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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[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
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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,
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            vt a C in C B ad quadratum C B (nam poſuimus H F ad F b, vt C B ad
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            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>
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          <note position="left" xml:space="preserve">Defin. 2.
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          huius.</note>
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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
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              <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>
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            B a, & </s>
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            <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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