Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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        <div xml:id="echoid-div96" type="section" level="1" n="71">
          <pb o="93" file="0107" n="107" rhead="SECTIO QUINTA."/>
          <p>
            <s xml:id="echoid-s2629" xml:space="preserve">Debet vero iſtud incrementum æquari deſcenſui actuali centri gravitatis;
              <lb/>
            </s>
            <s xml:id="echoid-s2630" xml:space="preserve">Atqui iſte deſcenſus, poſita D L = a, eſt per paragraphum ſeptimum ſect. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">
              <lb/>
            = {nadx/M}; </s>
            <s xml:id="echoid-s2633" xml:space="preserve">habetur igitur talis æquatio
              <lb/>
            {N/M}dv - {n
              <emph style="super">3</emph>
            /mmM}vdx + {n/M}vdx = {nadx/M}, ſeu
              <lb/>
            dx = Ndv: </s>
            <s xml:id="echoid-s2634" xml:space="preserve">(na - nv + {n
              <emph style="super">3</emph>
            /mm} v);</s>
            <s xml:id="echoid-s2635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2636" xml:space="preserve">Hæc vero ſi ita integretur, ut v & </s>
            <s xml:id="echoid-s2637" xml:space="preserve">x ſimul evaneſcant, dat
              <lb/>
            x = {mmN/n
              <emph style="super">3</emph>
            - nmm} log. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">{mma - mmv + nnv/mma}
              <lb/>
            quæ æquatio, poſito c pro numero cujus logarithmus eſt unitas, æquivalet
              <lb/>
            huic @alteri
              <lb/>
            v = {mma/mm - nn} X (1 - c{n
              <emph style="super">3</emph>
            - nmm/mmN} x)</s>
          </p>
          <p>
            <s xml:id="echoid-s2639" xml:space="preserve">Hæc vero ſolutio quadrat pro caſu primo, ubi aqua ſuperne motu af-
              <lb/>
            ſunditur communi cum deſcenſu ſuperficiei proximæ.</s>
            <s xml:id="echoid-s2640" xml:space="preserve"/>
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        <div xml:id="echoid-div97" type="section" level="1" n="72">
          <head xml:id="echoid-head97" xml:space="preserve">Caſus II.</head>
          <p>
            <s xml:id="echoid-s2641" xml:space="preserve">Quod ſi jam particula c d f e lateraliter continue affundi ponatur, tunc
              <lb/>
            propter inertiam ſuam motui aquæ inferioris reſiſtit atque proinde aſcenſus
              <lb/>
            potentialis ipſius aliter in computum venit. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Tunc autem prius conſideran-
              <lb/>
            dus eſt aſcenſus potentialis maſſæ aqueæ c d m l p i c auctæ guttula mox affunden-
              <lb/>
            da; </s>
            <s xml:id="echoid-s2643" xml:space="preserve">deinde indagandus aſcenſus potent. </s>
            <s xml:id="echoid-s2644" xml:space="preserve">ejusdem aquæ in ſitu c d m l o n p i c,
              <lb/>
            poſtquam nempe guttula jam effluxit, eorumque differentia eſt æquanda cum
              <lb/>
            deſcenſu actuali. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">{nadx/M}. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">Verum aſcenſus potentialis omnis prædictæ aquæ ante
              <lb/>
            affuſionem particulæ ejusdemque poſt affuſionem ita invenitur: </s>
            <s xml:id="echoid-s2647" xml:space="preserve">nempe aſcen-
              <lb/>
            ſus potentialis aquæ c d m l p i c eſt = {Nv/M}, & </s>
            <s xml:id="echoid-s2648" xml:space="preserve">aſcenſus potent. </s>
            <s xml:id="echoid-s2649" xml:space="preserve">particulæ affundi
              <lb/>
            paratæ nullus eſt, quia lateraliter affuſa motum communem nondum habet
              <lb/>
            cum maſſa inferiore; </s>
            <s xml:id="echoid-s2650" xml:space="preserve">Igitur aſcenſus potentialis utriusque aquæ (qui ſcilicet
              <lb/>
            habetur multiplicando maſſam reſpective per ſuum aſcenſum potentialem, di-
              <lb/>
            videndoque productorum aggregatum per aggregatum maſſarum) eſt </s>
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