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

Conicor. Lib. VI. pespendicularis B E, & perficiatur
planũ E I. Et quia A I, A E æquã-
tur C N, C F, vnaquæque ſuo ho-
mologo: igitur planum I E, nempe
(12. ex 1.) quadratum B E æquale
eſt rectangulo F N, nempe quadrato
D F (12. ex 1.) ergo B E æqualis
eſt D F; ſi autem ſuperponatur axis
axi cadet D ſuper B, quæ tamẽhaud
cadere conceſſum fuerat: & hoc eſt
abſurdum; ergo fieri non poteſt, vt
duæ ſectiones æquales non ſint.

169.1.

b
0177-01
11. lib. 1.
Ibidcm.

Præterea ſupponamus duas illas ſe-
ctiones æquales eſſe inter ſe, & fiat
F C æqualis E A, & educamus ad
axes perpendiculares B E, D F, & per-
ficiamus plana rectangula F N, E I. Quia ſectio A B cadit ſuper ſectionem C D, & A E ſuper C F cadet; alioquin eſſent in eadem parabola duo axes: ergo F cadit ſuper E, & D
ſuper B, & propterea B E potens planum E I (12. ex 1.) æqualis erit
D F potenti planum F N (12. ex 1.) ; ergo duo plana ſunt æqualia; ſed
ſunt applicata ad æquales F C, A E; igitur C N, A I erectæ æquales
ſunt. Et hoc erat oſtendendum.

169.1.

c
11 lib. 1.
Ibidem.
d

170. PROPOSITIO II.

SI duæ ſectiones hyperbolicæ, aut duæ ellipſes A B C, D E
F habuerint axium figuras G I, H K ſimiles, & æquales; duæ illæ ſectiones æquales erunt. Si verò duæ ſectiones æquales
fuerint, earũ figuræ axiũ erunt æquales, ſimiles, & ſimiliter poſitæ.

170.1.

a
0177-02
0177-03

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