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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 67, page id 1041163592:0101
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PRINCIDIA MATIIEMALIBI
C45. 2. Ponamus jam Trapezii latera Oppolita C a B D HON LIBIE
eNC parallela. AsC B d Parallelam AC _ Occurrentem cum rectae PRIWVS.
ST in t, tum Conicae lectioni in d.
ec ipsi Z Q Parallelam agc D MI
secantem C d in MI _E AB in IV.
Jam ob similia criangula B F +
DBN; Cst BF CCUT O ad Y+ uF
D N ad NB. Sic et Rr cA 2d
19 TCu FS uE D M 2d AN.
Erso, ducendo ancecedentes in
ancecedentes ex consequentes in
consequentes, ut rectangulum FO
in Rr est ad rectangulum F S in
TF ita rectangulum ND MI CA
funse a eCaeL L
ad rectangulum AN B, _E (pEF C a T. Z) R
ad rectangulum F S in FF, ac dirisim ia rectan
est ad rectangulum PSX FF. 9. F. D.
Ca5. 2. Ponamus denique lineas
QuatuOF P ∞ P R, P S, F F non
CsC parallelas laceribus AC, AB,
sed ad ea utcunque inclinatas. P. 2-
rum vice agc F9, Fr parallelas
ipA AC; ec F5, F+ Parallelas
ipA AB; SE Propcer datos anou-
los criangulorum P _g, F Rr,
P S5, F T+, dabuntur rationes
P ad P 9, PR ad Fr, F
ad F S, ec F Y ad P +; atque adeo rationes compolx L  X P R
ad P 9 X P r, _ F SX FT ad Fs X PF. Scd, per superius de
monstrata, ratio Pg X Fr ad FsX P + data cA: ErO ee ratio
Q X P R ad PS X FZ
d. F. D.
L E M M A XVIII.
lisdem positis, si rectanculum ductarum ad opposita duo latera Tra
pexii POX PR sit ad rectangulum ductarum ad reliqua duo late-
ra PSXPT in data ratione; punctum P, a quo lineae ducuntur,
tanset Conicam sectionem circa Trapezium descriptam.
K.
ang
t
atum
XT L
PeF