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-div572" type="section" level="1" n="186">
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              <pb o="153" file="0191" n="191" rhead="Conicor. Lib. VI."/>
            rentia A B C æqualis eſt circumferentiæ A D C, & </s>
            <s xml:id="echoid-s6010" xml:space="preserve">ſuperficies illius æ-
              <lb/>
            qualis ſuperficiei.</s>
            <s xml:id="echoid-s6011" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6012" xml:space="preserve">Iam linea G H tranſiens per centrum ellipſis non ſit axis. </s>
            <s xml:id="echoid-s6013" xml:space="preserve">Ducamus
              <lb/>
            ex G, H ſuper axim C A duas perpendiculares G I, H K, quæ pertin-
              <lb/>
            gant ad L, M. </s>
            <s xml:id="echoid-s6014" xml:space="preserve">Et quia ſi ponatur A D C ſuper A B C, congruit G I
              <lb/>
            ſuper L I (7. </s>
            <s xml:id="echoid-s6015" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s6016" xml:space="preserve">& </s>
            <s xml:id="echoid-s6017" xml:space="preserve">cadet G ſuper L, quia G I æqualis eſt I L, & </s>
            <s xml:id="echoid-s6018" xml:space="preserve">
              <lb/>
            cadit circumferentia C G ſuper circumferentiam C L; </s>
            <s xml:id="echoid-s6019" xml:space="preserve">ergo ſuperſicies C
              <lb/>
            I G æqualis eſt ſuperficiei C I L: </s>
            <s xml:id="echoid-s6020" xml:space="preserve">& </s>
            <s xml:id="echoid-s6021" xml:space="preserve">quia B C D congruit B A D, & </s>
            <s xml:id="echoid-s6022" xml:space="preserve">ſu-
              <lb/>
            perficies ſuperficiei, cadet C I ſuper A K, & </s>
            <s xml:id="echoid-s6023" xml:space="preserve">L I ſuper K H, & </s>
            <s xml:id="echoid-s6024" xml:space="preserve">circum-
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            ferentia C L ſuper circumferentiam A H (quia E I æqualis eſt E K) & </s>
            <s xml:id="echoid-s6025" xml:space="preserve">
              <lb/>
            ſuperficies C I L congruit ſuperficiei A K H; </s>
            <s xml:id="echoid-s6026" xml:space="preserve">& </s>
            <s xml:id="echoid-s6027" xml:space="preserve">propterea ſuperficies A
              <lb/>
            K H æqualis eſt G I C, & </s>
            <s xml:id="echoid-s6028" xml:space="preserve">triangulum E G I æquale eſt triangulo E K H;
              <lb/>
            </s>
            <s xml:id="echoid-s6029" xml:space="preserve">igitur ſuperficies A E H æqualis eſt ſuperficiei G E C, & </s>
            <s xml:id="echoid-s6030" xml:space="preserve">circumferentia
              <lb/>
            A H æqualis eſt circumferentiæ G C, eritque circumferentia C D H, & </s>
            <s xml:id="echoid-s6031" xml:space="preserve">
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            ſuperficies eius æqualis A B G, & </s>
            <s xml:id="echoid-s6032" xml:space="preserve">ſuperficiei illius. </s>
            <s xml:id="echoid-s6033" xml:space="preserve">Quare G H tranſiens
              <lb/>
            per centrum ſectionis A B C D bifariam eam diuidit. </s>
            <s xml:id="echoid-s6034" xml:space="preserve">Et hoc erat oſten-
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            dendum.</s>
            <s xml:id="echoid-s6035" xml:space="preserve"/>
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        <div xml:id="echoid-div574" type="section" level="1" n="187">
          <head xml:id="echoid-head241" xml:space="preserve">PROPOSITIO VIII.</head>
          <p>
            <s xml:id="echoid-s6036" xml:space="preserve">SImiliter conſtat, quod ſi ex quolibet quadrante ellipſis ſe-
              <lb/>
            centur circumferentiæ, per quarum extremitates rectæ li-
              <lb/>
            neæ coniunctæ ſint ad eundem axim ordinatim applicatæ, & </s>
            <s xml:id="echoid-s6037" xml:space="preserve">
              <lb/>
            æquè à centro remotæ; </s>
            <s xml:id="echoid-s6038" xml:space="preserve">vtique ſunt congruentes, & </s>
            <s xml:id="echoid-s6039" xml:space="preserve">æquales,
              <lb/>
            nec alicui portioni eiuſdem ſectionis vna illarum æqualis eſt.</s>
            <s xml:id="echoid-s6040" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6041" xml:space="preserve">Nam demonſtrauimus, quod duæ ſuperficies
              <lb/>
              <note position="left" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0191-01" xlink:href="fig-0191-01a" number="206">
                <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0191-01"/>
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            G I C, L I C ſibi congruunt, nec non congru-
              <lb/>
            unt, duabus ſuperficiebus H A K, M A K (5.
              <lb/>
            </s>
            <s xml:id="echoid-s6042" xml:space="preserve">ex 6.)</s>
            <s xml:id="echoid-s6043" xml:space="preserve">; </s>
            <s xml:id="echoid-s6044" xml:space="preserve">& </s>
            <s xml:id="echoid-s6045" xml:space="preserve">ſi eduxerimus duas ordinationes N
              <lb/>
            O, P Q, quarum diſtantiæ à centro ſint æqua-
              <lb/>
            les, ſimili modo oſtendetur, quod ſuperficies
              <lb/>
            N R C, O R C, A S Q, A S P ſint congruen-
              <lb/>
            tes (5. </s>
            <s xml:id="echoid-s6046" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s6047" xml:space="preserve">& </s>
            <s xml:id="echoid-s6048" xml:space="preserve">quod circumferentiæ N C, C
              <lb/>
            O, A Q, A P ſint congruentes, remanebunt
              <lb/>
            quatuor ſegmenta G N, L O, H Q, M P con-
              <lb/>
            gruentia, & </s>
            <s xml:id="echoid-s6049" xml:space="preserve">ſuperficies quoque eorum congru-
              <lb/>
            entes. </s>
            <s xml:id="echoid-s6050" xml:space="preserve">Et inſuper dico, quod quodlibet horum
              <lb/>
              <note position="left" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">b</note>
            ſegmentorum non congruit alicui alio ſegmen-
              <lb/>
            to; </s>
            <s xml:id="echoid-s6051" xml:space="preserve">nam ſequeretur, quod in eadem ellipſi ſint
              <lb/>
              <note position="right" xlink:label="note-0191-03" xlink:href="note-0191-03a" xml:space="preserve">48. lib. 2.</note>
            tres axes, vti dictum eſt, Quare patet propoſitum.</s>
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