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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[201.] COROLLARIVM I.
Page: 199 (161)
[202.] COROLLARIVM II.
Page: 199 (161)
[203.] Notæ in Propoſit. XI.
Page: 203 (165)
[204.] Notæ in Propoſit. XII.
Page: 204 (166)
[205.] Notæ in Propoſit. XIII.
Page: 205 (167)
[206.] Notæ in Propoſit. XIV.
Page: 206 (168)
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
Page: 206 (168)
[208.] PROPOSITIO Præmiſſa VI.
Page: 209 (171)
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
Page: 209 (171)
[210.] Notæ in Propoſit. Præmiſſ. VI.
Page: 212 (174)
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
Page: 213 (175)
[212.] PROPOSITIO XVI.
Page: 215 (177)
[213.] PROPOSITIO XVII.
Page: 216 (178)
[214.] Notæ in Propoſit. XV.
Page: 219 (181)
[215.] MONITVM.
Page: 221 (183)
[216.] LEMMA VI.
Page: 221 (183)
[217.] LEMMA VII.
Page: 222 (184)
[218.] LEMMA VIII.
Page: 224 (186)
[219.] Notæ in Propoſit. XVI.
Page: 225 (187)
[220.] Notæ in Propoſit. XVII.
Page: 226 (188)
[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
Page: 229 (191)
[222.] Notæ in Propoſit. XVIII. & XIX.
Page: 230 (192)
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
Page: 231 (193)
[224.] PROPOSITIO XXI.
Page: 233 (195)
[225.] PROPOSITIO XXII.
Page: 235 (197)
[226.] PROPOSITIO XXIII.
Page: 236 (198)
[227.] PROPOSITIO XXIV.
Page: 236 (198)
[228.] Notæ in Propoſit. XX.
Page: 237 (199)
[229.] Notæ in Propoſit. XXI.
Page: 241 (203)
[230.] Notæ in Propoſit. XXII.
Page: 243 (205)
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320282Apollonij Pergæi ſecet axim in M, & I S ad axim perpendicularem, ſeu ordinatim applica-
tam, eum ſecans in S. Et quia trianguli A C B duo latera A C, A B ſecan-
tur proportionaliter, ſcilicet bifariam in D, & K; ergo I D parallela eſt baſi
C B: eſtquè tangens I M parallela ipſi B A, cum ambo ad diametrum I L ſint
11Prop. 5.
lib. 2. ordinatim applicatæ; pariterquè I S parallela eſt B E ( cum ſint ad axim per-
pendiculares ) igitur triangula M I S, A B E ſimilia erunt; pariterquè trian-
gula D I S, C B E erunt ſimilia: & ideo M S ad S I erit vt A E ad E B, &
S I ad S D erit, vt B E ad E C: quarè ex æquali ordinata M S ad S D ean-
dem proportionem habebit, quàm A E ad E C: eſtquè quadratum I M ad qua-
dratum N D, vt M S ad S D; ergo quadratum I M ad quadratum N D eſt,
22Prop. 4.
huius. vt A E ad E C, & c.
372[Figure 372]
SECTIO TERTIA
Continens Propoſit. Apollonij VIII. IX. X.
XI. XV. XIX. XVI. XVIII.
XVII. & XX.
VIII. IN hyperbola, vel ellipſi quadratum axis inclinati, ſiue
tranſuerſi ad quadratum ſummæ duarum diametrorum
coniugatarum eiuſdem ſectionis habebit eandem proportionem,
quàm productum præſectæ axis in ſuam interceptam compara-
tam ad quadratum ſummæ ſuæ interceptæ, & potentis compa-
ratarum.

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