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

Page: 5

[5.] IO: ALFONSVS BORELLVS

Page: 5

[6.] AD SERENISSIMVM COSMVM III. ETRVRIÆ PRINCIPEM FLORENTIÆ, Ex Typographia Ioſephi Cocchini ad inſigne Stellæ MDCLXI. SVPERIORVM PERMISSV.

Page: 5

[7.] COSMVM TERTIVM ETRVRIÆ PRINCIPEM. 10: AL FONSVS BORELLIVS F.

Page: 7

[8.] CAVE CHRISTIANE LECTOR.

Page: 14

[9.] IN NOMINE DEI MISERICORDIS MISERATORIS. PROOE MIVM ABALPHATHI FILII MAHMVDI, FILII ALCASEMI, FILII ALPHADHALI ASPHAHANENSIS. LAVS DEO VTRIVSQVE SECVLI DOMINO.

Page: 15

[10.] ABRAHAMI ECCHELLENSIS IN LATINAM EX ARABICIS Librorum Apollonij Pergæi verſionem PRÆFATIO.

Page: 23

[11.] PRÆFATIO AD LECTOREM.

Page: 31

[12.] INDEX

Page: 37

[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.

Page: 43 (5)

312274Apollonij Pergæi cum quadrato D B, quod eſt æquale ipſi A D in A F; igitur eſt æqua-
le ipſi F D in D A. Quod erat oſtendendum.

PROPOSITIO V. & XXIII.

IN parabola A B C cuiuſcumque diametri B F erectus B H ex-
cedit axis A D erectum A E quadruplo abciſſæ A D potentis
à termino illius diametri ad axim ductæ 23. & diametri C G, re-
11a motioris ab axe, erectus C I maior eſt erecto B H diametri propin-
quioris B F quadruplo differentiæ axis abſciſſarum potentium à
terminis diametrorum ad axim ductorum.

360[Figure 360]

Educamus A L, B K tangentes in A, B, & B N perpendicularem ad
B K, erit K D in D N æquale quadrato D B, quod eſt æquale ipſi A E
2211. lib. 1. in A D; ergo K D ad D A eandem proportionem habet, quàm A E ad
D N: eſtque D K dupla ipſius A D (37. ex 1.) igitur A E eſt dupla
3335. lib. 1. ipſius D N; quarè A E cum duplo D K, nempe cum quadruplo A D eſt
44b æqualis duplo K N, nempe B H (eo quod N K ad B K tangentem ean-
dem proportionem habet, quàm aſſumpta M B ad B L coniugatam (57.
5544. lib. 1. ex 1.) (propter ſimilitudinem duorum triangulorum); ergo B H æqualis
eſt quadruplo A D cum A E; quarè erectus diametri B F excedit A E
quadruplo A D. & A O maior eſt, quàm A D; ergo erectus diametri
66c C G remotioris maior eſt, quàm erectus B F proximioris quadruplo D
O differentiæ abſciſſarum. Et hoc erat oſtendendum.

Notæ in Propoſit. I.

QVia quadratum A B eſt æquale quadrato D A, & c. Quoniam re-
77a ctangulum F D A æquale eſt rectangulo F A D ſubſegmentis vna cum
quadrato reliqui ſegmenti D A; eſtque latus rectum A E

Table of contents

Text layer

Text normalization

Search