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 |< < (33) of 458 > >|
7133Conicor. Lib. V. in ellipſi, vt menſura ſumatur in maiori duorum axium, & rami
egrediantur ad eius ſectionem.
PROPOSITIO IL. & L.
EXE concurſu ſuper perpendicularem ED educamus E B ſe-
cantem menſuram A D in F, &
ſectionem A B in B, &
11b ſit A H dimidium erecti;
ſitque menſura A D non maior, quàm
H A.
Dico quod BF non erit breuiſſima, & minima egrediens
22c ex B abſcindit ex ſagitta maiorem lineam, quàm F A:
at ſi fue-
rit A D maior , quàm A H, tunc B F poteſt eſſe linea breuiſ-
ſima.
49[Figure 49]
EDucamus iam B I perpendicularem ad axim, & ſupponamus prius A
D non maiorem quàm A H , &
ſit ſectio parabole ; igitur D I mi-
33d nor eſt , quàm A H, &
ponatur G I æqualis A H, erit B G minima (8.
ex quinto) & abſcindit G A ex ſagitta maiorem , quàm A F; ſi verò ſe-
ctio fuerit hyperbole, aut ellipſis, ſit centrum C;
ergo A C ad A H non
44e habet maiorem proportionem, quàm ad A D, quare C I ad I F maiorem
proportionem habet, quàm C A ad A H;
ponatur ergo I C ad I G , vt
A C ad A H;
ergo B G eſt minima , & abſcindit (9. & 10. ex quinto)
G A maiorem , quam F A, quod erat oſtendendum.

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