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

Conicor. Lib. VI. perpendicularis eſt ad circuli diametrum C A, & propterea A D, planorum
H A I, & A C M communis ſectio, tanget circulum A C, & ideo ſuperficiem
ipſam conicam, & ſectionem in ea exiſtentem continget; & diameter A L non
erit perpendicularis ad tangentem, ſeu ordinatim applicatam A D per verticem
A, alias A L eſſet axis, quod non ponitur. Deinde in plano D A B ex A du-
catur recta linea A E perpendicularis ad A D ſupra, vel infra circulum, & vertice quolibet puncto E ſumpto in recta linea A E, & baſi circulo A C M fiat
alter conus E A C, in cuius ſuperficie planũ D A H I deſignet ſectionẽ F A G, & in ea triangulum per axim E A C efficiat diametrum A K: Et quia eadem re-
cta linea D A perpendicularis eſt ad A C, atque ad A E ſe ſecantes in A; ergo
D A perpendicularis eſt ad planum C E A, atque planum D A C extenſum
per perpendicularem D A, erit quoque perpendiculare ad planum trianguli per
axim C E A, quare triangulum per axim efficiet diametrum A K, quæ erit
axis ſectionis F A G, atque D A perpendicularis erit ad axim A K exiſtentem
in plano C E A, ad quod D A eſt perpendicularis, & cum ea conuenit: quare
D A ordinatim ad axim applicata perverticem A tanget ſectionem F A G, quæ
prius in eodem puncto A tangebat ſectionem H A I in eodem plano exiſtentem; & propterea eadem recta A D vtramque ſectionem tangit in puncto A. Poſtea
coniungatur recta linea B E, & quia rectæ lineæ B A, A D, A E ſunt in eo-
dem plano tangente vtrumque conum (cum per vertices B, & E, atque per D
A contingentem circulum baſis communis ducatur) & E A, & B A angulum
conſtituunt, cum E A poſita ſit perpendicularis ad D A, at B A ad eandem ſit
inclinata, & exiſtunt in eodem plano; ergo recta B E parallela eſt, aut ſecat
contingentem D A extra circulum vt in D. Poterit igitur ex propoſ. 15. addi-
tarum duci per rectam B E planum aliud B E M V vtrumq; conum contingens,

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