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
33e14[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
88a15[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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