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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318280Apollonij Pergæi dens quartum caſum in poſtrema figura, quàm ſuperaddidi, vti neceſſariam,
pro intelligentia octauæ propoſitionis.

Et componendo in hyperbola, & diuidendo in ellipſi prima deindè
11b coniungendo in duabus figuris prioribus, & occurrere faciamus reſpe-
ctiuum cum reſpectiuo in reliquis figuris poſt inuerſionem, vt fiat, & c.

368[Figure 368] Ideſt componendo in byperbolis, & in ellipſibus comparando differentias termi
norum ad conſequentes, deinde comparando homologorum differentias in duabus
figuris prioribus, & ſumas in reliquis, innc enim A H ad G E eſt, vt A C
ad C G, & ſumpta communi altitudine E A, erit tectangulum H A E ad re-
ctangulum G E A, vt A C ad C G. Seà rectangulum H A E æquale eſt qua-
drato A E vna cum rectangulo H E A, cui æquale eſt quadratum B E, ergo
quadratum A B æquale eſt rectangulo H A E (propterea quod A B ſubtendit
angulum rectum E in triangulo B A E) quare quadratũ A B ad rectangulum
A G E eandem proportionẽ habet quàm C A ad C G.

Notæ in Propoſit. IV.

SI hyperbolen, aut ellipſim A B tangat recta linea I M, & occurrat
22a axi A C in M, vtique ipſius I M quadratum, & c. Suppleri debet

369[Figure 369]

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