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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8749Conicor. Lib. V. mas in ellipſi, & eo-

64[Figure 64] rundem differentias
in hyperbola C X ad
11Lem. 4. c V, vel (propter
ſimilitudinem triã-
gulorum X C Z, V c
Z) C Z ad Z c ma-
iorem proportionem
habet, quàm I C ad
C S, vel C D ad D
F; & componendo
in ellipſi, & diui-
dendo in hyperbola
C c ad c Z maiorẽ
proportionem habe-
bit, quàm C F ad
229. 10.
huius. F D, & ideo breuiſ-
ſima egrediens ex V
abſcindit lineã ma-
iorem, quàm A Z.

Simili modo cõ-
ſtat, quod breuiſ-
33t ſima egrediens ex
l eiuſdem ſit ratio-
nis, & c. Abſque no-
ua demonſtratione
in ſecunda, & quar
ta figura propoſitum oſtenſum erit.

Deinde ſit E D æqualis Q, inde demonſtrabitur (quemadmodum ſu-
44a pra factum eſt) quod B H tantum ſit linea breuiſſima, & c.

Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac
ratione ſuppleri poteſt.

Sit E D æqualis Trutinæ Q habebunt E D, atque Q eandem proportionem
ad B O, componitur verò proportio E D ad B O ex rationibus E D ad D K, &
D K ad B O, ſeu O G ad B O; componebatur autem proportio Trutinæ Q ad B O
ex rationibus C D ad D F, & F O ad O C; ergo ablata communiter proportione
E D ad D K, vel C D ad D F, relinquetur proportio G O ad O B eadem propor-
tioni F O ad O C; ergo rectangulum G O C ſub extremis contentum æquale erit
rectangulo B O F ſub intermedĳs compræbenſo, addatur in hyperbola, & aufe-
ratur in ellipſi communiter rectangulum F G, erit rectangulum F S æquale re-
ctangulo B G M; Et quia I S ad S C, vel E K ad K D, velad F M erat, vt C
F ad F D, vel vt S M ad M K; ergo rectangulum E M æquale eſt rectangulo
F S; & propterea rectangulum E M æquale erit rectangulo B G M; quapropter
vt E K ad B G, ſeu K R ad R G, ita erit G M ad M K, & componendo,

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