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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9961Conicor. Lib. V.76[Figure 76] ſimiliter C L ad L E, vt proportio figuræ, & producamus per L ip-
ſam O M parallelam A I F, &
per F ipſam G M parallelam C E, & fa-
ciamus ſectionem H C B hyperbolen tranſeuntem per punctum C circa
114. lib. 2. continentes G M, O M, quæ occurret ſectioni A B (in ellipſi quidem vt
2256.
huius.
demonſtrauimus) in hyberbola vero eo quod O M parallela axi D A in-
33b clinato ſubtendit, ſi producatur, angulum ſubſequentem continentiæ an-
gulum ſecabit A B, &
corda, ſi producatur, occurret ſectioni; Ergo O
M ingreditur ſectionem A B, &
ampliatur ſectio A B per extenſionem,
longè à duabus lineis O M, M G, &
ſectio B C prope illas ducitur (deci-
4414. lib. 2. moſexta, ex ſecundo) igitur duæ ſectiones A B, C B ſibi occurrunt, vt
in B, &
ducamus per B, C lineam occurrentem D F A in I, & G F in G;
Et quia B O æqualis eſt ipſi C G (octaua ex ſecundo) erit O N æqualis
55c ipſi M L, &
O L ipſi N M; ergo O L, nempe N M, ſeu K F ad E I eſt,
vt C L ad C E, nempe D F ad D E, ergo K F ad E I eſt, vt D F
ad E D comparando homologorum ſummas in hyperbola, &
eorundem
66d77Lem. 3. differentias in ellipſi, &
iterum comparando antecedentes ad differen-
88Lem. 1. tias terminorum
77[Figure 77] fiet D K ad K
I, vt D F ad F
E, quæ eſt vt
proportio figu-
ræ;
igitur B I eſt
linea breuiſſima
(9.
10. ex quin-
to) &
hoc erat
probandum.

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