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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          <head xml:id="echoid-head135" xml:space="preserve">Notæ in Propoſit. XXIX. XXX.
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          & XXXI.</head>
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            <s xml:id="echoid-s3090" xml:space="preserve">A Lioquin producatur perpendicularis C E, &</s>
            <s xml:id="echoid-s3091" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3092" xml:space="preserve">Exiſtente C A lineæ
              <lb/>
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            breuiſsima, & </s>
            <s xml:id="echoid-s3093" xml:space="preserve">A D tangente, ſi C A non eſt perpendicularis ad tangen-
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            tem ducatur ex origine C recta C E perpendicularis ad tangentem A D, ſecans
              <lb/>
            eam in E, & </s>
            <s xml:id="echoid-s3094" xml:space="preserve">ſectionem in F, erit in triangulo A C E angulus C A E acutus,
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            & </s>
            <s xml:id="echoid-s3095" xml:space="preserve">minor angulo recto E, & </s>
            <s xml:id="echoid-s3096" xml:space="preserve">propterea C A ſubtendens maiorem angulum re-
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            ctum, maior erit quàm C E, quæ acutum ſubtendit: </s>
            <s xml:id="echoid-s3097" xml:space="preserve">cumque punctum E tan-
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            gentis cadat extra ſectionem, erit C F minor, quàm C E; </s>
            <s xml:id="echoid-s3098" xml:space="preserve">ideoque C A multo
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            maior eſt, quàm C F, quapropter C A non erit breuiſsima, quod eſt contra,
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            hypotheſin.</s>
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            <s xml:id="echoid-s3100" xml:space="preserve">Si vero fuerit D A C rectus, &</s>
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            <s xml:id="echoid-s3102" xml:space="preserve">Quia C A ſupponitur breuiſsima,
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              <note position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">33. 34.
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              lib. 2.</note>
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            <s xml:id="echoid-s3103" xml:space="preserve">angulus D A C rectus, erit A D tangens; </s>
            <s xml:id="echoid-s3104" xml:space="preserve">nam ſi hoc verum non eſt,
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            ducatur ex puncto A recta linea A G, contingens ſectionem in
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            A; </s>
            <s xml:id="echoid-s3105" xml:space="preserve">ſecabit vtique tangens A G ipſam D A, & </s>
            <s xml:id="echoid-s3106" xml:space="preserve">erit an-
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            gulus C A G rectus nimirum contentus à breuiſsima
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            <s xml:id="echoid-s3108" xml:space="preserve">ergo duo anguli recti
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            <s xml:id="echoid-s3109" xml:space="preserve">C A G æquales ſunt
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            inter ſe, pars, & </s>
            <s xml:id="echoid-s3110" xml:space="preserve">totum, quod
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            eſt abſurdum.</s>
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