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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236198Apollonij Pergæi268[Figure 268] tione figuræ diametri A L (40. ex 1.) erit vt quadratum E Q ad M Q
1137. lib. 1. in O Q, nempe in eadem proportione figuræ diametri D M (40.
ex 1.)
22Ibidem. quapropter duæ proportiones figurarum earundem ſectionum ſunt eædem
inter ſe;
& propterea duæ ſectiones ſunt ſimiles (12. ex 6.) at ſuppoſitæ
fuerunt non ſimiles.
Quod eſt abſurdum.
PROPOSITIO XXIII.
SI autem ſectio A B C fuerit parabola, & ſectio D E F hy-
perbola, aut ellipſis:
manifeſtum eſt, ſectiones non eſſe in-
3313. huius. ter ſe ſimiles.
Et dico quod duo ſegmenta G C, H F non ſunt
ſimilia.
Si enim ſimilia eſſent haberent conditiones ſimilitudinis, quod eſt im-
44a poſſibile, quemadmodum oſtenſum eſt in omnibus ſectionibus ad propo-
ſitionem 13.
ſi vero vna earum fuerit hyperbole, altera verò ellipſis,
idipſum oſtenſum eſt ad propoſitionem 14.
Et hoc erat propoſitum.
PROPOSITIO XXIV.
CViuslibet coniſectionis A C D portio B A C D non erit
arcus circuli.
Si enim hoc verum non eſt educamus in illa chordas A B, C D, A C,
quarum nulla alteri ſit parallela:
& educamus E F parallelam A B, & E
G parallelam A C, atque G H parallelam C D, &
per ſingularum dua-
rum æquidiſtantium ſemipartitiones iungamus K I, L M, N O, quæ

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