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

Table of Notes

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          <pb o="265" file="0279" n="279" rhead="SECTIO DUODECIMA."/>
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        <div xml:id="echoid-div272" type="section" level="1" n="206">
          <head xml:id="echoid-head263" xml:space="preserve">Exemplum 1.</head>
          <p>
            <s xml:id="echoid-s7762" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7763" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7764" xml:space="preserve">Sit vas A B F G (Fig. </s>
            <s xml:id="echoid-s7765" xml:space="preserve">75.) </s>
            <s xml:id="echoid-s7766" xml:space="preserve">ex cujus fundi medio deſcendit tubus
              <lb/>
              <note position="right" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">Fig. 75.</note>
            D E formam habens coni truncati inferiora verſus divergentis: </s>
            <s xml:id="echoid-s7767" xml:space="preserve">Affundantur
              <lb/>
            perpetuo aquæ in A G, ita ut ſic vas plenum conſervetur.</s>
            <s xml:id="echoid-s7768" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7769" xml:space="preserve">Sit autem altitudo ſuperficiei aqueæ ſupra orificium E = a, & </s>
            <s xml:id="echoid-s7770" xml:space="preserve">ſupra D
              <lb/>
            (qui locus eſt pro quo preſſio aquæ quæritur) = c: </s>
            <s xml:id="echoid-s7771" xml:space="preserve">amplitudo orificii in E = m;
              <lb/>
            </s>
            <s xml:id="echoid-s7772" xml:space="preserve">& </s>
            <s xml:id="echoid-s7773" xml:space="preserve">amplitudo ſeu ſectio horizontalis in D = n. </s>
            <s xml:id="echoid-s7774" xml:space="preserve">Erit preſſio aquæ in D =
              <lb/>
            c - {mm/nn} a, quæ quantitas vi hypotheſium eſt negativa, ſic ut latera canalis
              <lb/>
            introrſum premantur à columna aquea altitudinis {mm/nn} a - c.</s>
            <s xml:id="echoid-s7775" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7776" xml:space="preserve">Igitur ſi concipiatur tubus incurvus D L N alteri D E inſertus, erit aqua
              <lb/>
            præterfluens in D in æquilibrio cum aqua D L N, quando altitudo D ſupra N
              <lb/>
            eſt = {mm/nn} a - c. </s>
            <s xml:id="echoid-s7777" xml:space="preserve">Si altitudo hæc minor eſt, ſua ſponte aqua aſcendet nec aſ-
              <lb/>
            cendere deſinet, quamdiu aquis orificium N ſubmerſum eſt, ita ut ſic aquæ
              <lb/>
            ex loco humiliori in ſublimiorem ſine ulla vi externa elevari poſſint, ſi in A G
              <lb/>
            aquæ ſufficiente copia affluant. </s>
            <s xml:id="echoid-s7778" xml:space="preserve">At vero cum altitudo verticalis D ſupra N ma-
              <lb/>
            jor eſt quam {mm/nn} a - c, aſcendet aqua in crure L N, donec illi fuerit æqualis.</s>
            <s xml:id="echoid-s7779" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7780" xml:space="preserve">Cæterum hic in memoriam revoc
              <unsure/>
            andum eſt, quod paſſim monui ex-
              <lb/>
            perientiam docere, nempe multum abeſſe quominus aquæ per tubos à vaſe,
              <lb/>
            cui implantati ſunt, divergentes tota ſua velocitate, quam vi theoriæ obtinere
              <lb/>
            deberent, effluant; </s>
            <s xml:id="echoid-s7781" xml:space="preserve">cujus rei rationes indicavi paragrapho 26. </s>
            <s xml:id="echoid-s7782" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s7783" xml:space="preserve">3.</s>
            <s xml:id="echoid-s7784" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7785" xml:space="preserve">Fit inde ut altitudo D ſupra N admodum minor ſit, quam vi theoriæ
              <lb/>
            expoſita eſſe deberet: </s>
            <s xml:id="echoid-s7786" xml:space="preserve">Error corrigetur ſi loco {mm/nn} a ponatur altitudo velo-
              <lb/>
            citatis, quam aqua in D habet; </s>
            <s xml:id="echoid-s7787" xml:space="preserve">quæ altitudo per experimentum de quantitate
              <lb/>
            aquæ dato tempore effluentis ſumtum obtinetur.</s>
            <s xml:id="echoid-s7788" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div274" type="section" level="1" n="207">
          <head xml:id="echoid-head264" xml:space="preserve">Exemplum 2.</head>
          <p>
            <s xml:id="echoid-s7789" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7790" xml:space="preserve">13. </s>
            <s xml:id="echoid-s7791" xml:space="preserve">Si ſimili vaſi appenſus ſit tubus verticalis, qualis repræſentatur
              <lb/>
            in Fig. </s>
            <s xml:id="echoid-s7792" xml:space="preserve">76. </s>
            <s xml:id="echoid-s7793" xml:space="preserve">per C E, in quo amplitudines ubique rationem habeant inverſam
              <lb/>
              <note position="right" xlink:label="note-0279-02" xlink:href="note-0279-02a" xml:space="preserve">Fig. 76.</note>
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