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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241203Conicor. Lib. VI. 274[Figure 274]
Notæ in Propoſit. XXI.
QVoniam G B ad B I, ſuppoſita eſt vt H E ad E K, & c. Quia L B
11a ad B G ex bypotheſi erat, vt M E ad E H, &
inuertendo G B ad B I
erat vt H E ad E K;
ergo ex æqualitate L B ad B I erit vt M E
ad E K;
& per conuerſionem rationis B L ad L I erit vt E M ad M K.
Et propter ſimilitudinem duarum ſectionum N L ad A I, nempe L O
22b ad O I eſt, vt P M ad F K, nempe M Q ad Q K, &
c. Quoniam duæ ſe-
ctiones N B, &
P E ſimiles ſuppoſitæ ſunt, & axiũ abſciſſæ L B, M E, nec non
I B, K E ad latera recta B G,
275[Figure 275]Cc 2&
H E proportionales ſunt; igitur N L ad A I eandem 33ex 12.
huius.
portionem habebit, quàm P M ad D K:
& quia triangula N L O, & A I O ſimilia ſunt pro- pter parallelas N L, & I A, pariterque triangula P M Q,& D K Q ſimilia ſunt; igitur L O ad O I erit vt N L ad I A; pariterque M Q ad Q K erit vt P M ad D I, ſeu vt N L ad A I: & propterea L O ad O I erit vt M Q ad QK.
Et ex æqualitate L O ad
44c L B erit vt Q M ad M E, ſed
L B ad L N eſt vt M E ad
M P, cum ex ſuppoſitione
ſectiones ſint ſimiles, &

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