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-div35" type="section" level="1" n="31">
          <pb o="6" file="0044" n="44" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div36" type="section" level="1" n="32">
          <head xml:id="echoid-head56" xml:space="preserve">PROPOS. III.</head>
          <figure number="9">
            <image file="0044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0044-01"/>
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          <p>
            <s xml:id="echoid-s850" xml:space="preserve">SI verò in ellipſi cadat B G infrà cen-
              <lb/>
            trum, poterit duplum differentię duo-
              <lb/>
            rum triangulorum D A F, & </s>
            <s xml:id="echoid-s851" xml:space="preserve">D G H, nem-
              <lb/>
            pè duplum plani G L. </s>
            <s xml:id="echoid-s852" xml:space="preserve">Et hoc erat pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s853" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div37" type="section" level="1" n="33">
          <head xml:id="echoid-head57" xml:space="preserve">Notæ in Propoſitionem primam.</head>
          <p style="it">
            <s xml:id="echoid-s854" xml:space="preserve">VOcat in primo libro interpres ſectiones habentes centrum hyperbolem, & </s>
            <s xml:id="echoid-s855" xml:space="preserve">
              <lb/>
            ellipſim, & </s>
            <s xml:id="echoid-s856" xml:space="preserve">vocat erectum latus rectum ſectionis, vocat etiam ordina-
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            tionem axis eam, quam nos ordinatim ad axim applicatam appellamus.</s>
            <s xml:id="echoid-s857" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s858" xml:space="preserve">Quia BG poteſt comparatum applicatum ad abſciſſam AG, &</s>
            <s xml:id="echoid-s859" xml:space="preserve">c. </s>
            <s xml:id="echoid-s860" xml:space="preserve">Vocat
              <lb/>
              <note position="right" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve">a</note>
            inſuper parallelogrammum comparatum applicatum ad axis abſciſſam A G re-
              <lb/>
            ctangulum ipſum A G I, quod quidem adiacet lateri recto A E latitudinem ha-
              <lb/>
              <note position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve">12. 13. lib.
                <lb/>
              primi.</note>
            bens abſciſſam A G excedens in hyperbola, & </s>
            <s xml:id="echoid-s861" xml:space="preserve">deficiens in ellipſi rectangulo ſi-
              <lb/>
            mile ei, quod latere recto, & </s>
            <s xml:id="echoid-s862" xml:space="preserve">tranſuerſo continetur; </s>
            <s xml:id="echoid-s863" xml:space="preserve">ſcilicèt rectangulo C A E.</s>
            <s xml:id="echoid-s864" xml:space="preserve"/>
          </p>
          <figure number="10">
            <image file="0044-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0044-02"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s865" xml:space="preserve">Et planum G F dimidium eſt illius comparati, &</s>
            <s xml:id="echoid-s866" xml:space="preserve">c. </s>
            <s xml:id="echoid-s867" xml:space="preserve">Non erit inutile
              <lb/>
              <note position="right" xlink:label="note-0044-03" xlink:href="note-0044-03a" xml:space="preserve">b</note>
            paulo fuſius oſtendere id quod ob nimiam facilitatem Apollonius tantummodò in-
              <lb/>
            nuit. </s>
            <s xml:id="echoid-s868" xml:space="preserve">Ducatur recta linea F K parallela axi D A ſecans ordinatam B G produ-
              <lb/>
            ctam in K: </s>
            <s xml:id="echoid-s869" xml:space="preserve">quia figuræ latera C A, & </s>
            <s xml:id="echoid-s870" xml:space="preserve">A E ſunt ipſarum D A, A F duplicia
              <lb/>
            ergo C E, & </s>
            <s xml:id="echoid-s871" xml:space="preserve">D F H parallelæ ſunt, eſtque K H parallela A E, cum ambo poſitæ
              <lb/>
            ſint perpendiculares ad axim, & </s>
            <s xml:id="echoid-s872" xml:space="preserve">C A, F K ſunt quoquè æquidiſtantes, ergò
              <lb/>
            triangulum F K H ſimile eſt triangulo C A E, & </s>
            <s xml:id="echoid-s873" xml:space="preserve">proptereà parallelogramma
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            rectangula F K H, & </s>
            <s xml:id="echoid-s874" xml:space="preserve">C A E ſimilia erunt. </s>
            <s xml:id="echoid-s875" xml:space="preserve">Et quoniam quadratum ordinatæ
              <lb/>
              <note position="left" xlink:label="note-0044-04" xlink:href="note-0044-04a" xml:space="preserve">Ibidem.</note>
            B G æquale eſt rectangulo contento ſub latere recto E A, & </s>
            <s xml:id="echoid-s876" xml:space="preserve">abſciſſa A G </s>
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