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-div941" type="section" level="1" n="296">
          <pb o="309" file="0347" n="348" rhead="Conicor. Lib. VII."/>
          <p style="it">
            <s xml:id="echoid-s11074" xml:space="preserve">Quia C G ad A G, nempe quadratum A C ad ſuam figuram in ma-
              <lb/>
              <note position="left" xlink:label="note-0347-01" xlink:href="note-0347-01a" xml:space="preserve">c</note>
            iori, & </s>
            <s xml:id="echoid-s11075" xml:space="preserve">in figura ſecunda ellipſi in minori proportione, &</s>
            <s xml:id="echoid-s11076" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11077" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s11078" xml:space="preserve">In,
              <lb/>
              <figure xlink:label="fig-0347-01" xlink:href="fig-0347-01a" number="409">
                <image file="0347-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0347-01"/>
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            prima, & </s>
            <s xml:id="echoid-s11079" xml:space="preserve">ſecunda figura hyperboles,
              <lb/>
            & </s>
            <s xml:id="echoid-s11080" xml:space="preserve">in prima figura ellipſis habet C G ad
              <lb/>
            G A maiorem proportionem, quàm ad
              <lb/>
            G E, eo quod G E maior eſt, quàm G
              <lb/>
            A: </s>
            <s xml:id="echoid-s11081" xml:space="preserve">at in ſecunda figura ellipſis propor-
              <lb/>
            tio minor eſt; </s>
            <s xml:id="echoid-s11082" xml:space="preserve">quia G E minor eſt, quã
              <lb/>
            A G. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">Propoſitum verò aliter oſtendetur
              <lb/>
            hac ratione.</s>
            <s xml:id="echoid-s11084" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11085" xml:space="preserve">Quoniam ex demonſtratis in nota
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s11086" xml:space="preserve">27. </s>
            <s xml:id="echoid-s11087" xml:space="preserve">in hyperbola, atquè ex
              <lb/>
            propoſitione 11. </s>
            <s xml:id="echoid-s11088" xml:space="preserve">libri quinti in ellipſi
              <lb/>
            erit axis minor, & </s>
            <s xml:id="echoid-s11089" xml:space="preserve">rectus Q R minor
              <lb/>
            diametro recta N O, & </s>
            <s xml:id="echoid-s11090" xml:space="preserve">N O minor
              <lb/>
            remotiore V X, ideoquè quadratum Q
              <lb/>
            R minus erit quadrato N O, & </s>
            <s xml:id="echoid-s11091" xml:space="preserve">qua-
              <lb/>
            dratum N O minus quàm quadratum
              <lb/>
            V X : </s>
            <s xml:id="echoid-s11092" xml:space="preserve">eſt verò figura, ſeu rectangulum
              <lb/>
            C A F ſub extremis contentum ęquale
              <lb/>
            quadrato Q R ex media proportionali
              <lb/>
              <note position="right" xlink:label="note-0347-02" xlink:href="note-0347-02a" xml:space="preserve">15. lib. 1.</note>
            inter illas deſcriptum: </s>
            <s xml:id="echoid-s11093" xml:space="preserve">pariterquè re-
              <lb/>
            ctangulum L I K ęquale eſt quadrato
              <lb/>
            diametri ei coniugatę N O, nec non,
              <lb/>
            rectangulum T S Z ęquale erit qua-
              <lb/>
            drato V X, ergo rectangulum C A F
              <lb/>
            minus eſt rectangulo L I K, atque rectangulum L I K minus eſt rectangulo T
              <lb/>
              <figure xlink:label="fig-0347-02" xlink:href="fig-0347-02a" number="410">
                <image file="0347-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0347-02"/>
              </figure>
            S Z. </s>
            <s xml:id="echoid-s11094" xml:space="preserve">E contra in ellipſi ſecunda. </s>
            <s xml:id="echoid-s11095" xml:space="preserve">Quia. </s>
            <s xml:id="echoid-s11096" xml:space="preserve">Q R maior eſt, quàm N O, & </s>
            <s xml:id="echoid-s11097" xml:space="preserve">hęc
              <lb/>
            maior, quàm V X ; </s>
            <s xml:id="echoid-s11098" xml:space="preserve">ergo rectangulum C A F maius eſt rectangulo L I K, & </s>
            <s xml:id="echoid-s11099" xml:space="preserve">
              <lb/>
            hoc maius erit rectangulo T S Z.</s>
            <s xml:id="echoid-s11100" xml:space="preserve"/>
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