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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 68, page id 1041163592:0102
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68
PHTLOSOPMILLE NATDRALIS
Per puncta , B, C, D ec aliquod infinitorum punctorum P, p1-
Copronon ed p. concipe Conicam sectionem describi: dico punctum P hanc
Tempertangere. Si negas,
junse  Cecantem hanc
Conicam sectionem alibi
quam in F, S Acri PocCA,
puta in b. Ergo ( ab his
punctis p ee b ducantur in
dacisangulis ad latera Tra-
Perii rect_ P9, pF, P5, pF
e bk, bF, bs, b d; eric
uE bk X bF ad bfX b d ita
(Der LCm. XVIL) p9XpY
2d p5 X pF, d ita (per
FIypOch.) P QX P R ad
FSX P T. F.H _C DFOD.
ter similicudinem Traperiorum bk As, P _ A5, ut bk ad bs ita
P
terminos correspondentes hujus, erit br ad b d ut F R ad FT. RF-
80 Trapezia requiangula Drb a D R F T Cimilia PunE, S corum
diaronales Db, D F proxeeren coincidunt. Incidic itaque b in
intersectionem rectarum AP, D P adeoque coincidit cum puncto
P. Ouare punctum P, ubicunque Cumatur, incidic in assignacam
Conicam sectionem. 9. F. D.
Corol. HIinc A rectae ErCS P Q F R, PSa puncto communi F
ad alias rocidem posicione datas rectas AB, CD, AC, singulx ad
singulas, in datis angulis ducantur, Aieque rectangulum sub duabus
ductis P _X P R ad quadratum tertis P S quad. in daca racione:
punctum F, 2 quibus rectae ducuntur, locabitur in sectione Conica
quae tansit lincas AB, CD in A e C; e contra. Nam cocac linca
B D cum linca AC manente positione crium AB, C D, AC; de-
in cocac etiam linca F F cum linea F S: sc rectangulum FSX P Y
erader PS quad. rectae que AB, C D quae curvam in punctis A_B,
C_ D secabane, jam Curram in punctis illis cocuntibus non am-
plius secare PoNune sed tancum tangenE.
Scholium.
Nomen Conieae sectionis in hoc Lemmate late sumieur, ita ve
sectio tam Rectilinca per verricem Coni cransiens, quam Circutaris
basi parallela includatur. Nam s punctum p incidie in rectam, qua
quaeris ex punctis quatuor A, B, C, D junsuntur, Conica sectio
VertE.
DE MOZV