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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167129Conicor. Lib. V.

PROPOSITIO XXXXVIII.

T Res lineæ maximæ E F, G H,
11a

164[Figure 164] I K ad vnum ellipſis quadrã-
tem A F B cadentens non cõueniunt
in vno puncto.

Alioquin cõueniant in O, & quia ſunt
lineæ maximæ erunt M K, H N, L F, li-
neæ breuiſſimæ (32. ex 5.) & conueniunt
in puncto O; quod eſt abſurdũ (54. ex 5.)
oſtenſum ergo eſt, quod fuerat propoſitũ.

Notæ in Propoſit. XXXII.

L Inea maxima ſecat tranſuerſam in pũ-
22a

165[Figure 165] cto, cuius intercepta inter punctum
illud, & ſectionem, eſt linea breuiſſima,
& c. Verba, quæ in textu Arabico deſideran-
tur ſupplenda cenſui, vt æquiuocationes tolle-
rentur.

Quia G H eſt linea maxima, erit D A
33b ad A F, nempe B E ad B D, & c. Quia
in 22. huius oſtenſum eſt, lineæ maximæ G
H potentialem H O ſecare ſemiaxim minorẽ
A D in O, vt ſit D O ad O G in eadẽ propor-
tione figuræ axis minoris A C; ſcilicet erit,
vt D A ſemiaxis minor ad A F eius ſemie-
rectum; ſed vt A D ad A F, ita eſt B E ſe-
miſsis lateris recti axis tranſuerſi ad B D
ſemiſſem eiuſdem tranſuerſi; igitur D O ad
O G eandem proportionem habebit, quàm E
B ad B D; ſed propter parallelas N D, H O,
eſt N H ad H G, vt D O ad O G; pariter-
que propter parallelas D G, H P, erit N P ad P D, vt N H ad H G; & pro-
pterea N P ad P D eandem proportionem habebit, quàm D O ad O G, ſeu
quàm E B ad B D; & permutando D P ad P N erit, vt D B ad B E, ſeu vt
4415. huius. axis tranſuerſus ad eius, erectum; & propterea linea N H erit breuiſsima.

Notæ in Propoſit. XXXIII. XXXIV.

E Contra oſtendetur, quod duæ breuiſſimæ, ſi educantur ex parte ſuæ
55a originis ad rectum, fient duo maximi cum relatione ad rectum:

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