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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 78, page id 1041163592:0112
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8
BTITLOSOPTITA NATORALIS
DF Moro tique occurrentibus in YY e T. SccetuT tangens in A, itd II H
daronon YI A ad AT, uc cA rectan-
culum sub media proportio-
nali Inter C G _ C F et me-
dia proportionali inter BII8
HD, ad rectangulum subme-
dia proportionali inter D G SE
GB ee media proportionali in-
TeF P Pe IC; e erit A punc.
cum contactus. Nam s rectae
P T Parallela HIX Trajecto-
riam secet in punctis quibus-
vis X a T: erit (ex Conicis)
punctum A ita locandum, ue fuerit PI A quad. 2d. AT quad. in r2-
tione compolita exratione rectanguli X IIY ad rectangulum B FY D
seu rectanouli CC F ad rectangulum D CB EE ex ratione rectan
guli BII D ad rectangulum P IC. Invento autem contactus
puncto A, describetur Trajectoria uE in CaTU PRIMO. O. F P
Capi aurem pocest: punctum  vel inter puncta I _ Y, vel extra;
ee perinde Trajectoria dupliciter delcribi.
PRODOSITTO ZXIV. PROBLEMA XVI.
Trajectoriam describere quae transibit per data tria puncta  rectas
duas positione datas contine et.
DEnEUE TanGenteS TYY, K L. &
puncta B, C, D. Per punctorum
duo quaris B, D avc rectam in-
Finitam BD tansentibus OCCur-
rentem in punctis LI, R. Deinde
etiam per alia duo quaeris C) D
asc intinitam C D tangentibusoc-
currentem in punctis L, L. ACtaS
Ita (eCa In R EE S, UE SIE F R 2d
R R ut est media proporcionalis
inter BTI _ F D ad mediam
proportionalem inter BK _ R D;
ec (S ad L. S ut eAt media prO-
portionalis inter CT_ PD ad me-
diam proporrionalem inter C. L
E
u0-