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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193155Conicor. Lib. VI.

208[Figure 208]

Ponamus itaque C B ad B D, vt H F ad F I, & diuidantur tam B C,
quàm F H in punctis K, L, M, N in eiſdem rationibus, & educamus ſu-
per eas ordinationes O P, Q R, A S, T V, X Y , E Z. Quia B C ad
B D eſt vt H F ad F I, & A C eſt media proportionalis inter C B, B D
11Ex 11.
Lib. 1. (12. ex 1.) pariterque E H inter H F, F I (12. ex 1.) igitur A C ad C
B eſt, vt E H ad H F , & A S dupla ipſius A C ad C B eſt, vt E Z ad
H F; cumque B C ad B L poſita ſit, vt H F ad F N, erit B D ad B L, vt
22a I F ad F N; igitur Q R ad L B eſt vt X Y ad N F; atque ſic oſtendetur,
quod O P ad K B eſt, vt T V ad M F, quare proportio ordinationum
axis vnius ſectionum ad ſua abſciſſa eſt, vt proportio ordinationum alte-
rius ad ſua abſciſſa, & proportiones abſciſſarum vnius ſectionis ad abſciſ-
ſa alterius ſectionis eædem ſunt. Quare ſectio A B ſimilis eſt ſectioni E
33Defin. 2. huius. F. Quod erat oſtendendum.

PROPOSITIO XII.

SI duarum hyperbolarum, aut ellipſium duæ axium figuræ
fuerint ſimiles, vtique ſectiones ſimiles erunt: Si verò fue-
rint ſectiones ſimiles, figuræ etiam ſimiles erunt.

209[Figure 209]

Sint ſectiones A B, E F, earum axes inclinati, vel tranſuerſi B a, F b,
& erecti earum B D, F I, & maneant ſigna, ordinationes, & proportio-
44a nes eædem, quæ in præcedenti propoſitione. Quoniam figura ſectionis
55b

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