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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479Conicor. Lib. V. tum I L duplum eſt trianguli I C H vnà cum duplo trianguli Q H O, nem-
pe cum plano rectanguli QZ; ſed quadratum I C eſt duplum trianguli I
H C (eò quod C H æqualis eſt C I) ergo quadratum C I minus eſt qua-
drato L I plano rectanguli Q Z.

Deindè ponamus in ellipſi Y F æqualem differentiæ, & in hyperbola
11c æqualem aggregato D C, C F; ergo propter ſimilitudinem duorum trian-
22d gulorum G M Q, H V Q, & H V O, M I O, erit H V æqualis V O, & H
V, vel ei æqualis O V ad V Q eſt, vt M G ad M Q, nempe vt G C ad
33e

14[Figure 14] H C, ſeù vt D C ad C F, igi-
tur V O ad V Q eſt vt D C
44f ad CF, & comparando ſum-
mas terminorum ad antece-
dentes in hyperbola, & dif-
ferentias eorundem ad ante-
cedentes in ellipſi fiet O Q
ad V O (quæ æqualis eſt O
Z, nempè M C) vt Y F ad
55g Y C, & eſt Y C, æqualis D
C, & Y F æqualis ſummæ
in hyperbola, & differentiæ
in ellipſi ipſarum D C, & C
F; quadratum igitur I C mi-
66h77Def. 8. 9.
huius. nus eſt quadrato I L rectangulo Q Z, quod eſt exemplar ſimile
plano rectanguli C D in Y F, quæ eſt figura comparata. Atque ſic de-
monſtrabitur, quod quadratum I C minus ſit quadrato I K exemplari ap-
plicato ad N C, & minus eſt quadrato B I exemplari applicato ad I C,
& minus quadrato A I exemplari applicato ad E C: Eſtque M C minor,
quàm N C, & N C, quam C I, & C I, quàm C E; igitur L I maior eſt,
quàm I C, & I K maior, quàm L I, & I B maior, quàm I K, & I A, quàm
I B. Et hoc erat oſtendendum.

Notæ in pro poſitionem quartam.

QVoniam in parabola L M poteſt
88a

15[Figure 15] duplum M C, & c. Quadratum
enim L M æquale eſt rectangu-
lo ſub abſciſſa M C, & latere recto C F,
eſtque C H ſemiſsis erecti C F; ergo L M
poteſt duplum rectanguli M C H.

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