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-div88" type="section" level="1" n="49">
          <p style="it">
            <s xml:id="echoid-s1468" xml:space="preserve">
              <pb o="24" file="0062" n="62" rhead="Apollonij Pergæi"/>
            aggregato differentiali ab-
              <lb/>
              <figure xlink:label="fig-0062-01" xlink:href="fig-0062-01a" number="35">
                <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-01"/>
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            ſciſſarum ramorum I L, I
              <lb/>
            M ab abſciſſa rami breuiſ-
              <lb/>
            ſimi.</s>
            <s xml:id="echoid-s1469" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1470" xml:space="preserve">Pari modo in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s1471" xml:space="preserve">ellipſi quadratum I L ſu-
              <lb/>
            perat quadratum I M eodẽ
              <lb/>
            exceſſu, quo exemplar ap-
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">Ex 9. 10. h.</note>
            plicatum ad H P ſuperat
              <lb/>
            exemplar applicatum ad H
              <lb/>
            L; </s>
            <s xml:id="echoid-s1472" xml:space="preserve">ſed differentia exem-
              <lb/>
            plarium applicatorum ad H
              <lb/>
            P, & </s>
            <s xml:id="echoid-s1473" xml:space="preserve">H Q æqualis eſt re-
              <lb/>
            ctangulo ſub P Q exceſſu
              <lb/>
            differentiali, & </s>
            <s xml:id="echoid-s1474" xml:space="preserve">recta linea
              <lb/>
            compoſita ex X m, & </s>
            <s xml:id="echoid-s1475" xml:space="preserve">u l, ad quam ſumma
              <lb/>
            differentialis P H Q eandem proportionem
              <lb/>
              <figure xlink:label="fig-0062-02" xlink:href="fig-0062-02a" number="36">
                <image file="0062-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-02"/>
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            habet, quam latus trãſuerſum ad ſummam
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s1476" xml:space="preserve">ad differentiam in ellipſi
              <lb/>
            laterum tranſuerſi, & </s>
            <s xml:id="echoid-s1477" xml:space="preserve">recti, vt in nota
              <lb/>
            propoſitionis 5. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">oſtenſum eſt; </s>
            <s xml:id="echoid-s1479" xml:space="preserve">igitur quadra-
              <lb/>
            tum I L ſuperat quadratum I M iam dicto
              <lb/>
            rectangulo ſub P Q, & </s>
            <s xml:id="echoid-s1480" xml:space="preserve">ſub X m, & </s>
            <s xml:id="echoid-s1481" xml:space="preserve">u l,
              <lb/>
            quod erat oſtendendum.</s>
            <s xml:id="echoid-s1482" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div102" type="section" level="1" n="50">
          <head xml:id="echoid-head76" xml:space="preserve">SECTIO IV.</head>
          <head xml:id="echoid-head77" xml:space="preserve">Continens Propoſit. VII.
            <lb/>
          & XII. Apollonij.</head>
          <p>
            <s xml:id="echoid-s1483" xml:space="preserve">SIfuerit menſura A
              <lb/>
              <figure xlink:label="fig-0062-03" xlink:href="fig-0062-03a" number="37">
                <image file="0062-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-03"/>
              </figure>
            D minor com-
              <lb/>
              <note position="right" xlink:label="note-0062-02" xlink:href="note-0062-02a" xml:space="preserve">a</note>
            parata A E, (12.) </s>
            <s xml:id="echoid-s1484" xml:space="preserve">aut
              <lb/>
            ſit pars lineæ breuiſſi-
              <lb/>
            mæ, & </s>
            <s xml:id="echoid-s1485" xml:space="preserve">axis in ellipſi
              <lb/>
            ſit maior, erit A D
              <lb/>
            breuiſſimus ramorum
              <lb/>
            egredientium ex ori-
              <lb/>
            gine eius in omnibus
              <lb/>
            ſectionibus, vt ſunt F
              <lb/>
            D, G D, B D, C D,
              <lb/>
            & </s>
            <s xml:id="echoid-s1486" xml:space="preserve">proximior illi minor eſt remotiore, nempe F D quam G D, & </s>
            <s xml:id="echoid-s1487" xml:space="preserve">G
              <lb/>
            D, quàm B D.</s>
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