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-div515" type="section" level="1" n="169">
          <p>
            <s xml:id="echoid-s5429" xml:space="preserve">
              <pb o="139" file="0177" n="177" rhead="Conicor. Lib. VI."/>
            pespendicularis B E, & </s>
            <s xml:id="echoid-s5430" xml:space="preserve">perficiatur
              <lb/>
            planũ E I. </s>
            <s xml:id="echoid-s5431" xml:space="preserve">Et quia A I, A E æquã-
              <lb/>
              <figure xlink:label="fig-0177-01" xlink:href="fig-0177-01a" number="176">
                <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-01"/>
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            tur C N, C F, vnaquæque ſuo ho-
              <lb/>
            mologo: </s>
            <s xml:id="echoid-s5432" xml:space="preserve">igitur planum I E, nempe
              <lb/>
              <note position="right" xlink:label="note-0177-01" xlink:href="note-0177-01a" xml:space="preserve">11. lib. 1.
                <lb/>
              Ibidcm.</note>
            (12. </s>
            <s xml:id="echoid-s5433" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5434" xml:space="preserve">quadratum B E æquale
              <lb/>
            eſt rectangulo F N, nempe quadrato
              <lb/>
            D F (12. </s>
            <s xml:id="echoid-s5435" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5436" xml:space="preserve">ergo B E æqualis
              <lb/>
            eſt D F; </s>
            <s xml:id="echoid-s5437" xml:space="preserve">ſi autem ſuperponatur axis
              <lb/>
            axi cadet D ſuper B, quæ tamẽhaud
              <lb/>
            cadere conceſſum fuerat: </s>
            <s xml:id="echoid-s5438" xml:space="preserve">& </s>
            <s xml:id="echoid-s5439" xml:space="preserve">hoc eſt
              <lb/>
            abſurdum; </s>
            <s xml:id="echoid-s5440" xml:space="preserve">ergo fieri non poteſt, vt
              <lb/>
            duæ ſectiones æquales non ſint.</s>
            <s xml:id="echoid-s5441" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5442" xml:space="preserve">Præterea ſupponamus duas illas ſe-
              <lb/>
              <note position="left" xlink:label="note-0177-02" xlink:href="note-0177-02a" xml:space="preserve">c</note>
            ctiones æquales eſſe inter ſe, & </s>
            <s xml:id="echoid-s5443" xml:space="preserve">fiat
              <lb/>
            F C æqualis E A, & </s>
            <s xml:id="echoid-s5444" xml:space="preserve">educamus ad
              <lb/>
            axes perpendiculares B E, D F, & </s>
            <s xml:id="echoid-s5445" xml:space="preserve">per-
              <lb/>
            ficiamus plana rectangula F N, E I.
              <lb/>
            </s>
            <s xml:id="echoid-s5446" xml:space="preserve">Quia ſectio A B cadit ſuper ſectionem C D, & </s>
            <s xml:id="echoid-s5447" xml:space="preserve">A E ſuper C F cadet; </s>
            <s xml:id="echoid-s5448" xml:space="preserve">
              <lb/>
            alioquin eſſent in eadem parabola duo axes: </s>
            <s xml:id="echoid-s5449" xml:space="preserve">ergo F cadit ſuper E, & </s>
            <s xml:id="echoid-s5450" xml:space="preserve">D
              <lb/>
            ſuper B, & </s>
            <s xml:id="echoid-s5451" xml:space="preserve">propterea B E potens planum E I (12. </s>
            <s xml:id="echoid-s5452" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5453" xml:space="preserve">æqualis erit
              <lb/>
              <note position="right" xlink:label="note-0177-03" xlink:href="note-0177-03a" xml:space="preserve">11 lib. 1.</note>
            D F potenti planum F N (12. </s>
            <s xml:id="echoid-s5454" xml:space="preserve">ex 1.)</s>
            <s xml:id="echoid-s5455" xml:space="preserve">; </s>
            <s xml:id="echoid-s5456" xml:space="preserve">ergo duo plana ſunt æqualia; </s>
            <s xml:id="echoid-s5457" xml:space="preserve">ſed
              <lb/>
              <note position="right" xlink:label="note-0177-04" xlink:href="note-0177-04a" xml:space="preserve">Ibidem.</note>
            ſunt applicata ad æquales F C, A E; </s>
            <s xml:id="echoid-s5458" xml:space="preserve">igitur C N, A I erectæ æquales
              <lb/>
              <note position="left" xlink:label="note-0177-05" xlink:href="note-0177-05a" xml:space="preserve">d</note>
            ſunt. </s>
            <s xml:id="echoid-s5459" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s5460" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div519" type="section" level="1" n="170">
          <head xml:id="echoid-head224" xml:space="preserve">PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s5461" xml:space="preserve">SI duæ ſectiones hyperbolicæ, aut duæ ellipſes A B C, D E
              <lb/>
            F habuerint axium figuras G I, H K ſimiles, & </s>
            <s xml:id="echoid-s5462" xml:space="preserve">æquales;
              <lb/>
            </s>
            <s xml:id="echoid-s5463" xml:space="preserve">duæ illæ ſectiones æquales erunt. </s>
            <s xml:id="echoid-s5464" xml:space="preserve">Si verò duæ ſectiones æquales
              <lb/>
              <note position="left" xlink:label="note-0177-06" xlink:href="note-0177-06a" xml:space="preserve">a</note>
            fuerint, earũ figuræ axiũ erunt æquales, ſimiles, & </s>
            <s xml:id="echoid-s5465" xml:space="preserve">ſimiliter poſitæ.</s>
            <s xml:id="echoid-s5466" xml:space="preserve"/>
          </p>
          <figure number="177">
            <image file="0177-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-02"/>
          </figure>
          <figure number="178">
            <image file="0177-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-03"/>
          </figure>
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