Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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        <div type="section" level="1" n="40">
          <p>
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              <pb o="30" file="0071" n="71" rhead="DE IIS QVAE VEH. IN AQVA."/>
            eadem ratione oſtẽdetur p y ipſius y f dupla. </s>
            <s xml:space="preserve">Itaque quo
              <lb/>
            niam d s ſeſquialtera eſt ipſius _k_ r; </s>
            <s xml:space="preserve">erit b s exceſſus, quo
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            axis eſt maior, quàm ſeſquialter eius, quæ uſque ad axem.
              <lb/>
            </s>
            <s xml:space="preserve">Si igitur portio ad humidũ in grauitate eã habet propor-
              <lb/>
            tionem, quam quadratum, quod fit à linea b ſ ad quadra-
              <lb/>
            tum, quod à b d, aut maiorem; </s>
            <s xml:space="preserve">in hnmidum demiſſa, ita
              <lb/>
            ut baſis ipſius non contingat humidum, recta conſiſtet. </s>
            <s xml:space="preserve">de
              <lb/>
            monſtratum eſt enim ſuperius, portionem, cuius axis eſt
              <lb/>
              <anchor type="note" xlink:label="note-0071-01a" xlink:href="note-0071-01"/>
            maior, quàm ſeſquiaiter eius, quæ uſque ad axem, ſi ad hu-
              <lb/>
            midum in grauitate non minorem proportionem habeat,
              <lb/>
            quàm quadratum, quod fit ab exceſſu, quo axis maior eſt,
              <lb/>
            quam ſeſquialter eius, quæ uſque ad axem, ad quadratum,
              <lb/>
            quod ab axe; </s>
            <s xml:space="preserve">demiſſam in humidum, ita ut dictum eſt, re-
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            ctam conſiſtere.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">F</note>
            <note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">G</note>
            <note position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">H</note>
            <figure xlink:label="fig-0069-01" xlink:href="fig-0069-01a">
              <image file="0069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0069-01"/>
            </figure>
            <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">K</note>
            <note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">L</note>
            <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">M</note>
            <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a">
              <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0070-01"/>
            </figure>
            <note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">N</note>
            <note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve">O</note>
            <note position="left" xlink:label="note-0070-06" xlink:href="note-0070-06a" xml:space="preserve">P</note>
            <note position="left" xlink:label="note-0070-07" xlink:href="note-0070-07a" xml:space="preserve">Q</note>
            <note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">R</note>
          </div>
        </div>
        <div type="section" level="1" n="41">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">_
              <emph style="sc">Qvae</emph>
            _ hac decima propoſitione continentur, Archimedes in
              <lb/>
            quinque partes diſſecuit, & </s>
            <s xml:space="preserve">ſingulas ſeorſum demonſtrauit.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Nonnunquam quidem recta conſiſtat.</s>
            <s xml:space="preserve">] _Hæc eſt prima_
              <lb/>
              <anchor type="note" xlink:label="note-0071-02a" xlink:href="note-0071-02"/>
            _pars, cuius demonstr ationem ſtatim ſubiungit._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">A</note>
          </div>
          <p>
            <s xml:space="preserve">Etinterdum adeo inclinata, ut baſis ipſius in uno pun-
              <lb/>
              <anchor type="note" xlink:label="note-0071-03a" xlink:href="note-0071-03"/>
            cto contingat ſuperficiem humidi; </s>
            <s xml:space="preserve">idq; </s>
            <s xml:space="preserve">in duabus diſpoſi-
              <lb/>
            tionibus.</s>
            <s xml:space="preserve">] _Demonſtratum eſt illud in tertia parte._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">B</note>
          </div>
          <p>
            <s xml:space="preserve">Interdum ita, ut baſis in humidum magis demergatur.</s>
            <s xml:space="preserve">]
              <lb/>
              <anchor type="note" xlink:label="note-0071-04a" xlink:href="note-0071-04"/>
            _Pertinet id ad quartam partem._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0071-04" xlink:href="note-0071-04a" xml:space="preserve">C</note>
          </div>
          <p>
            <s xml:space="preserve">Interdum uero ita, ut ſuperficiem humidi nullo modo
              <lb/>
              <anchor type="note" xlink:label="note-0071-05a" xlink:href="note-0071-05"/>
            contingat.</s>
            <s xml:space="preserve">] _Hoc duobus item modis fit, quorum unus in ſecunda,_
              <lb/>
            _alter in quarta parte explicatur._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="right" xlink:label="note-0071-05" xlink:href="note-0071-05a" xml:space="preserve">D</note>
          </div>
          <p>
            <s xml:space="preserve">Secundum proportionem, quam habet ad humidum in
              <lb/>
              <anchor type="note" xlink:label="note-0071-06a" xlink:href="note-0071-06"/>
            grauitate.</s>
            <s xml:space="preserve">] _In translatione ita legebatur, quam autem proportio_
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            _nem habet ad humidum in grauitate._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="5">
            <note position="right" xlink:label="note-0071-06" xlink:href="note-0071-06a" xml:space="preserve">E</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Conſtat igitur k c maiorem eſſe, quàm quæ uſque ad_
              <lb/>
              <anchor type="note" xlink:label="note-0071-07a" xlink:href="note-0071-07"/>
            _axem.</s>
            <s xml:space="preserve">]_ Nam cum b d ad k c eandem habeat proportionem, quam</s>
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