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-div540" type="section" level="1" n="176">
          <p style="it">
            <s xml:id="echoid-s5747" xml:space="preserve">
              <pb o="146" file="0184" n="184" rhead="Apollonij Pergæi"/>
            gruent, & </s>
            <s xml:id="echoid-s5748" xml:space="preserve">ideo à communi vertice A,
              <lb/>
              <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a" number="190">
                <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0184-01"/>
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            ducta qualibet diametro A E, vel C
              <lb/>
            F, ad quàm ordinatim applicetur quæ-
              <lb/>
            libet B E, ſeu D F in angulo non re-
              <lb/>
            cto; </s>
            <s xml:id="echoid-s5749" xml:space="preserve">ſintque latera tranſuerſa, & </s>
            <s xml:id="echoid-s5750" xml:space="preserve">recta
              <lb/>
            G A, A I, atque H C, C N. </s>
            <s xml:id="echoid-s5751" xml:space="preserve">Dico,
              <lb/>
            huinſmodi latera, & </s>
            <s xml:id="echoid-s5752" xml:space="preserve">ſiguræ ſeu rectã-
              <lb/>
            gula G A I, H C N æqualia, & </s>
            <s xml:id="echoid-s5753" xml:space="preserve">ſimi-
              <lb/>
            lia eſſe inter ſe, & </s>
            <s xml:id="echoid-s5754" xml:space="preserve">ſibi mutuò congru-
              <lb/>
            entia. </s>
            <s xml:id="echoid-s5755" xml:space="preserve">Si enim hoc verum non eſt, eo-
              <lb/>
            rum diametri G I, & </s>
            <s xml:id="echoid-s5756" xml:space="preserve">H N ſimiliter
              <lb/>
            poſitæ, & </s>
            <s xml:id="echoid-s5757" xml:space="preserve">ſubtendentes communem an-
              <lb/>
            gulum A non coincident; </s>
            <s xml:id="echoid-s5758" xml:space="preserve">& </s>
            <s xml:id="echoid-s5759" xml:space="preserve">ideo æquidiſtantes erunt aut ſe mutuò ſecabunt in
              <lb/>
            vno puncto: </s>
            <s xml:id="echoid-s5760" xml:space="preserve">ducatur ergo à termino E alicuius ordinatim applicatæ B E recta
              <lb/>
            linea E M parallela lateribus rectis A I, C N, ita vt ſecet diametros ſigurarum
              <lb/>
            ſupra aut inſra occurſum in duobus punctis M, & </s>
            <s xml:id="echoid-s5761" xml:space="preserve">O. </s>
            <s xml:id="echoid-s5762" xml:space="preserve">Igitur in ſectione A B
              <lb/>
            idem quadratum ordinatim applicatæ B E, ſeu D F æquale erit rectangulo A E
              <lb/>
            M, & </s>
            <s xml:id="echoid-s5763" xml:space="preserve">in ſectione D C æquale erit rectangulo C F O, ſuntque abſciſſæ A E, & </s>
            <s xml:id="echoid-s5764" xml:space="preserve">
              <lb/>
            C F æquales; </s>
            <s xml:id="echoid-s5765" xml:space="preserve">ergo M E, & </s>
            <s xml:id="echoid-s5766" xml:space="preserve">O F æquales inter ſe ſunt: </s>
            <s xml:id="echoid-s5767" xml:space="preserve">pars, & </s>
            <s xml:id="echoid-s5768" xml:space="preserve">totum quod
              <lb/>
            eſt abſurdum: </s>
            <s xml:id="echoid-s5769" xml:space="preserve">Non ergo latera ſigurarum inequalia ſunt. </s>
            <s xml:id="echoid-s5770" xml:space="preserve">Quod erat oſtenden-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s5771" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div545" type="section" level="1" n="177">
          <head xml:id="echoid-head231" xml:space="preserve">SECTIO SECVNDA
            <lb/>
          Continens Propoſit. III. VI. VII. & IX.
            <lb/>
          PROPOSITIO III.</head>
          <p>
            <s xml:id="echoid-s5772" xml:space="preserve">COniſectio non eſt æqualis ſectioni quæ eiuſdem generis cũ
              <lb/>
            illa non ſit.</s>
            <s xml:id="echoid-s5773" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5774" xml:space="preserve">Etenim elli-
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              <figure xlink:label="fig-0184-02" xlink:href="fig-0184-02a" number="191">
                <image file="0184-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0184-02"/>
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            pſis non erit æ-
              <lb/>
            qualis alicui pa-
              <lb/>
            rabolæ, aut hy-
              <lb/>
            perbolæ quia
              <lb/>
            illa eſt termina-
              <lb/>
            ta, hæ verò ſunt
              <lb/>
            indeterminatæ.
              <lb/>
            </s>
            <s xml:id="echoid-s5775" xml:space="preserve">At parabola D
              <lb/>
            E F, cuius axis
              <lb/>
            D I non erit æ-
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            qualis hyperbolæ A B C, cuius axis A G, & </s>
            <s xml:id="echoid-s5776" xml:space="preserve">inclinatus A H. </s>
            <s xml:id="echoid-s5777" xml:space="preserve">Quia ſi
              <lb/>
            abſcindantur A K, K G æquales D L, L I, & </s>
            <s xml:id="echoid-s5778" xml:space="preserve">educamus ad axes perpen-
              <lb/>
            diculares B K, C G, E L, F I: </s>
            <s xml:id="echoid-s5779" xml:space="preserve">Dico, quod ſectio D F non eſt </s>
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