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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