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-div677" type="section" level="1" n="225">
          <p>
            <s xml:id="echoid-s7456" xml:space="preserve">
              <pb o="198" file="0236" n="236" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0236-01" xlink:href="fig-0236-01a" number="268">
                <image file="0236-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0236-01"/>
              </figure>
            tione figuræ diametri A L (40. </s>
            <s xml:id="echoid-s7457" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s7458" xml:space="preserve">erit vt quadratum E Q ad M Q
              <lb/>
              <note position="left" xlink:label="note-0236-01" xlink:href="note-0236-01a" xml:space="preserve">37. lib. 1.</note>
            in O Q, nempe in eadem proportione figuræ diametri D M (40. </s>
            <s xml:id="echoid-s7459" xml:space="preserve">ex 1.)
              <lb/>
            </s>
            <s xml:id="echoid-s7460" xml:space="preserve">
              <note position="left" xlink:label="note-0236-02" xlink:href="note-0236-02a" xml:space="preserve">Ibidem.</note>
            quapropter duæ proportiones figurarum earundem ſectionum ſunt eædem
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s7461" xml:space="preserve">& </s>
            <s xml:id="echoid-s7462" xml:space="preserve">propterea duæ ſectiones ſunt ſimiles (12. </s>
            <s xml:id="echoid-s7463" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7464" xml:space="preserve">at ſuppoſitæ
              <lb/>
            fuerunt non ſimiles. </s>
            <s xml:id="echoid-s7465" xml:space="preserve">Quod eſt abſurdum.</s>
            <s xml:id="echoid-s7466" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div679" type="section" level="1" n="226">
          <head xml:id="echoid-head286" xml:space="preserve">PROPOSITIO XXIII.</head>
          <p>
            <s xml:id="echoid-s7467" xml:space="preserve">SI autem ſectio A B C fuerit parabola, & </s>
            <s xml:id="echoid-s7468" xml:space="preserve">ſectio D E F hy-
              <lb/>
            perbola, aut ellipſis: </s>
            <s xml:id="echoid-s7469" xml:space="preserve">manifeſtum eſt, ſectiones non eſſe in-
              <lb/>
              <note position="left" xlink:label="note-0236-03" xlink:href="note-0236-03a" xml:space="preserve">13. huius.</note>
            ter ſe ſimiles. </s>
            <s xml:id="echoid-s7470" xml:space="preserve">Et dico quod duo ſegmenta G C, H F non ſunt
              <lb/>
            ſimilia.</s>
            <s xml:id="echoid-s7471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7472" xml:space="preserve">Si enim ſimilia eſſent haberent conditiones ſimilitudinis, quod eſt im-
              <lb/>
              <note position="right" xlink:label="note-0236-04" xlink:href="note-0236-04a" xml:space="preserve">a</note>
            poſſibile, quemadmodum oſtenſum eſt in omnibus ſectionibus ad propo-
              <lb/>
            ſitionem 13. </s>
            <s xml:id="echoid-s7473" xml:space="preserve">ſi vero vna earum fuerit hyperbole, altera verò ellipſis,
              <lb/>
            idipſum oſtenſum eſt ad propoſitionem 14. </s>
            <s xml:id="echoid-s7474" xml:space="preserve">Et hoc erat propoſitum.</s>
            <s xml:id="echoid-s7475" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div682" type="section" level="1" n="227">
          <head xml:id="echoid-head287" xml:space="preserve">PROPOSITIO XXIV.</head>
          <p>
            <s xml:id="echoid-s7476" xml:space="preserve">CViuslibet coniſectionis A C D portio B A C D non erit
              <lb/>
            arcus circuli.</s>
            <s xml:id="echoid-s7477" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7478" xml:space="preserve">Si enim hoc verum non eſt educamus in illa chordas A B, C D, A C,
              <lb/>
            quarum nulla alteri ſit parallela: </s>
            <s xml:id="echoid-s7479" xml:space="preserve">& </s>
            <s xml:id="echoid-s7480" xml:space="preserve">educamus E F parallelam A B, & </s>
            <s xml:id="echoid-s7481" xml:space="preserve">E
              <lb/>
            G parallelam A C, atque G H parallelam C D, & </s>
            <s xml:id="echoid-s7482" xml:space="preserve">per ſingularum dua-
              <lb/>
            rum æquidiſtantium ſemipartitiones iungamus K I, L M, N O, quæ </s>
          </p>
        </div>
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    </echo>
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