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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5618Apollonij Pergæi
PROPOSITIO IX. & X.
AT in hyper-
11g26[Figure 26] bola (10.)
& ellipſi educa-
mus rectas lineas,
G F quidem ſecã-
tem A D in a, &

N H occurrẽtem
F G in S, &
I S
ſecantem C G in
T, pariterque M
Q ſecantem F G
in m, &
I T in X,
&
ex punctis m, S,
x educamus inter
N S, M X rectas
m y, X n, S Z pa-
rallelas ipſi C I.

Et quia C F ad C
G, nempe F H ad
H S poſita eſt, vt
F H ad H I erit H I æqualis H S;

22h27[Figure 27] quadratum igitur I H eſt æquale
duplo trianguli I H S, &
quadra-
tum N H ęquale eſt duplo trape-
zij H G;
quare quadratum N I
33Prop. I. h. æquale eſt duplo trapezij I G;
ſimiliter quadratum I Q ęquale eſt
44i duplo trianguli I Q X, &
quadra-
tum M Q eſt æquale duplo trape-
zij Q G;
itaque quadratum ex I M
æquale eſt duplo trapezij I G cum
duplo trianguli m S X, quod eſt æ-
quale plano m n:
Et C F ad C G,
nempe proportio figuræ eſt, vt S Z,
nempe Z X ad Z m (&
hoc quidem
propter ſimilitudinem triangulorũ)
quare comparãdo priores ad ſum-
55Lem. 1. h. mas terminorum in hyperbola, &

66k ad eorundem differentias in ellipſi
fiet X Z (quæ eſt æqualis ipſi X n)
ad X m, vt proportio inclinati, ſiue
77l tranſuerſæ ad latitudinem figuræ
comparatæ;
igitur planum m n eſt exemplar, eſtque applicatum ad X n,
88Def 9.

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