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-div141" type="section" level="1" n="62">
          <p>
            <s xml:id="echoid-s1790" xml:space="preserve">
              <pb o="33" file="0071" n="71" rhead="Conicor. Lib. V."/>
            in ellipſi, vt menſura ſumatur in maiori duorum axium, & </s>
            <s xml:id="echoid-s1791" xml:space="preserve">rami
              <lb/>
            egrediantur ad eius ſectionem.</s>
            <s xml:id="echoid-s1792" xml:space="preserve"/>
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        <div xml:id="echoid-div143" type="section" level="1" n="63">
          <head xml:id="echoid-head95" xml:space="preserve">PROPOSITIO IL. & L.</head>
          <p>
            <s xml:id="echoid-s1793" xml:space="preserve">EXE concurſu ſuper perpendicularem ED educamus E B ſe-
              <lb/>
            cantem menſuram A D in F, & </s>
            <s xml:id="echoid-s1794" xml:space="preserve">ſectionem A B in B, & </s>
            <s xml:id="echoid-s1795" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">b</note>
            ſit A H dimidium erecti; </s>
            <s xml:id="echoid-s1796" xml:space="preserve">ſitque menſura A D non maior, quàm
              <lb/>
            H A. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">Dico quod BF non erit breuiſſima, & </s>
            <s xml:id="echoid-s1798" xml:space="preserve">minima egrediens
              <lb/>
              <note position="left" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">c</note>
            ex B abſcindit ex ſagitta maiorem lineam, quàm F A: </s>
            <s xml:id="echoid-s1799" xml:space="preserve">at ſi fue-
              <lb/>
            rit A D maior , quàm A H, tunc B F poteſt eſſe linea breuiſ-
              <lb/>
            ſima.</s>
            <s xml:id="echoid-s1800" xml:space="preserve"/>
          </p>
          <figure number="49">
            <image file="0071-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071-01"/>
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            <s xml:id="echoid-s1801" xml:space="preserve">EDucamus iam B I perpendicularem ad axim, & </s>
            <s xml:id="echoid-s1802" xml:space="preserve">ſupponamus prius A
              <lb/>
            D non maiorem quàm A H , & </s>
            <s xml:id="echoid-s1803" xml:space="preserve">ſit ſectio parabole ; </s>
            <s xml:id="echoid-s1804" xml:space="preserve">igitur D I mi-
              <lb/>
              <note position="left" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">d</note>
            nor eſt , quàm A H, & </s>
            <s xml:id="echoid-s1805" xml:space="preserve">ponatur G I æqualis A H, erit B G minima (8.
              <lb/>
            </s>
            <s xml:id="echoid-s1806" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s1807" xml:space="preserve">abſcindit G A ex ſagitta maiorem , quàm A F; </s>
            <s xml:id="echoid-s1808" xml:space="preserve">ſi verò ſe-
              <lb/>
            ctio fuerit hyperbole, aut ellipſis, ſit centrum C; </s>
            <s xml:id="echoid-s1809" xml:space="preserve">ergo A C ad A H non
              <lb/>
              <note position="left" xlink:label="note-0071-04" xlink:href="note-0071-04a" xml:space="preserve">e</note>
            habet maiorem proportionem, quàm ad A D, quare C I ad I F maiorem
              <lb/>
            proportionem habet, quàm C A ad A H; </s>
            <s xml:id="echoid-s1810" xml:space="preserve">ponatur ergo I C ad I G , vt
              <lb/>
            A C ad A H; </s>
            <s xml:id="echoid-s1811" xml:space="preserve">ergo B G eſt minima , & </s>
            <s xml:id="echoid-s1812" xml:space="preserve">abſcindit (9. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">& </s>
            <s xml:id="echoid-s1814" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1815" xml:space="preserve">ex quinto)
              <lb/>
            G A maiorem , quam F A, quod erat oſtendendum.</s>
            <s xml:id="echoid-s1816" xml:space="preserve"/>
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