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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150112Apollonij Pergæi

Lineæ vero breuiſſimæ, quæ ca-

136[Figure 136]11d dunt ad peripheriam ſectionis B
A, continent angulos minores,
quàm B C D, vtique non occur-
runt D F, & c. Ideſt: quia quælibet
breuiſsima ex puncto peripheriæ A B
ad axim ducta efſicit angulum propin-
2226. 27.
huius. quiorem vertici, minorem ipſo angulo
C; & propterea quælibet breuiſsima,
ad peripheriam A B extenſa ſecabit ne-
3328. huius. ceſſario ipſam B C vlterius productam
ad partes C: ſed prius oſtenſa fuit B
C parallela asymptoto D F; igitur quæ-
libet breuiſsima ad peripheriam A B
educta ideſt inter parallelas poſita non
occurret alteri æquidiſtantium D F ad partes F, ſed ad partes oppoſitas verſus
D; eo quod quælibet recta linea intra hyperbolam ducta non ſecat peripheriam ſe-
44Conuerſ.
8. lib. 2.
26. 27.
huius.
28. huius. ctionis in ea parte, in qua continentem D F nõ ſecat; At quælibet alia breuiſsima
infra C B ducta, neceſſario efſiciet ad axim angulum maiorem, quàm C; & pro-
pterea vlterius producta ſecabit ipſam B C ad partes C; ſed quælibet breuiſsima
extra parallelas poſita quæ ſecat vnam æquidiſtantium B C, ſecabit quoq; reli-
quam ad eaſdem partes F C; quare prius ſectioni occurret, vt dictum eſt.

SECTIO DECIMASEXTA

Continens XVI. XVII. XVIII. Propoſ.
Apollonij.

SI menſura comparata ſumpta fuerit in axe recto minore elli-
55a pſis, erit maximus ramorum ab eius origine egredientium,
& illi propinquior maior eſt remotiore: minimus vero ramorũ
eſt differentia recti, & comparatæ, & illi propinquior, minor
eſt remotiore, atque exceſſus quadrati comparatæ ſupra qua-
dratum cuiuſcunque rami aſſignati æqualis eſt exemplari appli-
cato ad abſciſſam illius rami, ſiue comparata ſit minor, aut
æqualis, aut maior recto.

Sit D C rectus a-

137[Figure 137] xis minor ſectionis
ellipticæ A B C ſit-
que C I comparata,
& rami I H, I K, I
B, I L, I A, I D, &
ſemiſſis erecti ſit C
F, & centrum E, &

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