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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211173Conicor. Lib. VI. ſectæ non erunt proportionaliter in punctis G, [& M, ſed prius oſtenſa fuit E
I ad I G vt K L ad L M; quod eſt abſurdum.

233[Figure 233]

In ſecunda verò ſecentur bifariam E G, K M in N O, & c. Sunt enim
11d in tertio caſu K M, & E G perpendiculares ad baſim D F; igitur ſi ſecentur
bifariam in O, & N coniuncta recta linea N O diameter circuli erit, quando-
quidem diuidit bifariam duas equidiſtantes in circulo applicatas; & ideo eas
ſecat ad angulos rectos, ſicuti D F eaſdem perpendiculariter ſecabat; & propte-
rea I N O L parallelogram-
mum erit, cuius latera op-

234[Figure 234] poſita N I, & O L æqualia
crunt. Poſtea quia oſtenſa
fuit I G ad I E, vt L M
ad L K; ergo ſummæ termi-
22Lem. 1. norum ad conſequentespro
portionales erunt; ſcilice
G E ad E I erit vt M K ad
K L, & antecedentiũ ſemiſ-
ſes N E ad E I, vt O K ad
K L: & diuidendo, duæ æ-
quates N I, O L eandem
proportionem habebunt ad I E, & L K; ideoq; I E æqualis eſt L K. Et quoniã
triangulum A B H ſimile eſt triangulo D K L; ergo A H ad H B eandem pro-
portionem habet, quàm D L ad L K; eſtque triangulum B H C ſimile triangu-
lo K L F; ergo B H ad H C eſt vt K L ad L F, & ex æqualitate vt A H ad H C
ita eſt D L ad L F; erat autem ſegmentum A H non maius ſegmento H C; ergo
D L maius non erit ſegmento L F; ſed erat ſegmentum D I non maius ſegmen-
to I F, igitur duo ſegmenta D I, & D L non ſunt maiora, ideſt non ſunt ma-
iora medietate totius D F, ſed diameter parallela ipſis K M, & E G ſecat D F
biſariam; ergo K M, E G ad eaſdem partes diametri cadunt verſus D, & ſunt
inter ſe parallelæ; ergo inæqualiter à centro diſtant; ideoque inæquales erunt in-
ter ſe, & earum meditates N E, O K inæquales erunt; & ablatis æqualibus

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