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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156118Apollonij Pergæi
Quoniam proportio E G ad G I facta eſt, vt E C ad C F, nempè E
11b G ad G V, erit G V æqualis G I;
& propterea quadratum G I æquale.
eſt duplo trianguli G I V, & quadratum G B æquale eſt duplo trapezij
G F (1.
ex 5.) ergo quadratum I B æquale eſt duplo trianguli I C S cum
147[Figure 147] duplo trianguli F S V;
& ſic conſtat, quod quadratum I K æquale eſt du-
plo trianguli I C S cum duplo trapezij S L;
& propterea quadrati I B ex-
ceſſus ſupra quadratũ I K æqualis erit duplo trianguli L T V, quæ æqua-
lia ſunt exemplari applicato ad G P (6.
ex 5.) atque ſic oſtendetur, quod
I B potentia ſuperat I H;
eſtque exceſſus exemplar applicatum ad G O,
&
ſuperat quoque I A poteſtate, eſtque exceſſus æqualis exemplari ap-
plicato ad G Q;
eſt vero G O maior, quàm G P; ergo I B maior eſt quã
I K, &
quàm I H; & ſic oſtendetur, quod I B maior ſit, quàm I A; &
hoc erat oſtendendum.
PROPOSITIO XXIII. & XXIV.
EContra, ſi maximi rami origo
148[Figure 148]22a ponatur in axi minore, at non in
cẽtro ellipſis, nec ſit menſura continet
cum ipſa menſura angulum acutum,
&
eius inuerſa ad abſciſſam à poten-
tiali cum origine habet eandem pro-
portionem figuræ axis recti minoris:
ſi vero educatur ex centro, erit per-
pendicularis ſuper rectum.
Sit ſectio elliptica A B C centrum D, & E origo, quæ ſit in axi mino-
33b ri C A, &
E F ramus omnium maximus; erit vtique E C, vel

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