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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            <s xml:id="echoid-s876" xml:space="preserve">
              <pb o="7" file="0045" n="45" rhead="Conicor. Lib. V."/>
            dente in hyperbola, & </s>
            <s xml:id="echoid-s877" xml:space="preserve">deficiente in ellipſi rectangulo F K H ſimile ei, quod la-
              <lb/>
            teribus recto, & </s>
            <s xml:id="echoid-s878" xml:space="preserve">tranſuerſo continetur, ſcilicet G A E, & </s>
            <s xml:id="echoid-s879" xml:space="preserve">eſt A F ſemiſsis la-
              <lb/>
            teris recti, igitur quadratum B G æquale eſt ſummæ in hyperbole, & </s>
            <s xml:id="echoid-s880" xml:space="preserve">differen-
              <lb/>
            tiæ in ellipſi rectanguli G A F bis ſumpti, & </s>
            <s xml:id="echoid-s881" xml:space="preserve">rectanguli F K H, quod eſt æqua-
              <lb/>
            le duplo trianguli F K H: </s>
            <s xml:id="echoid-s882" xml:space="preserve">ſed quadrilaterum A G H F æquale eſt aggregato in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s883" xml:space="preserve">differentiæ in ellipſi rectanguli G A F, & </s>
            <s xml:id="echoid-s884" xml:space="preserve">trianguli F K H, ergò
              <lb/>
            quadratum B G æquale eſt duplo quadrilateri A G H F, ſeù diſſerentiæ triangu-
              <lb/>
            lorum D A F, & </s>
            <s xml:id="echoid-s885" xml:space="preserve">D G H.</s>
            <s xml:id="echoid-s886" xml:space="preserve"/>
          </p>
          <figure number="11">
            <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0045-01"/>
          </figure>
        </div>
        <div xml:id="echoid-div40" type="section" level="1" n="34">
          <head xml:id="echoid-head58" xml:space="preserve">Notæ in Propoſitionem
            <lb/>
          ſecundam.</head>
          <p>
            <s xml:id="echoid-s887" xml:space="preserve">SEcunda propoſitio facilè ex prima deducitur;
              <lb/>
            </s>
            <s xml:id="echoid-s888" xml:space="preserve">nam, quando ordinata B G H I tranſit per cen-
              <lb/>
            trum D ellipſis; </s>
            <s xml:id="echoid-s889" xml:space="preserve">tunc tria puncta G, D, H conue-
              <lb/>
            niunt, & </s>
            <s xml:id="echoid-s890" xml:space="preserve">triangulum D G H euaneſcit, & </s>
            <s xml:id="echoid-s891" xml:space="preserve">ideò
              <lb/>
            differentia trianguli D A F, & </s>
            <s xml:id="echoid-s892" xml:space="preserve">trianguli D G H
              <lb/>
            nullum ſpatium habentis, erit triangulum ipſum
              <lb/>
            D A F.</s>
            <s xml:id="echoid-s893" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div41" type="section" level="1" n="35">
          <head xml:id="echoid-head59" xml:space="preserve">Notæ in Propoſitionem
            <lb/>
          tertiam.</head>
          <figure number="12">
            <image file="0045-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0045-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s894" xml:space="preserve">IN tertia propoſitione ſimilitèr, quandò ordinata
              <lb/>
            B H G I cadit infrà centrum D ellipſis, tunc
              <lb/>
            ducta C L parallela ipſi A E, erunt duo triangula
              <lb/>
            D A F, & </s>
            <s xml:id="echoid-s895" xml:space="preserve">D C L æqualia inter ſe, cum ſint ſimi-
              <lb/>
            lia, & </s>
            <s xml:id="echoid-s896" xml:space="preserve">latera homologa D A, D C ſint æqualia,
              <lb/>
            quia ſunt ſemiaxes; </s>
            <s xml:id="echoid-s897" xml:space="preserve">proptereà differentia triangu-
              <lb/>
            lorum D G H, & </s>
            <s xml:id="echoid-s898" xml:space="preserve">D A F, ſeù D C L erit trapezium
              <lb/>
            C G H L, quod ſubduplum eſt quadrati ordinatæ
              <lb/>
            B G.</s>
            <s xml:id="echoid-s899" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div42" type="section" level="1" n="36">
          <head xml:id="echoid-head60" xml:space="preserve">SECTIO SECVNDA</head>
          <head xml:id="echoid-head61" xml:space="preserve">Continens propoſitiones IV. V. VI. Apollonij.</head>
          <p>
            <s xml:id="echoid-s900" xml:space="preserve">COmparata eſt minima ramorum egredientium ex ſua origine
              <lb/>
            (4) in parabola (5) & </s>
            <s xml:id="echoid-s901" xml:space="preserve">hyperbola (6) pariterque in ellipſi (ſi
              <lb/>
            comparata fuerit portio maioris duorum axium, & </s>
            <s xml:id="echoid-s902" xml:space="preserve">tunc maxi-
              <lb/>
            mus eſt reſiduum tranſuerſi axis.) </s>
            <s xml:id="echoid-s903" xml:space="preserve">Reliquorum verò </s>
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