Full text: Pergaeus, Apollonius: Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi

Apollonij Pergæi & per rectam B E extendatur aliud planum E N O B inter duo plana contin-
gentia prope verticem A vbicumq; cadens, quod ſecet vtrumque conum, & cir-
culum baſis in recta linea N O, & ſuperficies duorum conorum in lateribus B
N Q, E N, B O, E O R, quarum B N occurret ſemiſectioni A H in quolibet
eius puncto Q prope verticem A, eo quod portio A H, & peripheria A N C ex
cepto puncto eius A totæ inter duo plana conos tangentia intercipiuntur; & eadem
ratione E O occurret ſemiſectioni A G in quolibet eius puncto R vltra verticem
A ad partes G. Et quoniam in eo-
dem plano trianguli E N B (ſcili-
cet plani B N O E ſecantis vtrum-
que conum) à puncto E ducitur re-
cta linea E O intra angulum N E B; ergo vlterius producta ſecabit latus
B N ſubtendentem angulum N E B
inter puncta N, & B, vt in X, & propterearecta linea N X intra triã-
gulum E N O, & ideo intra conum
E A C intercepta erit; ſimiliter re-
cta linea O X intra triangulum B N
O, & intra conum B A C interclu-
ſa erit: quare quodlibet aliud punctũ
Qlateris conici B N citra, vel vltra
interclusã portionẽ N X cadet neceſ-
ario extra ſuperficiem coni E A C,
& ideo quodlibet punctum Q in pro-
ductione lateris coni B N ſumptum
& in ſemiſſe ſectionis conicæ H A
prope verticem A cadet extra ſemiſ-
ſem ſectionis F A, quæ in ſuperfi-
cie coni E A C exiſtit, & ad eaſ-
dem partes vergit. Pari modo quod-
libet aliud punctum R lateris conici
E O citra, vel vltra intercluſam
portionẽ X O cadet extra ſuperſiciem
coni B A C, & ideo quodlibet punctũ
R ſumptum in medietate ſectionis
conicæ A G prope verticem A cadet
extra medietatem ſectionis A I, quæ
in ſuperficie coni B A C exiſtit, & ad eaſdem partes vergit. Igitur ſe-
ctio H A I abſcindit coniſectionem
F A G in vertice communi A, vbi
ambo tanguntur ab eadem recta li-
nea A D. Quod erat faciendum.

248.1.

0301-01
32. lib. I.
0302-01

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