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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446Apollonij Pergæi

PROPOS. III.

9[Figure 9]

SI verò in ellipſi cadat B G infrà cen-
trum, poterit duplum differentię duo-
rum triangulorum D A F, & D G H, nem-
pè duplum plani G L. Et hoc erat pro-
poſitum.

Notæ in Propoſitionem primam.

VOcat in primo libro interpres ſectiones habentes centrum hyperbolem, &
ellipſim, & vocat erectum latus rectum ſectionis, vocat etiam ordina-
tionem axis eam, quam nos ordinatim ad axim applicatam appellamus.

Quia BG poteſt comparatum applicatum ad abſciſſam AG, & c. Vocat
11a inſuper parallelogrammum comparatum applicatum ad axis abſciſſam A G re-
ctangulum ipſum A G I, quod quidem adiacet lateri recto A E latitudinem ha-
2212. 13. lib.
primi. bens abſciſſam A G excedens in hyperbola, & deficiens in ellipſi rectangulo ſi-
mile ei, quod latere recto, & tranſuerſo continetur; ſcilicèt rectangulo C A E.

10[Figure 10]

Et planum G F dimidium eſt illius comparati, & c. Non erit inutile
33b paulo fuſius oſtendere id quod ob nimiam facilitatem Apollonius tantummodò in-
nuit. Ducatur recta linea F K parallela axi D A ſecans ordinatam B G produ-
ctam in K: quia figuræ latera C A, & A E ſunt ipſarum D A, A F duplicia
ergo C E, & D F H parallelæ ſunt, eſtque K H parallela A E, cum ambo poſitæ
ſint perpendiculares ad axim, & C A, F K ſunt quoquè æquidiſtantes, ergò
triangulum F K H ſimile eſt triangulo C A E, & proptereà parallelogramma
rectangula F K H, & C A E ſimilia erunt. Et quoniam quadratum ordinatæ
44Ibidem. B G æquale eſt rectangulo contento ſub latere recto E A, & abſciſſa A G

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