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-div153" type="section" level="1" n="65">
          <p>
            <s xml:id="echoid-s1950" xml:space="preserve">
              <pb o="38" file="0076" n="76" rhead="Apollonij Pergæi"/>
            gulorum C g, g e, in hyperbola, vel eorum exceſſus in ellip ſi maior,
              <lb/>
            quàm M e in e V, ergo rectangulum C M, nempe rectangulum E M mul-
              <lb/>
            tò maius eſt, quàm V e in e M, & </s>
            <s xml:id="echoid-s1951" xml:space="preserve">propterea E K ad e V, nempe K Y ad
              <lb/>
            Y e maiorem proportionem habet, quàm e M ad M K, & </s>
            <s xml:id="echoid-s1952" xml:space="preserve">componendo
              <lb/>
              <note position="left" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve">Lem. 5.</note>
              <note position="right" xlink:label="note-0076-02" xlink:href="note-0076-02a" xml:space="preserve">r</note>
            patet, quod e Y minor ſit, quàm K M, & </s>
            <s xml:id="echoid-s1953" xml:space="preserve">conſtat (quemadmodum antea
              <lb/>
            demonſtrauimus) quod breuiſſima egrediens ex V abſcindit ab axi maio-
              <lb/>
              <note position="right" xlink:label="note-0076-03" xlink:href="note-0076-03a" xml:space="preserve">s</note>
            rem lineam quàm c Z.</s>
            <s xml:id="echoid-s1954" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1955" xml:space="preserve">Simili modo conſtat, quod breuiſſima egrediens ex l eiuſdem ſit rationis.</s>
            <s xml:id="echoid-s1956" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">t</note>
          <p>
            <s xml:id="echoid-s1957" xml:space="preserve">DEindè ſit E D æqualis Q, inde demonſtrabitur, (quemadmodum ſu-
              <lb/>
            pra factum eſt) quod B H tantùm ſit linea breuiſſima, & </s>
            <s xml:id="echoid-s1958" xml:space="preserve">quod mi-
              <lb/>
              <note position="right" xlink:label="note-0076-05" xlink:href="note-0076-05a" xml:space="preserve">a</note>
            nima egrediens ex V abſcindit ab axi cum A maiorem lineam, quàm A
              <lb/>
            Z, & </s>
            <s xml:id="echoid-s1959" xml:space="preserve">quod minima egrediens ex l ſecet maiorem lineam, quàm A m.</s>
            <s xml:id="echoid-s1960" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1961" xml:space="preserve">Tandem pona-
              <lb/>
              <figure xlink:label="fig-0076-01" xlink:href="fig-0076-01a" number="52">
                <image file="0076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0076-01"/>
              </figure>
            mus E D minorẽ,
              <lb/>
            quàm Q, ergo E
              <lb/>
            D ad B O minorẽ
              <lb/>
            proportionem ha-
              <lb/>
            bet, quàm Q ad
              <lb/>
            eandem; </s>
            <s xml:id="echoid-s1962" xml:space="preserve">& </s>
            <s xml:id="echoid-s1963" xml:space="preserve">demõ-
              <lb/>
            ſtrabitur (quemad-
              <lb/>
              <note position="right" xlink:label="note-0076-06" xlink:href="note-0076-06a" xml:space="preserve">b</note>
            modum dictũ eſt)
              <lb/>
            quod G O ad O B
              <lb/>
            minorem propor-
              <lb/>
            tionem habeat,
              <lb/>
            quàm F O ad O C;
              <lb/>
            </s>
            <s xml:id="echoid-s1964" xml:space="preserve">& </s>
            <s xml:id="echoid-s1965" xml:space="preserve">ponamus O G
              <lb/>
            ad O o, vt F O ad
              <lb/>
            O C; </s>
            <s xml:id="echoid-s1966" xml:space="preserve">& </s>
            <s xml:id="echoid-s1967" xml:space="preserve">produca-
              <lb/>
            mus per o ſectionẽ
              <lb/>
            hyperbolicam cir-
              <lb/>
            ca duas continen-
              <lb/>
            tes S M, M F, quę
              <lb/>
            ſecet ſectionem A
              <lb/>
            B in V, l, & </s>
            <s xml:id="echoid-s1968" xml:space="preserve">iun-
              <lb/>
            gamus E V, E l,
              <lb/>
              <note position="right" xlink:label="note-0076-07" xlink:href="note-0076-07a" xml:space="preserve">c</note>
            & </s>
            <s xml:id="echoid-s1969" xml:space="preserve">producamus ex
              <lb/>
            V, l duas perpendiculares V c, l P, quæ parallelæ ſint continenti M F,
              <lb/>
            ergo o G in G M eſt æquale V e in e M (12. </s>
            <s xml:id="echoid-s1970" xml:space="preserve">ex ſecundo) & </s>
            <s xml:id="echoid-s1971" xml:space="preserve">quia G O ad
              <lb/>
            O o eſt, vt F O ad O C erit o O in O F æquale rectangulo G C, & </s>
            <s xml:id="echoid-s1972" xml:space="preserve">pona-
              <lb/>
            mus rectangulum F G commune fiet rectangulum C M (quod erat ęquale
              <lb/>
            rectangulo M E) æquale ipſi o G in G M, quod eſt æquale ipſi V e in e
              <lb/>
              <note position="right" xlink:label="note-0076-08" xlink:href="note-0076-08a" xml:space="preserve">d</note>
            M; </s>
            <s xml:id="echoid-s1973" xml:space="preserve">ergo rectangulum E M æquale eſt ipſi V e in e M. </s>
            <s xml:id="echoid-s1974" xml:space="preserve">Tandem proſe-
              <lb/>
            quamur ſuperiorem demonſtrationem, vt oſtendatur veritas reliquarum
              <lb/>
              <note position="right" xlink:label="note-0076-09" xlink:href="note-0076-09a" xml:space="preserve">e</note>
            propoſitionum, & </s>
            <s xml:id="echoid-s1975" xml:space="preserve">hoc erat propoſitum.</s>
            <s xml:id="echoid-s1976" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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