Y uE (A MI CCU) BR 2d
B9 ec componendo NIF 2d MY uE B K ad R 9. 9. F. D
IECM RFY ad FY L uE (B X (CV) AM ad AF, ec diridendo R IY ad
RF. ut AM ad MF. 9. F. D.
Corol. T. Hlinc si dacur parallelogramum TK I. M, circa datam Sec-
tionem Conicam descriptum, dabitur rectangulum X QX M F, ut.
ee huic aequale rectansulum XIIX M Fi.
Corol. 2. FF sI (exFA duICatuE tansenS e g tangentibus RL, NII.
Occurrens in g de e; rectangulum K aX MF aequabicur rectan-
Sulo KgX Me; eritque K Q ad Me uF Kg ad M En d dirisim ut
92d l e.
Corol. 3. Vnde exiam l F. g. e Q jungantur d Bileceneur, ec recta
per puncta biseetionum agatur, cransibie haec per cenerum Sectio-
ao Coricae. Nam cum (it R 4 ad F. e uE K R dd Mes cransibic ea
dem
edran c fuinca Q
A
t
L.LBEK
PRINVS..