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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[161.] IV.
Page: 171 (133)
[162.] V.
Page: 171 (133)
[163.] VI.
Page: 171 (133)
[164.] VII.
Page: 171 (133)
[165.] VIII.
Page: 172 (134)
[166.] IX.
Page: 172 (134)
[167.] NOTÆ.
Page: 172 (134)
[168.] MONITVM.
Page: 175 (137)
[169.] SECTIO PRIMA Continens Propoſit. I. II. IV. & X. PROPOSITIO I.
Page: 176 (138)
[170.] PROPOSITIO II.
Page: 177 (139)
[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)
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page |< < (195) of 458 > >|
233195Conicor. Lib. VI. 263[Figure 263]
PROPOSITIO XXI.
SInt poſtea duæ illæ ſectiones hyperbolicæ, & ellipticæ ſi-
miles, & earum centra T, X (remanentibus lineis, & ſi-
gnis, vt prius) & ducantur duæ contingentes V e, & Y f.
264[Figure 264]
Quoniam B G ad B I ſuppoſita eſt, vt H E ad E K, & pariter G B ad
11a B L, vt H E ad E M; ergo ex æqualitate, & per conuerſionem rationis
B L ad L I eſt vt E M ad M K; & propter ſimilitudinem duarum ſectio-
22b num N L ad A I nempe L O ad O I eſt, vt M P ad D K, nempe M Q
ad Q K, & antecedentes ad ſummas vel differentias terminorum, ſcilicet
33Lem. 1.
lib. 5. O L ad L I eandem proportionem habebit, quàm Q M ad M K, & ex
44c æqualitate O L ad L B erit, vt Q M ad M E, ſed B L ad L N eſt, vt E
M ad M P, cum ex ſuppoſitione ſectiones ſint ſimiles; ergo O L ad L N
eſt, vt Q M ad M P; ſuntque L, M duo anguli recti: ergo anguli O,

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