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

S I rectæ lineæ A B bifariam ſectæ in C vtrinque addantur æquales
portiones A D, & B E, dico rectangulum ſub tota D E, &
ſub intermedia A B æquale eſſe differentiæ quadratorum ex A E, &
ex A D.

Apponatur F D æqualis D

470[Figure 470] A, vel B E: & quia F D æ-
qualis eſt B E addita communi
B D, erit F B æqualis D E,
& ideo rectangulum F B A æ-
quale erit rectangulo ſub D E,
& ſub A B, ſed quadratum
B D æquale eſt quadrato D A cum rectangulo F B A, (eo quod F A ſecta eſt
bifariam in D, & ei in directum additur A B), ergo quadratum D B æquale
eſt quadrato D A vna cum rectangulo ſub D E, & ſub A B, & propterea re-
ctangulum ſub D E, & ſub A B contentum æquale eſt differentiæ quadrati B D,
ſeu A E à quadrato D A, quod erat oſtendendum.

LEMMA XVII.

IN hyperbola, & ellypſi, cuius centrum D, axis A C, erectus A
F, præſectæ A H, G C, & in ea diameter I L, cuius erectus

471[Figure 471]

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