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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5820Apollonij Pergæi ſed potius ex vndecima libri primi;

29[Figure 29] eſt enim quadratum H N æquale re-
ctangulo contento ſub abſciſſa H C,
& ſub latere recto, eſtque rectangu-
lum ſub H C, & ſub ſemierecto C G
ſemiſsis illius; igitur quadratum H
N æquale eſt duplo rectanguli H C G.

11d

Hoc autem eſt æquale duobus
quadratis I H, H Q, & I H in H
Q bis, & c. Poſt hæc verba ſubiun-
go claritatis gratia, atque C H in H
I bis æquale eſt duplo C Q in H I
vna cum duplo Q H in H I.

Ergo quadratum B I æquale eſt
22e I C in I H bis, & c. Hìc pariter, vt
clarior reddatur demõſtratio, ſubiun-
go, ſcilicet duplo rectãguli C H I vna
cum duplo quadrati H I; erat autem
quadratum N I æquale duplo rectan-
guli C H I, & vnico quadrato H I,
ergo, & c.

Et quia quadratum OR æqua-
33f le eſt C R in I H bis, & c.

30[Figure 30] Subiungo hanc declarationem.
Scilicet duplo rectanguli C H
I, & duplo quadrati H I cum
duplo rectanguli R I H. Qua-
re quadratum I O æquale eſt
quadrato R I, duplo quadrati
H I, duplo rectanguli R I H,
& duplo rectanguli C H I: ſed
quadratũ H R æquale eſt qua-
drato R I, quadrato I H cum
duplo rectanguli R I H. Ergo
quadratum I O æquale eſt qua-
drato H R, quadrato H I cum duplo rectanguli C H I; erat autem prius qua-
dratum I N æquale quadrato I H cum duplo rectanguli C H I. Igitur exceßus
quadrati I O ſupra quadratum I N eſt quadratum H R.

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