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

Conicor. Lib. VI. parallela conſeruantur; igitur duæ ſectiones K H M, & L X S, exiſtentes in
eodem plano ſecante duas ſuperficies, quæ licet in infinitum producantur vbique
ſeparatæ ſunt, erunt aſymptoticæ. Quartò, quia duæ hyperbolæ H K M, & L
X S ſunt æquales, ſimiles, & ſimiliter poſitæ circa communem diametrum H X
I, earum diſtantiæ ſemper magis, ac magis diminuuntur; nunquam tamen mi-
nores efſici poſſunt interuallo duarum æquidiſtantium, hyperbolas continentium. Et hoc erat propoſitum.

235.1.

0270-01
Lem. 9.
huius.
Prop. 10.
add.
12. lib. 1.
10. 12.
huus.
Prop. 7.
addit.

Data hyperbola X duos conos ſimiles exhibere vt idem planum in eis
efficiat duas hyperbolas ſimiles, & æquales datæ, quæ aſymptoticæ ſint,
& ex vna parte ſibi ipſis viciniores fiant interuallo minori quolibet da-
to: ex altera verò parte ad ſe ipſas propius accedant interuallo tamen
maiore dato: oportet autem vt angulus ab aſymptotis ſectionis X con-
tentus ſit acutus.

235.1.

PROP.
13.
Addit.
0271-01

In quolibet @l@no fiat angulus A d O æqualis angulo inclinationis diametri,
& baſis hyperb l@ X; & per o d extenſo quolibet alio planol, ducatur in eo re-
cta linea B d C perpendicularis ad O d G, & ſumpto quolibet alio puncto b in
recta linea G O in plano per B G C O ducto, centris d, & b deſcribantur duo

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