Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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231193Conicor. Lib. VI. gulos æquales; ĳ verò anguli æquales ſunt angulis O, & N, cum baſes L M, &
A E parallelæ ſint contingentibus verticalibus eorundem ſegmentorum; igitur an-
guli L O B, & A N B æquales ſunt inter ſe; & propterea duorum ſegmentorũ
baſes L M, & A E parallelæ ſunt inter ſe.

SECTIO OCTAVA

Continens Propoſit. XX. & XXI.
Apollonij.

PROPOSITIO XX.

SI in quibuslibet ſimilibus coniſectionibus A B C, & D E F
11a ductæ fuerint ad axes B O, E Q ordinatim applicatæ A C,
D F, N L, P M, quarum illæ, quæ ad eaſdem partes verticum
B, & E ducuntur efficiant abſciſſas erectis proportionales, ſci-
licet I B ad B G ſit, vt K E ad E H, nec non L B ad B G, vt
M E ad E H: Dico ſegmenta facta ab ordinatis ſimiliter poſi-
tis eſſe inter ſe ſimilia, ac ſimiliter poſita, ſcilicet N A ipſi P D,
atque A B ipſi D E, nec non N B ipſi P E.

261[Figure 261]

Sintque primò ſectiones parabolæ; & educamus N A ad B L in O, &
22b P D ad M E in Q. Et quia G B ad B I eſt, vt H E ad E K, & B L ad
B G eſt vt M E ad E H; ergo L B ad B I, nempe L N ad I A potentia
(19. ex 1.) nempe L N ad O I eandem proportionem habet, quàm M E
3320. lib. 1.

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