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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194156Apollonij Pergæi

210[Figure 210] A B ſimilis eſt figuræ ſectionis E F, erit quadratum H E ad H b in H F,
vt quadratum A C ad C a in C B; & b H in H F ad quadratum H F,
vt a C in C B ad quadratum C B (nam poſuimus H F ad F b, vt C B ad
B a) ergo ex æqualitate, quadratũ E H ad quadratũ H F eſt, vt quadra-
tum A C ad quadratum C B: & propterea E Z ad H F eſt vt A S ad C
B; Atque ſic oſtendetur, quod X Y ad N F ſit vt Q R ad L B, & T V
ad M F ſit vt O P ad K B; ergo proportiones ordinationum axis vnius
earum ad ſua abſciſſa ſunt eædem rationibus aliarum ordinationum axis
ad ſua abſciſſa, & alternatiuè. Quare duæ ſectiones ſunt ſimiles.

11Defin. 2.
huius.

E contra oſtendetur, quod
ſi duæ ſectiones fuerint ſimi-

211[Figure 211] les, earũ figuræ ſimiles quo-
que erunt. Quia eſt A C ad
22Ex def. 2.
buius. C B, vt E H ad H F, & ean-
dem proportionem habent
earum quadrata, atque
quadratum H F ad H F in
H b eſt, vt quadratum C B
ad C B in C a (eo quod
H F ad F b poſita fuit, vt
C B ad B a); ergo ex æ-
qualitate quadratum E H ad
b H in H F, nempe I F
ad F b (20. ex 1.) eſt, vt quadratum A C ad a C in C B, nempe vt
3321. lib. 1.
Ibidem. D B ad B a (20. ex 1.) ; quare figuræ duarum ſectionum ſunt ſimiles.
Et hoc erat oſtendendum.

PROPOSITIO XIII.

PArabola non eſt ſimilis hyperbolæ, neque ellipſi.

Hyperbolæ, ſeu ellipſis A B ſit axis B C, & inclinatus, ſeu tranſuerſus
B a, & E F ſit ſectio parabolæ, cuius axis F H. Dico, quod ſectio E F
non eſt ſimilis ſectioni A B hyperbolicæ, aut ellipticæ, alioquin ſit

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