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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[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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page |< < (73) of 458 > >|
11173Conicor. Lib. V.
Notæ in Propoſit. XXIX. XXX.
& XXXI.
A Lioquin producatur perpendicularis C E, & c. Exiſtente C A lineæ
11a breuiſsima, & A D tangente, ſi C A non eſt perpendicularis ad tangen-
tem ducatur ex origine C recta C E perpendicularis ad tangentem A D, ſecans
eam in E, & ſectionem in F, erit in triangulo A C E angulus C A E acutus,
& minor angulo recto E, & propterea C A ſubtendens maiorem angulum re-
ctum, maior erit quàm C E, quæ acutum ſubtendit: cumque punctum E tan-
gentis cadat extra ſectionem, erit C F minor, quàm C E; ideoque C A multo
maior eſt, quàm C F, quapropter C A non erit breuiſsima, quod eſt contra,
hypotheſin.
Si vero fuerit D A C rectus, & c. Quia C A ſupponitur breuiſsima,
22b3333. 34.
lib. 2.& angulus D A C rectus, erit A D tangens; nam ſi hoc verum non eſt,
ducatur ex puncto A recta linea A G, contingens ſectionem in
A; ſecabit vtique tangens A G ipſam D A, & erit an-
gulus C A G rectus nimirum contentus à breuiſsima
C A, & tangente A G, ex proxime demon-
ſtrata propoſitione; ergo duo anguli recti
C A D, & C A G æquales ſunt
inter ſe, pars, & totum, quod
eſt abſurdum.
93[Figure 93]

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