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

[Item 1.]

[2.] APOLLONII PERGÆI CONICORVM LIB. V. VI. VII. & ARCHIMEDIS ASVMPTOR VM LIBER.

[3.] APOLLONII PERGÆI CONICORVM LIB. V. VI. VII. PARAPHRASTE ABALPHATO ASPHAHANENSI

[4.] ADDITVS IN CALCE ARCHIMEDIS ASSVMPTORVM LIBER, EX CODICIBVS ARABICIS M.SS. SERENISSIMI MAGNI DVCIS ETRVRIÆ ABRAHAMVS ECCHELLENSIS MARONITA

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[5.] IO: ALFONSVS BORELLVS

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[6.] AD SERENISSIMVM COSMVM III. ETRVRIÆ PRINCIPEM FLORENTIÆ, Ex Typographia Ioſephi Cocchini ad inſigne Stellæ MDCLXI. SVPERIORVM PERMISSV.

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[7.] COSMVM TERTIVM ETRVRIÆ PRINCIPEM. 10: AL FONSVS BORELLIVS F.

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[8.] CAVE CHRISTIANE LECTOR.

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[9.] IN NOMINE DEI MISERICORDIS MISERATORIS. PROOE MIVM ABALPHATHI FILII MAHMVDI, FILII ALCASEMI, FILII ALPHADHALI ASPHAHANENSIS. LAVS DEO VTRIVSQVE SECVLI DOMINO.

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[10.] ABRAHAMI ECCHELLENSIS IN LATINAM EX ARABICIS Librorum Apollonij Pergæi verſionem PRÆFATIO.

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[11.] PRÆFATIO AD LECTOREM.

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[12.] INDEX

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[13.] APOLLONII PERGAEI CONICORVM LIB. V. DEFINITIONES. I.

[14.] II.

[15.] III.

[16.] IV.

[17.] V.

[18.] VI.

[19.] VII.

[20.] VIII.

[21.] IX.

[22.] X.

[23.] XI.

[24.] XII.

[25.] XIII.

[26.] XIV.

[27.] XV.

[28.] XIV.

[29.] NOTÆ.

[30.] SECTIO PRIMA Continens propoſitiones I. II. & III. Apollonij. PROPOSITIO I.

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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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