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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9860Apollonij Pergæi
SECTIO NONA
Continens Propoſ. LVIII. LIX. LX. LXI.
LXII. & LXIII.
I Am ex puncto dato C extra, vel intra ſectionem A B (quod
11a in axi I A non ſit) poſſumus rectam lineam ducere, cuius
portio intercepta inter ſectionem, &
axim ſit linea breuiſſima.
PROPOSITIO LVIII.
Sit ſectio parabole, & producamus perpendicularem C E ſu-
per I E A, &
ponamus E F æqualem dimidio erecti, & du-
camus G F parallelam ipſi C E, &
per C ducamus hyperbolen
224. lib. 2.33b H C B circa duas continentes illam G F, I F, quæ occurat ſe-
ctioni A B in B, &
per B, C producatur linea occurrens con-
tinenti I A in I, &
continenti G F in G: Dico, quod B I eſt
linea breuiſsima.
75[Figure 75]
Producatur perpendicularis B K. Quoniam C I æqualis eſt B G (sexta
44C ex ſecundo) erit E I æqualis K F, &
E F, K I erunt æquales, atque ſup-
558. lib. 2. poſita, eſt E F æqualis dimidio erecti;
ergo K I ita eſt pariter; Quare
B I eſt breuiſsima, (octaua ex quinto) &
hoc erat probandum.
PROPOSITIO LIX. LXII. & LXIII.
D Einde fit ſectio hyperbole, aut ellipſis, cuius centrum D, & lineis,
66a atque ſignis in eodem ſtatu manentibus, ponamus D F ad F E, &

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