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

Apollonij Pergæi ſeu axium (in hoc caſu) L B, & M E ſiguræ ſimiles inter ſe; & ideò ſectiones
A B C, & D E F ſimiles erunt.

230.1.

Lem. 8.
huius.
0243-02
ex 11. 12.
huius.

Itaque propter ſimilitudinem duorum ſegmẽtorum ſimlia erunt B N L,
E O M, & pariter L B P, & M E Q atque quadratum B P ad L P in P
N nempe, & c. Huius ſecundæ partis demonſtrationem, quàm non ſinceram Pa-
raphraſtes Arabicus nobis tranſmiſit omittere opere pretium erit, eandemq; bre-
uius demonſtrare hac ratione. Quia ſegmenta C B G, & F E H ſimilia ponun-
tur; ergo erunt figuræ diametrorum B I, E K ſimiles inter ſe in angulis I, K
æqualibus, & ſectiones ipſæ C B G, & F E H ſimiles inter ſe erunt; quod eſt
contra hypotheſin.

230.1.

b
0244-01
Lem. 8.
huius.
Prop. 15.
huius.

231. Notæ in Propoſit. XXIII.

SI enim ſimilia eſſent haberent conditiones ſimilitudinis, quod eſt im-
poſſibile, & c. Si enim concedantur ſegmenta G B C in parabola, & H E
F in hyperbole, vel ellipſi, ſimilia inter ſe; igitur in vnaquaque earũ duci poſ-
ſent ad diametros ordinatim applicatæ numero æquales, efficientes angulos æqua-

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