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-div352" type="section" level="1" n="114">
          <pb o="91" file="0129" n="129" rhead="Conicor. Lib. V."/>
          <figure number="112">
            <image file="0129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0129-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3734" xml:space="preserve">Quoniam I K, H M ſunt duæ breuiſſimæ conſtat, quod E I maximus
              <lb/>
              <note position="left" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">b</note>
            ſit ramorum cadentium ad illam ſectionem (72. </s>
            <s xml:id="echoid-s3735" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3736" xml:space="preserve">& </s>
            <s xml:id="echoid-s3737" xml:space="preserve">propinquior
              <lb/>
            illi maior eſt remotiore: </s>
            <s xml:id="echoid-s3738" xml:space="preserve">nec non; </s>
            <s xml:id="echoid-s3739" xml:space="preserve">quia H M, G N ſunt duæ breuiſſimæ
              <lb/>
              <note position="left" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">c</note>
              <note position="right" xlink:label="note-0129-03" xlink:href="note-0129-03a" xml:space="preserve">74. huius.</note>
            conſtat, vt dictum eſt, quod G E ſit maximus ramorum cadentium vtrin-
              <lb/>
            que ad ſectionẽ A H. </s>
            <s xml:id="echoid-s3740" xml:space="preserve">Dico etiam, E G maiorem eſſe, quàm E I; </s>
            <s xml:id="echoid-s3741" xml:space="preserve">nam
              <lb/>
              <note position="left" xlink:label="note-0129-04" xlink:href="note-0129-04a" xml:space="preserve">d</note>
            ſi producatur I O parallela ipſi A C, & </s>
            <s xml:id="echoid-s3742" xml:space="preserve">iungatur E O, ducanturque per-
              <lb/>
              <note position="right" xlink:label="note-0129-05" xlink:href="note-0129-05a" xml:space="preserve">15, huius.</note>
            pendiculares I P, O Q, G R, E F S, quia G N, I K ſunt breuiſſimæ er it
              <lb/>
            D P ad P K, quæ eſt, vt proportio figuræ, vt D R ad R N; </s>
            <s xml:id="echoid-s3743" xml:space="preserve">ergo F P
              <lb/>
            ad P K minorem proportionem habet, quàm F R ad R N, & </s>
            <s xml:id="echoid-s3744" xml:space="preserve">diuidendo
              <lb/>
            F K ad K P, nempe F E ad I P, minorem proportionem habet, quàm,
              <lb/>
            F N ad N R, nempe F E ad G R: </s>
            <s xml:id="echoid-s3745" xml:space="preserve">ergo F E ad I P minorem proportio-
              <lb/>
            nem habet, quàm ad G R, & </s>
            <s xml:id="echoid-s3746" xml:space="preserve">propterea G R minor eſt, quàm I P, quæ
              <lb/>
            eſt æqualis O Q, cuius punctum O remotior eſt à vertice, quàm G,
              <lb/>
            & </s>
            <s xml:id="echoid-s3747" xml:space="preserve">ideo E G maior eſt, quàm E O. </s>
            <s xml:id="echoid-s3748" xml:space="preserve">(74. </s>
            <s xml:id="echoid-s3749" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3750" xml:space="preserve">Et quia O T æqualis
              <lb/>
            eſt T I erit O S maior quàm S I, & </s>
            <s xml:id="echoid-s3751" xml:space="preserve">S E perpendicularis ad O I eſt com-
              <lb/>
            munis; </s>
            <s xml:id="echoid-s3752" xml:space="preserve">igitur O E maior eſt, quàm E I; </s>
            <s xml:id="echoid-s3753" xml:space="preserve">& </s>
            <s xml:id="echoid-s3754" xml:space="preserve">oſtenſa eſt E G maior, quàm
              <lb/>
            O E; </s>
            <s xml:id="echoid-s3755" xml:space="preserve">Ergo E G maior eſt, quàm E I, quod erat oſtendendum.</s>
            <s xml:id="echoid-s3756" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div355" type="section" level="1" n="115">
          <head xml:id="echoid-head158" xml:space="preserve">PROPOSITIO LXXVI.</head>
          <p>
            <s xml:id="echoid-s3757" xml:space="preserve">SI ex concurſu E in recto E B
              <lb/>
              <figure xlink:label="fig-0129-02" xlink:href="fig-0129-02a" number="113">
                <image file="0129-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0129-02"/>
              </figure>
              <note position="left" xlink:label="note-0129-06" xlink:href="note-0129-06a" xml:space="preserve">a</note>
            poſito ellipſis A B C nõ edu-
              <lb/>
            catur breuiſecans præter E B, qui
              <lb/>
            tranſeat per centrum; </s>
            <s xml:id="echoid-s3758" xml:space="preserve">erit E B ma-
              <lb/>
            ximus ramorum ſecantium ex con-
              <lb/>
            curſu ad ſectionem egredientium.</s>
            <s xml:id="echoid-s3759" xml:space="preserve"/>
          </p>
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