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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[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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413Conicor. Lib. V.

NOTÆ.

HAE definitiones non ſunt Apollonij, ſed Interpretis Arabici, qui in proe-
mio huius operis apertè ait, addidiſſe plurimas definitiones in libris Apol-
lonij, quibus theoremata breuiſsimè propo-

1[Figure 1] ni poſſe profitetur, vt in prioribus quatuor
libris videre eſt. Eas autem exemplis illu-
ſtrare conabor.

I. Sit quælibet coni ſectio A B C, cuius
axis B D, & in eo ſumatur quodlibet pun-
ctum D intrà ſectionem, à quo educantur
rectæ lineæ D A, D E, D F, D C vſque ad
ſectionem. Tùnc vocatnr punctum D, Origo.

II. Et lineæ D A, D E, & cæteræ vo-
cantur, Rami.

III. Portio verò axis B D intèr origi-
nem D, & verticem B interpoſita vocatur
Menſura. Sed in ellipſi A B C G, ſi axis
portiones D B, & D G inæquales fuerint,
tantummodò minor portio B D vocatur Mẽ-
ſura, non autem maior D G.

2[Figure 2]

IV. Sit poſteà recta B I ſemiſsis lateris
recti B H iam ſi menſura D B æqualis fue-
rit ſemierecto B I, vocatur D B, Menfura
comparata.

V. At ſi à terminis ramorum A, E, F
C educantur ad axim perpendiculares A K,
E L, F M, C N, ipſum ſecantes in K, L,
M, N vocantur illærectæ lineæ Potentes illo-
rum ramorum.

VI. Recta verò K B vocatur Abſciſſa
rami D A, & L B Abſciſſa rami D E, &
ſic reliquæ omnes.

3[Figure 3]

VII. Sit poſteà O centrum ſectionis, iam
axis portio ex centro O vſquè ad potentia-
lem A K educta, ſcilicet O K vocatur In-
uerſa rami D A, pariterque O M eſt Inuer-
ſa rami D F.

VIII. Si ponatur recta linea B P ad
axim perpendicularis, quæ in hyperbola
fiat æqualis aggregato, in ellipſi verò fiat
æqualis differentiæ laterum recti B H, &
tranſuerſi G B, tunc rectangulum contentum
ſub G B, & B P vocatur, Figura comparata.

IX. Poſteà ſi, vt G B ad B P ità ſiat

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