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

[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

Page: 5

[5.] IO: ALFONSVS BORELLVS

Page: 5

[6.] AD SERENISSIMVM COSMVM III. ETRVRIÆ PRINCIPEM FLORENTIÆ, Ex Typographia Ioſephi Cocchini ad inſigne Stellæ MDCLXI. SVPERIORVM PERMISSV.

Page: 5

[7.] COSMVM TERTIVM ETRVRIÆ PRINCIPEM. 10: AL FONSVS BORELLIVS F.

Page: 7

[8.] CAVE CHRISTIANE LECTOR.

Page: 14

[9.] IN NOMINE DEI MISERICORDIS MISERATORIS. PROOE MIVM ABALPHATHI FILII MAHMVDI, FILII ALCASEMI, FILII ALPHADHALI ASPHAHANENSIS. LAVS DEO VTRIVSQVE SECVLI DOMINO.

Page: 15

[10.] ABRAHAMI ECCHELLENSIS IN LATINAM EX ARABICIS Librorum Apollonij Pergæi verſionem PRÆFATIO.

Page: 23

[11.] PRÆFATIO AD LECTOREM.

Page: 31

[12.] INDEX

Page: 37

[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.

Page: 43 (5)

5921Conicor. Lib. V.

Notæ in Propoſitionem IX. & X.

AT in hyper-
11g

31[Figure 31] bola, & el-
lipſi educamus G
F ad a ex A D, &
H N ad s ex F G,
& I S ad T ex C
G, ſi educta oc-
currat ſectioni ad
A, & M Q poſita
ad m ex a, F G,
& X in I T, & ex
m, S X, m y, x n,
S Z inter N S, M
X, & c. Eadẽ phraſi
inconcinna exponi-
tur vniuerſa con-
ſtructio buius pro-
poſitionis, ideo cu-
raui eam reddere
clariorem, dicendo;
Educamus rectas lineas G F quidem ſec antem A D in a, & c.

Quadratum igitur I H eſt æquale triangulo I H S, & c. Qaia nimirum.
22h Quadratum I H eſt æquale duplo iſoſcelei, & rectanguli trianguli I H S.

Et ſimiliter quadratum I Q æquale eſt duplo trianguli I Q X, & c. Sci-
33i licet duplo trapezĳ I S m Q cum duplo trianguli S m X.

Et hoc quidem propter ſimilitudinem triangulorum, at componendo
44k proportionem in hyperbola, tum inuertendo, & reflectendo in ellipſi
fit, & c. Huiuſmodi verba inepta ad concluſionem inferendam commutaui di-
cendo; Quare comparando priores ad ſummas terminorum in hyperbola, & ad
eorum differentias in ellipſi fit, & c. Quæ quidem expeditè (vt in primo præce-
cedentium Lemmatum oſtenſum eſt) progreſſum declarant.

55l

Vt proportio inclinati, ſiue tranſuerſæ ad latitudinem figuræ compara-
tæ; igitur planum m n eſt exemplar, & c. Subiungo: nam, vt dictum eſt in
quinta, & ſexta huius, poteſt hìc demonſtrari, quod figura m n ſimilis eſt ei,
quæ continetur latere tranſuerſo E C, & ſumma in hyperbola, & differentia in
ellipſi laterum tranſuerſi, & recti iuxta definitiones octauam, & nonam.

Quadratum R I æquale eſt duplo trianguli R V I, & quadratum O R in
66m hyperbola æquale eſt duplo trapezij R G, & in ellipſi æquale eſt duplo
trapezij R K, & c. Legendum puto quadratum R I æquale eſt duplo trianguli
771. huius. R V I, & quadratum O R æquale eſt duplo trapezĳ R G, at in ellipſi quando
O R cadit infra centrum F æquale eſt duplo trapezĳ R K, & c. Deindè
quum triangulum R V I ſimile ſit triangulo I H S propter parallelas V R, S
H; ideò triangulum R V I erit quoque iſoſceleum, & rectangulum. Poſtea

Table of contents

Text layer

Text normalization

Search