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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310272Apollonij Pergæi reliquæ verò lineæ referuntur ad hoc latus.

VII.

Inſuper vocabo duas diametros coniugatas, & æquales in elli-
pſi, ÆQVALES.

Et ſi quidem ad vtraſque partes axis ſectionis duæ diame-
tri educantur, quæ ad ſua erecta eandem proportionem ha-
beant, vtique vocabo cas ÆQVALES.

VIII.

Diametros verò æquales ad vtraſque partes duarum axium elli-
pſis cadentes, voco Homologas illius axis: ſuntque homo-
logæ diametri in ellipſi tranſuerſa ad tranſuerſam, & recta
ad rectam.

NOTÆ.

I. P Rima definitio breuiſſimè exponi poteſt hac ratione. Si axis tranſuerſus
interius in hyperbola diuidatur, aut exterius in ellipſi, ſecundum pro-
portionem figuræ, ſegmentum homologum axis tranſuerſi vocabo Præſectum, vt
ſi fuerit hyperbole, vel ellipſis A B, cuius axis tranſuerſus A C, centrum D,
latus rectũ A F, & in hyperbola ſecetur C A inter vertices A, & C; in ellipſi
verò ſecetur exterius in puncto G, ita vt ſumma, vel differentia ipſarum G A,
& axis C A, ideſt C G ad G A habeat proportionem figuræ ſcilicet eandem,
quàm habet latus tranſuerſum C A ad latus rectum A F; tunc quidem vocatur
recta linea C G Præſecta.

II. Atque G A vocatur Intercepta.

III. Punctum verò A extremum

357[Figure 357] interceptæ G A, & diametri C A
vocabitur terminus communis dua-
rum linearum, ſcilicet axis C A, &
additæ, vel ablatæ A G.

IV. Punctum verò G, in quo axis
A C interius, vel exterius diuiditur
ſecundum proportionem figuræ voca-
tur terminus diuidens; Si verò ſece-
tur C H æqualis A G vocabitur etiã
C H intercepta, & A H præſecta,
atque C terminus communis, & H
terminus diuidens.

V. Si diameter I L ſecuerit biſa-
riam ſubtenſam A B à ſectionis ver
tice A eductam, atque à termino

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