Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="37" file="0085" n="85" rhead="DE IIS QVAE VEH. IN AQVA."/>
        </div>
        <div xml:id="echoid-div158" type="section" level="1" n="52">
          <head xml:id="echoid-head57" xml:space="preserve">DEMONSTRATIO SECVNDAE PARTIS.</head>
          <p>
            <s xml:id="echoid-s2176" xml:space="preserve">ITAQVE primum habeat portio ad humidum in
              <lb/>
            grauitate proportionem quidem maiorem, quàm qua dra
              <lb/>
            tum x o ad quadratum b d; </s>
            <s xml:id="echoid-s2177" xml:space="preserve">minorem uero, quàm quadra
              <lb/>
            tum, quod fit ab exceſſu, quo axis eſt maior, quàm ſeſquial-
              <lb/>
            ter eius, quæ uſque ad axem, ad quadratum b d: </s>
            <s xml:id="echoid-s2178" xml:space="preserve">& </s>
            <s xml:id="echoid-s2179" xml:space="preserve">quam
              <lb/>
            proportionem habet portio ad humidum in grauitate, eã
              <lb/>
            habeat quadratum, quod fit à linea ψ ad quadratum b d:
              <lb/>
            </s>
            <s xml:id="echoid-s2180" xml:space="preserve">erit ψ maior quidem, quàm x o, minor uero, quàm exceſ-
              <lb/>
              <note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">C</note>
            ſus, quo axis eſt maior, quàm ſeſquialter eius, quæ uſque ad
              <lb/>
            axem. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">aptetur quædam recta linea m n conicis ſectioni-
              <lb/>
            bus a m q l,
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              <figure xlink:label="fig-0085-01" xlink:href="fig-0085-01a" number="52">
                <image file="0085-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0085-01"/>
              </figure>
            a x d interiecta,
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            ac media, quæ li
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            neæ ψ ſit æqua-
              <lb/>
            lis; </s>
            <s xml:id="echoid-s2182" xml:space="preserve">ſecetq; </s>
            <s xml:id="echoid-s2183" xml:space="preserve">reli-
              <lb/>
            quã coni ſectio
              <lb/>
            nem in pun cto
              <lb/>
            h; </s>
            <s xml:id="echoid-s2184" xml:space="preserve">& </s>
            <s xml:id="echoid-s2185" xml:space="preserve">rectam li-
              <lb/>
            neam r g in u.
              <lb/>
            </s>
            <s xml:id="echoid-s2186" xml:space="preserve">demõſtrabitur
              <lb/>
              <note position="left" xlink:label="note-0085-02" xlink:href="note-0085-02a" xml:space="preserve">D</note>
            m h dupla ip-
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            ſius h n, ſicuti
              <lb/>
            demonſtratum
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            eſt o g ipſius g x
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            duplam eſſe. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">à
              <lb/>
            puncto autẽ m
              <lb/>
            ducatur m y contingens ſectionem a m q l in m: </s>
            <s xml:id="echoid-s2188" xml:space="preserve">& </s>
            <s xml:id="echoid-s2189" xml:space="preserve">m c a d
              <lb/>
            b d perpendicularis. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">poſtea ducta a n, & </s>
            <s xml:id="echoid-s2191" xml:space="preserve">producta ad q li
              <lb/>
            neæ a n, n q inter ſe æquales erunt. </s>
            <s xml:id="echoid-s2192" xml:space="preserve">quoniã enim in ſimi-
              <lb/>
              <note position="right" xlink:label="note-0085-03" xlink:href="note-0085-03a" xml:space="preserve">E</note>
            libus portionibus a m q l, a x d ductæ ſunt à baſibus ad
              <lb/>
            portiones lineæ a q, a n, quæ æquales angulos continent
              <lb/>
            cum ipſis baſibus, eandem proportionem habebit q a ad
              <lb/>
            an, quam la ad a d. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">æqualis eſt ergo a n ipſi n q; </s>
            <s xml:id="echoid-s2194" xml:space="preserve">& </s>
            <s xml:id="echoid-s2195" xml:space="preserve">a q
              <lb/>
              <note position="right" xlink:label="note-0085-04" xlink:href="note-0085-04a" xml:space="preserve">F</note>
            </s>
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