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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152114Apollonij Pergæi I D minus eſt, quàm quadratũ I C duplo trianguli N F M, quod æqua-
le eſt exemplari applicato ad D C, & quadratum I R æquale eſt duplo
trianguli I X R, & quadratum A R æquale eſt duplo trapezij R M (3. ex
5.) ergo quadratũ I A minus eſt, quàm quadratum I C duplo trianguli
F Z X, quod æquale ex exemplari applicato ad C R (6. ex 5.) ſimiliter
quadratum I L minus eſt, quàm quadratum I C exemplari applicato ad
C Q; eſtque C D maior, quàm C R, & C R quàm C Q; ergo I A ma-
ior eſt, quàm I D, & I L, quàm I A; quod erat propoſitum.

Notæ in Propoſit. XVI. XVII. XVIII.

COmparata ſi fuerit ex recto duorum axium ellipſis crit maximus ra-
11a morum, & c. Addidi particulam illam axis minoris, quæ in textu defi-
ciebat, nunquam enim C F ſemiſsis lateris recti, eſſe poteſt maior C E ſemiſſe
lateris tranſuerſi, niſi C D fuerit axis minor ellipſis.

Conſtat, quemadmodum demonſtrauimus in propoſitione 6. & c. Quo-
22b niã menſura I C ſupponitur cõparata, ideſt æqualis ipſi C F ſemiſsi lateris recti;
propterea triangulum I C F iſoſceleum erit, & rectangulum in C; & ideo qua-
dratum I C æquale erit duplo trianguli I C F: eadem ratione propter parallelas
S O, & C F, erit triangulum I O S ſimile triangulo I C F, & propterea illud
quoque iſoſceleum erit, & rectangulum in O, & ideo quadratum I O æquale,
erit duplo trianguli I O S: eſt verò quadratum O H æquale duplo trapezĳ F T
331. huius. O C; igitur quadratum I H ( quod eſt æquale duobus quadratis I O, O H circa
angulum rectum O) æquale erit duplo trianguli I O S cum duplo trapezĳ F T
O C, ſed hæc duo ſpatia minora ſunt duplo integri trianguli I C F, eſtque de-
fectus duplum trianguli F T S, ſiue rectangulum S T b a; igitur duplum trian-
guli I C F, ſiue quadratum I C maius eſt quadrato I H, & exceſſus eſt rectan-
gulum T a: quod vero rectangulum T a ſit exemplar demonſtrabitur modo, vt
in ſexta propoſitione huius.

140[Figure 140]

Et conſtat, vt dictum eſt, quod ſit exemplar applicatum ad O C, & c.
44c Quoniam rectæ S a, T b, I C ſunt parallelæ, erunt triangula I C F, & S a

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