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

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[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
[5.] IO: ALFONSVS BORELLVS
[6.] AD SERENISSIMVM COSMVM III. ETRVRIÆ PRINCIPEM FLORENTIÆ, Ex Typographia Ioſephi Cocchini ad inſigne Stellæ MDCLXI. SVPERIORVM PERMISSV.
[7.] COSMVM TERTIVM ETRVRIÆ PRINCIPEM. 10: AL FONSVS BORELLIVS F.
[8.] CAVE CHRISTIANE LECTOR.
[9.] IN NOMINE DEI MISERICORDIS MISERATORIS. PROOE MIVM ABALPHATHI FILII MAHMVDI, FILII ALCASEMI, FILII ALPHADHALI ASPHAHANENSIS. LAVS DEO VTRIVSQVE SECVLI DOMINO.
[10.] ABRAHAMI ECCHELLENSIS IN LATINAM EX ARABICIS Librorum Apollonij Pergæi verſionem PRÆFATIO.
[11.] PRÆFATIO AD LECTOREM.
[12.] INDEX
[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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page |< < (191) of 458 > >|
229191Conicor. Lib. VI. ad A M eandem
257[Figure 257] proportionem ha-
bebit, quàm X O
C ad quadratum
O C, ſeu eandẽ,
quàm habet X O
ad C O, &
com-
parando conſequẽ
tes ad differẽtias
terminorum M A
ad A T eandem
proportionem ha-
bebit, quàm O C
ad C X:
erat autẽ
prius T A ad A
E, vt X C ad C F;
igitur ex æquali M A ad A E erit, vt O C ad C F, & fue-
runt oſtenſi anguli E, &
F æquales. Quod erat oſtendendum.
SECTIO SEPTIMA
Continens Propoſit. XVIII. & XIX.
CViuslibet ſectionis A B C duo ſegmenta C F, A E ca-
dentia inter duas ordinationes A C, E F ad vtraſque par-
tes axis B V ſunt inter ſe ſimilia, &
ſimiliter poſita, nec ſunt
ſimilia alteri ſegmento (niſi
258[Figure 258] in ellipſi, in qua quatuor ſeg
menta memorata in propo-
ſitione 8.
ſunt æqualia, ſimi-
lia, &
ſimiliter poſita, quæ al-
teri ſegmẽto ſimilia nõ ſunt.
Quoniam vnumquodque eo-
11a rum alteri congruit, nec non cõ-
gruunt duo ſegmenta GI, K H
in ellipſi (7.
8. ex 6.) at non ſunt
ſimilia alteri ſegmento:
ſi enim
hoc fieri poteſt, ſit ſegmentum
L M ſimile ſegmento F C.
Et
quia F C congruit A E.
Ergo
duo ſegmenta L M, A E ſunt
ſimilia, producamus A E, L M
quouſque occurrant axi in N,
22b O, erit angulus N æqualis O (vti
demonſtrauimus in 16.
& 17.

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