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

Table of contents

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[171.] PROPOSITIO IV.
Page: 179 (141)
[172.] PROPOSITIO X.
Page: 179 (141)
[173.] Notæ in Propoſit. I.
Page: 179 (141)
[174.] Notæ in Propoſit. II.
Page: 180 (142)
[175.] Notæ in Propoſit. IV.
Page: 182 (144)
[176.] Notæ in Propoſit. X.
Page: 182 (144)
[177.] SECTIO SECVNDA Continens Propoſit. III. VI. VII. & IX. PROPOSITIO III.
Page: 184 (146)
[178.] PROPOSITIO VI.
Page: 185 (147)
[179.] PROPOSITIO VII.
Page: 185 (147)
[180.] PROPOSITIO IX.
Page: 186 (148)
[181.] Notæ in Propoſit. III.
Page: 187 (149)
[182.] Notæ in Propoſit. VI.
Page: 187 (149)
[183.] Notæ in Propoſit. VII.
Page: 187 (149)
[184.] Notæ in Propoſit. IX.
Page: 188 (150)
[185.] LEMMAI.
Page: 188 (150)
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
Page: 190 (152)
[187.] PROPOSITIO VIII.
Page: 191 (153)
[188.] Notæ in Propoſit. V.
Page: 192 (154)
[189.] Notæ in Propoſit. VIII.
Page: 192 (154)
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
Page: 192 (154)
[191.] PROPOSITIO XII.
Page: 193 (155)
[192.] PROPOSITIO XIII.
Page: 194 (156)
[193.] PROPOSITIO XIV.
Page: 195 (157)
[194.] MONITVM.
Page: 196 (158)
[195.] LEMMA II.
Page: 196 (158)
[196.] COROLLARIVM.
Page: 197 (159)
[197.] LEMMA III.
Page: 197 (159)
[198.] LEMMA IV.
Page: 198 (160)
[199.] COROLLARIVM.
Page: 198 (160)
[200.] LEMMAV.
Page: 199 (161)
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page |< < (280) of 458 > >|
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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