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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335296Apollonij Pergæi

Notæ in Propoſit. XIV. & XXV.

QVoniam nedum in hyperbola, ſed etiam in ellipſi quadratum A C ad ſum-
mam quadratorum ex I L, & ex N O eandem proportionem habet, quã
A H ad ſummam ipſarum H E, & E G, atque quadratorum ex I
L, & ex N O ſumma ad eorundem quadratorum differentiam eandem propor-
tionem habet, quàm ipſarum H E, & E G ſumma ad earundem differentiam;

387[Figure 387] evgo ex æquali quadratum A C ad quadratorum ex I L, & ex N O differen-
tiam eandem proportionem habet, quàm C G, ſiue H A ad ipſarum H E, &
E G differentiam; ſed in ellipſi ipſarum H E, & E G differentia æqualis eſt
duplo E D; igitur in ellipſi quadratum A C ad quadratorum ex I L, & ex
N O differentiam eandem proportionem habebit, quàm præſecta C G ad duplum
inuerſæ E D.

Notæ in Propoſit. XXVII.

ET oſtenſum iam eſt, quod I L in hyperbola maior eſt, quàm A C;
11C ergo differentia A C, & illius coniugati maior eſt, quàm differen-
tia homologorum ſuorum à ſuis coniugatis, & differentia proximioris ho-
mologi ad ſuam coniugatam maior eſt differentia remotioris à ſua coniu-
gata, & c. Hoc autem ſic demonſtrabitur. In diametris A C, & I L produca-
tur A M æqualis Q R, & I K æqualis N O, & ab ĳsdem ſecentur A S æqua-
lis Q R, & I T æqualis N O. Quoniam M S bifariam ſecatur in A, & e

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