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-div762" type="section" level="1" n="237">
          <p>
            <s xml:id="echoid-s9000" xml:space="preserve">
              <pb o="240" file="0278" n="278" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0278-01" xlink:href="fig-0278-01a" number="323">
                <image file="0278-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0278-01"/>
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            ad Z b, & </s>
            <s xml:id="echoid-s9001" xml:space="preserve">ad Z a eſt eadem; </s>
            <s xml:id="echoid-s9002" xml:space="preserve">& </s>
            <s xml:id="echoid-s9003" xml:space="preserve">propterea Z b æqualis eſt Z a, quod eſt
              <lb/>
            abſurdum.</s>
            <s xml:id="echoid-s9004" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9005" xml:space="preserve">Ponamus iam quadratum F G ad G H in G I maiorem proportionem
              <lb/>
            habere, quàm D B ad B E. </s>
            <s xml:id="echoid-s9006" xml:space="preserve">Dico in cono H F I exhiberi non poſſe ſe-
              <lb/>
            ctionem æqualem hyperbolæ A B. </s>
            <s xml:id="echoid-s9007" xml:space="preserve">Si enim exhiberi poſſet illius axi ali-
              <lb/>
            qua parallela reperiretur vt F N: </s>
            <s xml:id="echoid-s9008" xml:space="preserve">& </s>
            <s xml:id="echoid-s9009" xml:space="preserve">quadratum F N ad I N in N H ma-
              <lb/>
            iorem proportionem habens, quàm quadratum F G ad quadratum G H,
              <lb/>
            erit vt D B ad B E; </s>
            <s xml:id="echoid-s9010" xml:space="preserve">quæ minor eſt proportione quadrati F G ad qua-
              <lb/>
            dratum G H: </s>
            <s xml:id="echoid-s9011" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s9012" xml:space="preserve">Non ergo reperitur in cono H F I ſe-
              <lb/>
            ctio æqualis hyperbolæ A B. </s>
            <s xml:id="echoid-s9013" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s9014" xml:space="preserve"/>
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        <div xml:id="echoid-div767" type="section" level="1" n="238">
          <head xml:id="echoid-head299" xml:space="preserve">PROPOSITIO XXVIII.</head>
          <p>
            <s xml:id="echoid-s9015" xml:space="preserve">SIt iam ſectio elliptica A B, cuius axis tranſuerſus B D, & </s>
            <s xml:id="echoid-s9016" xml:space="preserve">
              <lb/>
            erectus illius B E, & </s>
            <s xml:id="echoid-s9017" xml:space="preserve">circa coni triangulum H F I deſcri-
              <lb/>
              <note position="right" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0278-02" xlink:href="fig-0278-02a" number="324">
                <image file="0278-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0278-02"/>
              </figure>
            </s>
          </p>
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