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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4810Apollonij Pergæi

Notæ in propoſitionem quintam.

ERit I M æqualis M O, & c. Propter parallelas M O, C H, & ſimilitudi-
11a nem triangulorum I M O, & I C H.

Ergo quadratum

16[Figure 16]22b I L duplum eſt triã-
guli I C H, & c. Eo
quod quadratum I L
æquale eſt duobus qua-
dratis I M, M L in
rectangulo triangulo I
M L; Quadratis au-
tẽ I M, & L M æqua-
lia ſunt triangulum
I M O bis ſumptum
cum trapezio C M Q
H bis ſumpto; & quia
331. huius. trapezium C M Q H
æquale eſt trapezio C
M O H, cum triangu-
lo H O Q; at triangulo I M O,
& trapezio C M Q H ſimul ſum-
ptis æqualia ſunt triangulum
I C H, cum triangulo H O Q.
Ergo quadratum L I æquale erit
duplo trianguli I C H cum duplo
trianguli H O Q.

Deindè ponamus in ellipſi
44c Y F æqualem D C, & in hy-
perbola, & c. Textus videtur
corruptus, quem ſic corrigendum
puto. Ponamus γ F in ellipſi æ-
qualem differentiæ, & in hyper-
bola æqualem aggregato D C, & C F.

Propter ſimilitudinem triangulorum, & c. Sunt enim duæ rectæ lineæ C G,
55d& V H æquidiſtantes, quæ ſecant rectas lineas conuenientes in Q, & O.

Erit H V æqualis V O, & c. Eo quòd M I oſtenſa eſt æqualis M O, eſtque
66e H V ad V O in eadem proportione æqualitatis propter iam dictam ſimilitudinem
triangulorum.

Igitur V O ad V Q eſt, vt D C ad C F, & conuerſa proportione dein-
77f dè componendo in hyperbola, & inuertendo in ellipſi fiet in hyperbola
Q O ad O V, & c. Textum corruptum, atque confuſum clariùs exponi poſſe
cenſeo per Lemma inferius appoſitum hac ratione. Et comparando ſummas in
hyperbola, & differentias terminorum in ellipſi ad antecedentes.

Vt Y F ad Y C, & in ellipſi, vt F C ad C F, & Y F in ellipſi æqualis
88g

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