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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        <div xml:id="echoid-div325" type="section" level="1" n="107">
          <head xml:id="echoid-head147" xml:space="preserve">Notæ in Propoſ. LXVI.</head>
          <p style="it">
            <s xml:id="echoid-s3429" xml:space="preserve">QVia ſi caderet inter C, D ducipoſ-
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              <note position="right" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">a</note>
            ſet, &</s>
            <s xml:id="echoid-s3430" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3431" xml:space="preserve">Quotieſcumq; </s>
            <s xml:id="echoid-s3432" xml:space="preserve">enim perpen-
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            dicularis E F cadit ſuper centrũ
              <lb/>
            D, vel ſecat ſemiaxim D C inter D, & </s>
            <s xml:id="echoid-s3433" xml:space="preserve">C, tũc
              <lb/>
            ex concurſu E vnicus ramus breuiſecans du-
              <lb/>
            ci poteſt ad ſectionem B A, qui nimirum ca-
              <lb/>
              <note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">45. 56.
                <lb/>
              huius.</note>
            dit inter verticem remotiorem A, & </s>
            <s xml:id="echoid-s3434" xml:space="preserve">axim
              <lb/>
            minorem D B: </s>
            <s xml:id="echoid-s3435" xml:space="preserve">ſed ex hypotheſi nullus ra-
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            mus ex concurſu E ad quadrantem ellipſis A
              <lb/>
            B duci poteſt, qui ſit breuiſecans; </s>
            <s xml:id="echoid-s3436" xml:space="preserve">igitur per-
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            pendicularis E F ſecat ſemiaxim A D in
              <lb/>
            puncto F poſito inter A, & </s>
            <s xml:id="echoid-s3437" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3438" xml:space="preserve"/>
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            <s xml:id="echoid-s3439" xml:space="preserve">Deinde patet, quemadmodum demon-
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            ſtrauimus in vtraque hyperbola, &</s>
            <s xml:id="echoid-s3440" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3441" xml:space="preserve">Permuto particulam [vtraque] vt
              <lb/>
            manifeſtè erroneam, legi enim debet in parabola, & </s>
            <s xml:id="echoid-s3442" xml:space="preserve">hyperbola. </s>
            <s xml:id="echoid-s3443" xml:space="preserve">Quod vero ra-
              <lb/>
            mus terminatus E A minimus ſit omnium ramorum ſecantium manifeſtum eſt
              <lb/>
            ex demonſtratione propoſitionis 64. </s>
            <s xml:id="echoid-s3444" xml:space="preserve">65.</s>
            <s xml:id="echoid-s3445" xml:space="preserve">, quæ compræhendit etiam ellipſim,
              <lb/>
            quando menſura F A minor eſt ſemiaxi A D, vt ex propoſitione 52. </s>
            <s xml:id="echoid-s3446" xml:space="preserve">patet. </s>
            <s xml:id="echoid-s3447" xml:space="preserve">Et ſi-
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            militer ramorũ ſecantium ex concurſu E ad ſectionem A B ductorum propinquio-
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            res vertici A minores ſunt remotioribus ex eadem demonſtratione 64. </s>
            <s xml:id="echoid-s3448" xml:space="preserve">65. </s>
            <s xml:id="echoid-s3449" xml:space="preserve">huius.</s>
            <s xml:id="echoid-s3450" xml:space="preserve"/>
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          <head xml:id="echoid-head148" style="it" xml:space="preserve">Ex demonſtratione præmiſſa propoſitionum 64. & 65.
            <lb/>
          deduci poteſt conſectarium, à quo notæ ſubſe-
            <lb/>
          quentes breuiores reddantur.</head>
          <head xml:id="echoid-head149" xml:space="preserve">COROLLARIVM PROPOSIT.
            <lb/>
          LXIV. & LXV.</head>
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            <s xml:id="echoid-s3451" xml:space="preserve">SI in aliqua peripheria cuiuslibet coniſectio-
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                <image file="0120-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-02"/>
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            nis omnes rami ſecantes, qui à concurſu
              <lb/>
            duci poſſunt, cum tangentibus ab eorum ter-
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            minis ductis conſtituunt angulos, qui verti-
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            cem reſpiciunt, acutos; </s>
            <s xml:id="echoid-s3452" xml:space="preserve">rami proximiores ver-
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            tici ſectionis minores erunt remotioribus.</s>
            <s xml:id="echoid-s3453" xml:space="preserve"/>
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            <s xml:id="echoid-s3454" xml:space="preserve">Ex eo enim, quod ïn propoſitionibus 64. </s>
            <s xml:id="echoid-s3455" xml:space="preserve">& </s>
            <s xml:id="echoid-s3456" xml:space="preserve">
              <lb/>
            65.</s>
            <s xml:id="echoid-s3457" xml:space="preserve">, omnes rami D A, D L, D B, D Q, D
              <lb/>
            C, & </s>
            <s xml:id="echoid-s3458" xml:space="preserve">reliqui omnes, qui duci poſſunt ex con-
              <lb/>
            curſu D ad ſectionem A B C efficiunt cum
              <lb/>
            tangentibus ſectionẽ à terminis A, L, B, Q, C
              <lb/>
            angulos, verticem A reſpicientes, acutos, </s>
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