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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[251.] II.
Page: 309 (271)
[252.] III.
Page: 309 (271)
[253.] IV.
Page: 309 (271)
[254.] V.
Page: 309 (271)
[255.] VI.
Page: 309 (271)
[256.] VII.
Page: 310 (272)
[257.] VIII.
Page: 310 (272)
[258.] NOTÆ.
Page: 310 (272)
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
Page: 311 (273)
[260.] PROPOSITIO V. & XXIII.
Page: 312 (274)
[261.] Notæ in Propoſit. I.
Page: 312 (274)
[262.] Notæ in Propoſit. V. & XXIII.
Page: 313 (275)
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
Page: 314 (276)
[264.] PROPOSITIO IV.
Page: 315 (277)
[265.] PROPOSITIO VI. & VII.
Page: 316 (278)
[266.] Notæ in Propoſit. II. III.
Page: 317 (279)
[267.] Notæ in Propoſit. IV.
Page: 318 (280)
[268.] Notæ in Propoſit. VI. & VII.
Page: 319 (281)
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
Page: 320 (282)
[270.] Notæ in Propoſit. VIII.
Page: 323 (285)
[271.] Notæ in Propoſit. IX.
Page: 324 (286)
[272.] Notæ in Propoſit. X.
Page: 325 (287)
[273.] Notæ in Propoſit. XI.
Page: 325 (287)
[274.] Notæ in Propoſit. XV.
Page: 326 (288)
[275.] Notæ in Propoſit. XIX.
Page: 326 (288)
[276.] Notæ in Propoſit. XVI.
Page: 327 (289)
[277.] Notæ in Propoſit. XVIII.
Page: 327 (289)
[278.] Notæ in Propoſit. XVII.
Page: 328 (290)
[279.] Notæ in Propoſit. XX.
Page: 328 (290)
[280.] SECTIO QVARTA Continens Propoſit. Apollonij XII. XIII. XXIX. XVII. XXII. XXX. XIV. & XXV.
Page: 329 (291)
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341302Apollonij Pergæi ſummam earundem: & ſumma duorum quadratorum ipſarum æqualis eſt
ſummæ duorum quadratorum A C, Q R ( 22. ex 7. ) ergo ſumma A C,
Q R minor eſt, quàm ſumma I L, N O, atque ſic oſtendetur, quod sũ-
ma I L, N O minor eſt, quàm ſumma S T, V X. Quod erat propoſitũ.
PROPOSITIO XXXXIII.
D Einde in ellipſi quadratum ſummæ A C, Q R minus eſt quadrato
ſummæ I L, N O; & ſumma duorum quadratorum A C, Q R
396[Figure 396] æqualis eſt ſummæ duorum quadratorum I L, N O (22. ex 7. ) igitur
remanet A C in Q R minus quàm I L in N O, & ſimiliter I L in N O
11f minus erit, quàm S T in V X.
Sed in hyperbola, quia quilibet axium minor eſt homologa diame-
tro coniugatarum; igitur planum rectangulum ab axibus contentum mi-
nus eſt eo quod à duabus coniugatis continetur hoc igitur in hyperbo-
le manifeſtum eſt.
In ellipſi autem, quia A C ad Q R maiorem proportionem habet;
22g quàm I L ad N O per conuerſionem rationis, & permutando maior A C
ad minorem I L minorem proportionem habebit, quàm differentia ipſa-
rum A C, Q R ad differentiam ipſarum I L & N O; & propterea diffe-
rentia ipſarum A C, & Q R maior erit differentia reliquarum I L, & N
O. Et ſimiliter oſtendetur, quod exceſſus I L ſuper N O maior ſit, quàm
exceſſus S T ſuper V X.

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