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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        <div xml:id="echoid-div317" type="section" level="1" n="106">
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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-
              <lb/>
              <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a" number="100">
                <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-01"/>
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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-
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            militer ramorũ ſecantium ex concurſu E ad ſectionem A B ductorum propinquio-
              <lb/>
            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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        <div xml:id="echoid-div327" type="section" level="1" n="108">
          <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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              <figure xlink:label="fig-0120-02" xlink:href="fig-0120-02a" number="101">
                <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-
              <lb/>
            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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