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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208170Apollonij Pergæi

229[Figure 229] litate, quod ſi fuerit A H in H C ad quadratum H B, vt D I in I F ad
quadratum I E, quod A H in H C ad quadratum H T ſit etiam, vt I D
in I F ad quadratum I G. Dico iam, quod triangulum A B C ſimile eſt
triangulo D E F. Si enim hoc verum non eſt, non erit angulus A æqua-
lis vni duorum angulorum D, vel F: ſitque angulus D maior, quàm A,
& fiat angulus K D F æqualis A, iungaturque F K; quia angulus K, ve-
luti E, eſt æqualis angulo B; ſimilia erunt triangula A B C, D K F, & e-
ducamus K L parallelam E I: quare K L F ſimile quoque erit B H C
11b ideoque H A ad H B eſt vt D L ad L K, & H C ad H B, vt F L ad L
K; igitur H A in H C, nempe B H in H T ad quadratum H B, quod eſt,
vt H T ad H B, quæ oſtenſa eſt; vt I G ad I E, erit vt D L in L F, nẽ-
pe K L in L M ad qua-

230[Figure 230] dratum K L: & propte-
rea M L ad L K erit vt G
I ad I E in omnibus fi-
guris; & hoc eſt abſurdũ
22c in prima figura: in ſecun-
33d da verò ſecentur bifariam
E G, K M in N, O, &
iungatur N O, quæ pa-
rallela erit L I, quia ſunt
duæ perpendiculares ſu-
per K M, E G, quæ ſunt
parallelæ; ergo I N eſt
æqualis L O, & quia E G ad E I iam oſtenſa eſt vt K M ad K L; ergo
E N ad E I eſt, vt O K ad K L: & diuidendo erit N I ad I E, vt O L,
quæ eſt æqualis N I ad L K. Et hoc quoque eſt abſurdum.

In figura autem tertia educamus duas perpendiculares E P Q, K R S
44e ſuper diametrum D F, cui occurrant in P, R: & iungamus G Q, M S,
quia erat G E ad E I, vt M K ad L K, & propter ſimilitudinem trian-
gulorum I E P, K L R, E I ad E P eſt, vt L K ad K R, atque E P ad E
Q eſt, vt R K ad K S, & angulus G E Q æqualis eſt M K S; ergo E

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