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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