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 |< < (43) of 458 > >|
8143Conicor. Lib. V. 58[Figure 58]
Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
11f extra S L, &
c. Ad vitandam confuſionem figuræ, & prolixitatem demonſtrationis
appoſui duas figuras, in quibus duo caſus ijſdem caracteribus notantur, itaque abſq;
nouo labore, ſi inſpiciatur ſecunda figura, ijſdem verbis prioris caſus, oſtendetur ca-
ſus ſecundus.
Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, & c. Pars ſecun-
22g da huius propoſitionis innuitur tantummodo pauciſsimis verbis;
quare maioris cla-
ritatis gratia integram demonſtrationem hìc afferre libuit.
Demonſtratio ſecundæ partis.
PROPOSITIONIS LI.
Eſto E D æqualis trutinæ H: Dico ex concurſu E vnicum tantùm breui-
ſecantem ramum duci poſſe.
In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
E D æqualis H;
ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
rum E D I, B G I) eſt, vt G F ad F D, &
componendo D G ad G I eſt, vt eadem G D
ad D F;
ideoque I G æqualis eſt D F, ſeu A C ſemierecto; igitur B I eſt breuiſsima.
338. huius.
Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & in-
fra in ſecunda) occurrente axi in R, &
ducta K M perpendiculari ad axim, quæ eum
ſecet in M, &
tangentem O B in P. Quoniam (vt dictum eſt) O F ſecatur

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