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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8547Conicor. Lib. V. figuræ compoſitæ, vel diuiſæ, & c. Quia E K ad K D, atque C F ad F D eandem
proportionem habebant, quàm latus tranſuerſum ad rectum; ergo componendo in
hyperbola, & diuidendo in ellipſi erit E D ad D K, vt C D ad D F.

Et ponamus re-
11h

62[Figure 62] ctangulum F G cõ-
mune, & c. Scilicet
rectangulũ F G ad-
datur in hyperbola,
& auferatur cõmu-
niter in ellipſi.

Et propterea E
22i K ad B G, nempe
K R ad R G, & c.
Quia propter ſimili-
tudinem triangulo-
rum E K R, & B G
R erit E K ad B G,
vt K R ad R G; qua-
re K R ad R G maio-
rem proportionẽ ha-
bet, quàm G M ad
M K; & componen-
do K G ad G R ma-
iorem rationem ha-
bet, quam eadem G
K ad K M, quare
K M, nẽpe e i æqua-
lis D F maior eſt,
quàm G R.

Et auferẽdo ho-
33k mologũ ab homo-
logo in hyperbola,
& coniungendo e
a in ellipſi, habebit, & c. Scilicet comparando homologorum differentias in hy-
44Lem. 4.
præmiſ. perbola, eorundem ſummas in ellipſi, ideſt C T ad B O, nempe C H ad H O (pro-
pter ſimilitudinem triangulorum C H T, & O H B) habebit maiorem proportionem,
quàm I C ad C S, nempe C D ad D F.

Poſtea educamus ex E lineam occurrentem ſectioni in V, & c. Educamus
55l ex E lineam occurrentem ſectioni in V, quæ ſecet axim in Z, & S M in Y.

Et per f producamus f g h parallelam axi A D, & c. Et per f ducamus f g pa-
66m rallelam axi A D, quæ ſecet tangentem B a in h, & L F in g, atque V c ſecet illam in
i, & S M in e.

Et ponamus rectangulum F f communiter, & c. Et communiter addamus in
77n hyperbola, & auferamus in ellipſi rectangulum F f, fiet rectangulum B fg æquale
rectangulo g F C. Nomina Inuerſi, & Trutinatæ definita fuerunt in primo libro ab
interprete Arabico.

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