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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195157Conicor. Lib. VI. lis alicui earum (ſi poſ-
11b ſibile eſt) ergo poſſu-

212[Figure 212] mus educere in ſingulis
ſectionibus potentes,
quæ habeant ad ſua ab-
ſciſſa axium eaſdẽ pro-
portiones, & abſciſſæ in
ter ſe ſint proportiona-
les; ſintque illæ V M,
Y N, P K, R L. Quia
Y N ad N F poſita fuit,
vt R L ad L B, & N F
ad F M, vt L B ad BK,
& F M ad M V, vt B
K ad K P; ergo Y N ad
M V in potentia, nem-
pe N F ad M F (cum
ſectio ſit parabola 19.
ex 1.) nempe L B ad B K ex contructione erit, vt R L ad K P potentia,
2220. lib. 1. quæ eandem proportionem habent, quàm a L in L B ad a K in K B;
3321. lib. 1. quia ſectio eſt hyperbolæ, aut ellipſis (20. ex 1.) quare a L in L B ad a
K in K B eſt, vt L B ad B K; quare a L eſt æqualis a K: quod eſt abſur-
dum. Igitur parabole non eſt ſimilis vlli reliquarum ſectionum. Et hoc
erat probandum.

PROPOSITIO XIV.

ET ſic oſtendetur, quod hyperbolæ non eſt ſimilis ellipſi.

Alioquin ſequitur, quod quadratum

213[Figure 213]44a R L ad quadratum K P, nempe a L in
L B ad a K in K B in hyperbola eſt, vt
quadratum Y N ad quadratum M V,
ſeu vt b N in N F ad b M in M F in el-
lipſi. His poſitis: quia L B ad B K po-
5521. lib. 1. ſita fuit, vt N F ad M F; ergo a L ad
a K eandem proportionem habet, quàm
b N ad b M: & hoc eſt abſurdum. Qua-
re ſectio A B non eſt ſimilis E F; vt fue-
rat propoſitum.

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