Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s1732" xml:space="preserve">
              <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:id="echoid-s1733" xml:space="preserve">Itaque quo
              <lb/>
            niam d s ſeſquialtera eſt ipſius _k_ r; </s>
            <s xml:id="echoid-s1734" xml:space="preserve">erit b s exceſſus, quo
              <lb/>
            axis eſt maior, quàm ſeſquialter eius, quæ uſque ad axem.
              <lb/>
            </s>
            <s xml:id="echoid-s1735" 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:id="echoid-s1736" xml:space="preserve">in hnmidum demiſſa, ita
              <lb/>
            ut baſis ipſius non contingat humidum, recta conſiſtet. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">de
              <lb/>
            monſtratum eſt enim ſuperius, portionem, cuius axis eſt
              <lb/>
              <note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">R</note>
            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:id="echoid-s1738" xml:space="preserve">demiſſam in humidum, ita ut dictum eſt, re-
              <lb/>
            ctam conſiſtere.</s>
            <s xml:id="echoid-s1739" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div123" type="section" level="1" n="41">
          <head xml:id="echoid-head46" xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:id="echoid-s1740" xml:space="preserve">_
              <emph style="sc">Qvae</emph>
            _ hac decima propoſitione continentur, Archimedes in
              <lb/>
            quinque partes diſſecuit, & </s>
            <s xml:id="echoid-s1741" xml:space="preserve">ſingulas ſeorſum demonſtrauit.</s>
            <s xml:id="echoid-s1742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1743" xml:space="preserve">Nonnunquam quidem recta conſiſtat.</s>
            <s xml:id="echoid-s1744" xml:space="preserve">] _Hæc eſt prima_
              <lb/>
              <note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">A</note>
            _pars, cuius demonstr ationem ſtatim ſubiungit._</s>
            <s xml:id="echoid-s1745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1746" xml:space="preserve">Etinterdum adeo inclinata, ut baſis ipſius in uno pun-
              <lb/>
              <note position="right" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">B</note>
            cto contingat ſuperficiem humidi; </s>
            <s xml:id="echoid-s1747" xml:space="preserve">idq; </s>
            <s xml:id="echoid-s1748" xml:space="preserve">in duabus diſpoſi-
              <lb/>
            tionibus.</s>
            <s xml:id="echoid-s1749" xml:space="preserve">] _Demonſtratum eſt illud in tertia parte._</s>
            <s xml:id="echoid-s1750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1751" xml:space="preserve">Interdum ita, ut baſis in humidum magis demergatur.</s>
            <s xml:id="echoid-s1752" xml:space="preserve">]
              <lb/>
              <note position="right" xlink:label="note-0071-04" xlink:href="note-0071-04a" xml:space="preserve">C</note>
            _Pertinet id ad quartam partem._</s>
            <s xml:id="echoid-s1753" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1754" xml:space="preserve">Interdum uero ita, ut ſuperficiem humidi nullo modo
              <lb/>
              <note position="right" xlink:label="note-0071-05" xlink:href="note-0071-05a" xml:space="preserve">D</note>
            contingat.</s>
            <s xml:id="echoid-s1755" xml:space="preserve">] _Hoc duobus item modis fit, quorum unus in ſecunda,_
              <lb/>
            _alter in quarta parte explicatur._</s>
            <s xml:id="echoid-s1756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1757" xml:space="preserve">Secundum proportionem, quam habet ad humidum in
              <lb/>
              <note position="right" xlink:label="note-0071-06" xlink:href="note-0071-06a" xml:space="preserve">E</note>
            grauitate.</s>
            <s xml:id="echoid-s1758" xml:space="preserve">] _In translatione ita legebatur, quam autem proportio_
              <lb/>
            _nem habet ad humidum in grauitate._</s>
            <s xml:id="echoid-s1759" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1760" xml:space="preserve">_Conſtat igitur k c maiorem eſſe, quàm quæ uſque ad_
              <lb/>
              <note position="right" xlink:label="note-0071-07" xlink:href="note-0071-07a" xml:space="preserve">F</note>
            _axem.</s>
            <s xml:id="echoid-s1761" xml:space="preserve">]_ Nam cum b d ad k c eandem habeat proportionem, quam</s>
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