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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[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
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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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