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>
            <s xml:id="echoid-s1381" xml:space="preserve">
              <pb o="22" file="0060" n="60" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0060-01" xlink:href="fig-0060-01a" number="32">
                <image file="0060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0060-01"/>
              </figure>
            dratum O R æquale eſt duplo trapezij R C G O;
              <lb/>
            </s>
            <s xml:id="echoid-s1382" xml:space="preserve">
              <note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">Prop. 1. h.</note>
            Sed in ellipſi quando ordinata O R cadit infra
              <lb/>
            centrum F, tunc quidem ducta E K parallela
              <lb/>
            C G, quæ ſecet G F in K, erit quadratum O R
              <lb/>
            æquale duplo differentiæ triangulorum F R
              <emph style="sub">o</emph>
            , & </s>
            <s xml:id="echoid-s1383" xml:space="preserve">
              <lb/>
            F C G, ſeu F E K, quæ differentia æqualis eſt
              <lb/>
            trapezio R E K
              <emph style="sub">o</emph>
            , ideoque duo quadrata ex I R,
              <lb/>
            & </s>
            <s xml:id="echoid-s1384" xml:space="preserve">ex R O, ideſt quadratum ex I O æquale erit
              <lb/>
            triangulis F C G, & </s>
            <s xml:id="echoid-s1385" xml:space="preserve">I R V bis ſumptis dempto
              <lb/>
            duplo trianguli F R
              <emph style="sub">o</emph>
            .</s>
            <s xml:id="echoid-s1386" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1387" xml:space="preserve">Quod eſt ęquale triangulo F C G cum
              <lb/>
              <note position="right" xlink:label="note-0060-02" xlink:href="note-0060-02a" xml:space="preserve">n</note>
            duplo trapezij V F, &</s>
            <s xml:id="echoid-s1388" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1389" xml:space="preserve">Addo, quævidentur
              <lb/>
            in textu deficere, ſeu cum duplo differentiæ triã-
              <lb/>
            gulorum I V R, & </s>
            <s xml:id="echoid-s1390" xml:space="preserve">F R
              <emph style="sub">o</emph>
            . </s>
            <s xml:id="echoid-s1391" xml:space="preserve">In hyperbola verò
              <lb/>
            quadratum O I æquale eſt ſpatio rectilineo V I C G
              <emph style="sub">o</emph>
            bis ſumpto, quare in hyperbo-
              <lb/>
            la, & </s>
            <s xml:id="echoid-s1392" xml:space="preserve">ellipſi quadratũ O I æquale eſt duplo trapezij I C G S cum duplo triãguli V
              <emph style="sub">o</emph>
            S.</s>
            <s xml:id="echoid-s1393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1394" xml:space="preserve">Quod eſt æquale exemplari applicato ad R H, &</s>
            <s xml:id="echoid-s1395" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1396" xml:space="preserve">Hoc enim conſtat ex
              <lb/>
              <note position="right" xlink:label="note-0060-03" xlink:href="note-0060-03a" xml:space="preserve">o</note>
            ijs, quæ ſupra dicta ſunt.</s>
            <s xml:id="echoid-s1397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1398" xml:space="preserve">Eſtque D H maior in hyperbola, quàm R H, itaque A I maior, quàm
              <lb/>
              <note position="right" xlink:label="note-0060-04" xlink:href="note-0060-04a" xml:space="preserve">p</note>
            OI, & </s>
            <s xml:id="echoid-s1399" xml:space="preserve">O I in omnibus maior, quàm B I, &</s>
            <s xml:id="echoid-s1400" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1401" xml:space="preserve">Textum hunc corruptum ſic
              <lb/>
            reſtituo: </s>
            <s xml:id="echoid-s1402" xml:space="preserve">Eſtque D H maior, quàm R H, & </s>
            <s xml:id="echoid-s1403" xml:space="preserve">R H maior quàm I H; </s>
            <s xml:id="echoid-s1404" xml:space="preserve">itaque A I
              <lb/>
            maior eſt, quàm O I, & </s>
            <s xml:id="echoid-s1405" xml:space="preserve">O I maior quàm B I.</s>
            <s xml:id="echoid-s1406" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1407" xml:space="preserve">Similiter, vt in præcedenti ſectione factum eſt, reperietur multitudo ramo-
              <lb/>
            rum inter ſe æqualium, qui ex origine ad ſectionem duci poſſunt. </s>
            <s xml:id="echoid-s1408" xml:space="preserve">Exiſtente
              <lb/>
            menſura I C maiore, quàm comparata, ſi differentia abſcißarum rami maioris,
              <lb/>
              <note position="left" xlink:label="note-0060-05" xlink:href="note-0060-05a" xml:space="preserve">PROP.
                <lb/>
              III. Add.</note>
            & </s>
            <s xml:id="echoid-s1409" xml:space="preserve">breuiſsimi æqualis fuerit abſciſſæ rami breuiſsimi, erunt tantummodo tres
              <lb/>
            rami inter ſe æquales; </s>
            <s xml:id="echoid-s1410" xml:space="preserve">ſi verò maior fuerit, duo rami ſolummodo æquales erunt;
              <lb/>
            </s>
            <s xml:id="echoid-s1411" xml:space="preserve">at ſi fuerit minor eadem abſciſſa, erunt quatuor rami tantùm æquales inter ſe.</s>
            <s xml:id="echoid-s1412" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1413" xml:space="preserve">Et primò ramorum I O, & </s>
            <s xml:id="echoid-s1414" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0060-02" xlink:href="fig-0060-02a" number="33">
                <image file="0060-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0060-02"/>
              </figure>
            breuiſsimi I N abſciſſæ ſint R
              <lb/>
            C, H C, & </s>
            <s xml:id="echoid-s1415" xml:space="preserve">eorum differen-
              <lb/>
            tia R H, ſitque R H æqualis
              <lb/>
            H C, & </s>
            <s xml:id="echoid-s1416" xml:space="preserve">producatur O R per-
              <lb/>
            pendicularis ad axim quouſ-
              <lb/>
            que ſecet ſectionem ex altera
              <lb/>
            parte in puncto o, coniunga-
              <lb/>
            turque ramus 10. </s>
            <s xml:id="echoid-s1417" xml:space="preserve">Dico quod
              <lb/>
            tres rami I O, 10, I C tan-
              <lb/>
            tũmodo inter ſe æquales ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s1418" xml:space="preserve">quoniam quadrata in para-
              <lb/>
            bola rectarum R H, & </s>
            <s xml:id="echoid-s1419" xml:space="preserve">H C,
              <lb/>
              <note position="left" xlink:label="note-0060-06" xlink:href="note-0060-06a" xml:space="preserve">8. huius.</note>
            ſeu in hyperbola, & </s>
            <s xml:id="echoid-s1420" xml:space="preserve">ellipſi,
              <lb/>
              <note position="left" xlink:label="note-0060-07" xlink:href="note-0060-07a" xml:space="preserve">9. 10. h.</note>
            rectangula exemplaria inter ſe ſimilia applicata ad R H, & </s>
            <s xml:id="echoid-s1421" xml:space="preserve">H C æqualia ſunt
              <lb/>
            inter ſe, cum eorum latera homologa R H, H C æqualia ſuppoſita ſint; </s>
            <s xml:id="echoid-s1422" xml:space="preserve">eſtque
              <lb/>
            exceſſus quadrati rami I O, vel 10, ſeu I C ſupra quadratum rami bre-
              <lb/>
            uiſsimi I N æqualis quadrato R H, vel C H in parabola, & </s>
            <s xml:id="echoid-s1423" xml:space="preserve">in reliquis
              <lb/>
            ſectionibus, exemplaribus ſimilibus applicatis ad eaſdem rectas æquales R </s>
          </p>
        </div>
      </text>
    </echo>
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