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)

164126Apollonij Pergæi

PROPOSITIO XXXVI.

IN ſectione elliptica quatuor lineæ

158[Figure 158] breuiſſimæ, vt B D, F I, G K,
H L, non conueniunt omnes in vno
puncto.

Alioquin ſit occurſus in E, & prius ſit
B D perpendicularis ſuper A C, tranſi-
ens per D centrum ſectionis; & quia E
eſt occurſus duarum breuiſſimarum B D,
1135. huius. F I, & B E tranſit per centrum; igitur

159[Figure 159] G K non eſt linea breuiſſima, quod eſt
contra hypotheſim. Si vero nullus eorũ
tranſit per centrum, educamus per cen-
trum D O perpendicularem ad A C; qua-
re duæ breuiſſimæ F I, G K conueniunt
intra angulum A D O (34. ex 5.) ſimi-
liter H L, M N breuiſſimæ occurrunt in-
tra angulum C D O (34. ex 5.) ſed cõ-
ueniunt in E, quod eſt abſurdum; igitur
quatuor lineæ breuiſſimæ non cõueniunt in vno puncto; quod erat oſten-
dendum.

PROPOSITIO XXXVII. XLVI.

IN coniſectione A B, cuius centrum D duci non poſſunt-duæ
lineæ maximæ in ellipſi, neque duæbreuiſſimæ in omnibus
ſectionibus, vt A E, A F ad vnum punctum A circumferentiæ
ſectionis terminatæ.

Educamus A G perpendicularem ad axim B E. Si itaque ſectio fue-
rit parabole, fiet E G æqualis F G, quia quælibet earum eſt æqualis di-
midio erecti (13. ex 5.) ſi vero fuerit hyperbole, aut ellipſis, fiet D G
ad G E, vt D G ad G F; quia quælibet earum eſt, vt proportio figuræ
(14. 15. ex 5.) igitur G F æqualis eſt G E, quod eſt abſurdum. Simi-
liter ſi B G fuerit minor duarum axium ellipſis, & fuerint A E, A F
rami maximi oſtendetur, quod G F æqualis ſit G E (23. ex 5.) Patet
igitur, vt dictum eſt, quod ex vno puncto ſectionis educi non poſſunt
ad axim illius duæ lineæ maximæ, neque breuiſſimæ, & hoc erat oſten-
dendum.

Table of contents

Text layer

Text normalization

Search