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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[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)
[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
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              <pb o="156" file="0194" n="194" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0194-01" xlink:href="fig-0194-01a" number="210">
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            A B ſimilis eſt figuræ ſectionis E F, erit quadratum H E ad H b in H F,
              <lb/>
            vt quadratum A C ad C a in C B; </s>
            <s xml:id="echoid-s6105" xml:space="preserve">& </s>
            <s xml:id="echoid-s6106" xml:space="preserve">b H in H F ad quadratum H F,
              <lb/>
            vt a C in C B ad quadratum C B (nam poſuimus H F ad F b, vt C B ad
              <lb/>
            B a) ergo ex æqualitate, quadratũ E H ad quadratũ H F eſt, vt quadra-
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            tum A C ad quadratum C B: </s>
            <s xml:id="echoid-s6107" xml:space="preserve">& </s>
            <s xml:id="echoid-s6108" xml:space="preserve">propterea E Z ad H F eſt vt A S ad C
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            B; </s>
            <s xml:id="echoid-s6109" xml:space="preserve">Atque ſic oſtendetur, quod X Y ad N F ſit vt Q R ad L B, & </s>
            <s xml:id="echoid-s6110" xml:space="preserve">T V
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            ad M F ſit vt O P ad K B; </s>
            <s xml:id="echoid-s6111" xml:space="preserve">ergo proportiones ordinationum axis vnius
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            earum ad ſua abſciſſa ſunt eædem rationibus aliarum ordinationum axis
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            ad ſua abſciſſa, & </s>
            <s xml:id="echoid-s6112" xml:space="preserve">alternatiuè. </s>
            <s xml:id="echoid-s6113" xml:space="preserve">Quare duæ ſectiones ſunt ſimiles.</s>
            <s xml:id="echoid-s6114" xml:space="preserve"/>
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          <note position="left" xml:space="preserve">Defin. 2.
            <lb/>
          huius.</note>
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            <s xml:id="echoid-s6115" xml:space="preserve">E contra oſtendetur, quod
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            ſi duæ ſectiones fuerint ſimi-
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            les, earũ figuræ ſimiles quo-
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            que erunt. </s>
            <s xml:id="echoid-s6116" xml:space="preserve">Quia eſt A C ad
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              buius.</note>
            C B, vt E H ad H F, & </s>
            <s xml:id="echoid-s6117" xml:space="preserve">ean-
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            dem proportionem habent
              <lb/>
            earum quadrata, atque
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            quadratum H F ad H F in
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            H b eſt, vt quadratum C B
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            ad C B in C a (eo quod
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            H F ad F b poſita fuit, vt
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            C B ad B a); </s>
            <s xml:id="echoid-s6118" xml:space="preserve">ergo ex æ-
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            qualitate quadratum E H ad
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            b H in H F, nempe I F
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            ad F b (20. </s>
            <s xml:id="echoid-s6119" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6120" xml:space="preserve">eſt, vt quadratum A C ad a C in C B, nempe vt
              <lb/>
              <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">21. lib. 1.
                <lb/>
              Ibidem.</note>
            D B ad B a (20. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">ex 1.)</s>
            <s xml:id="echoid-s6122" xml:space="preserve">; </s>
            <s xml:id="echoid-s6123" xml:space="preserve">quare figuræ duarum ſectionum ſunt ſimiles.
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            <s xml:id="echoid-s6124" xml:space="preserve">Et hoc erat oſtendendum.</s>
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          <head xml:id="echoid-head246" xml:space="preserve">PROPOSITIO XIII.</head>
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            <s xml:id="echoid-s6128" xml:space="preserve">Hyperbolæ, ſeu ellipſis A B ſit axis B C, & </s>
            <s xml:id="echoid-s6129" xml:space="preserve">inclinatus, ſeu tranſuerſus
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            B a, & </s>
            <s xml:id="echoid-s6130" xml:space="preserve">E F ſit ſectio parabolæ, cuius axis F H. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">Dico, quod ſectio E F
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            non eſt ſimilis ſectioni A B hyperbolicæ, aut ellipticæ, alioquin ſit </s>
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