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

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              <pb o="94" file="0108" n="108" rhead="HYDRODYNAMICÆ"/>
            (M X {Nv/M} + ndx X o): </s>
            <s xml:id="echoid-s2651" xml:space="preserve">(M + ndx) = {Nv/M + ndx}. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">Poſtquam vero particula
              <lb/>
            n d x ſuperne jam affuſa eſt, communem acquiſivit motum cum aqua proxi-
              <lb/>
            me inferiori, ſicque fit aſcenſus potentialis ejusdem aquæ in ſitu c d m l o n p i c
              <lb/>
            æqualis tertiæ proportionali ad ſpatium C D L O N P I C (M + ndx), ſpa-
              <lb/>
            tium D t u x y O L D (N + ndx) & </s>
            <s xml:id="echoid-s2653" xml:space="preserve">altitudinem v + dv, id eſt, =
              <lb/>
            {(N + ndx) x (v + dv)/M + ndx}, cujus exceſſus ſupra priorem aſcenſum potentialem eſt =
              <lb/>
            {Ndv + nvdx + ndxdv/M + dx} =, rejectis differentialibus ſecundi ordinis, {Ndv + nvdx/M}.
              <lb/>
            </s>
            <s xml:id="echoid-s2654" xml:space="preserve">Habetur igitur talis æquatio {Ndv + nvdx/M} = {nadx/M}, quæ ut prior per tra-
              <lb/>
            ctata & </s>
            <s xml:id="echoid-s2655" xml:space="preserve">ad finem deducta dat
              <lb/>
            x = {N/n} log. </s>
            <s xml:id="echoid-s2656" xml:space="preserve">{a/a - v}, vel
              <lb/>
            v = a X (1 - c {-nx/N})
              <lb/>
            quæ ſolutio valet pro affuſione laterali.</s>
            <s xml:id="echoid-s2657" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div98" type="section" level="1" n="73">
          <head xml:id="echoid-head98" xml:space="preserve">Scholion 1.</head>
          <p>
            <s xml:id="echoid-s2658" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2659" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2660" xml:space="preserve">Sunt hæ æquationes inter ſe admodum diverſæ; </s>
            <s xml:id="echoid-s2661" xml:space="preserve">diverſitas au-
              <lb/>
            tem eo major quo minoris eſt amplitudinis vas; </s>
            <s xml:id="echoid-s2662" xml:space="preserve">& </s>
            <s xml:id="echoid-s2663" xml:space="preserve">ſi quidem amplitudo va-
              <lb/>
            ſis ſuprema in cd quaſi infinita ſit præ amplitudine foraminis, evaneſcit n
              <lb/>
            præ m fitque in priori caſu ſicut in poſteriori.
              <lb/>
            </s>
            <s xml:id="echoid-s2664" xml:space="preserve">v = a X (1 - c
              <emph style="super">{-n/N}x</emph>
            )
              <lb/>
            Eſt igitur hâc in hypotheſi motus utrobique idem quod haud difficulter
              <lb/>
            quisque prævidere potuerit. </s>
            <s xml:id="echoid-s2665" xml:space="preserve">Celerior autem ſemper eſt cæteris paribus mo-
              <lb/>
            tus in priori affuſione, quam in altera.</s>
            <s xml:id="echoid-s2666" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2667" xml:space="preserve">Conveniet hic rem etiam phyſice explicare, ut eam diſtinctius in omni-
              <lb/>
            bus phænomenis percipere poſſimus.</s>
            <s xml:id="echoid-s2668" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2669" xml:space="preserve">Sit loco vaſis cujuſcunque & </s>
            <s xml:id="echoid-s2670" xml:space="preserve">quamcunque directionem habentis bre-
              <lb/>
            vioris delineationis gratia cylindrus verticalis cum foramine in fundo, nempe
              <lb/>
            G H N D (Fig. </s>
            <s xml:id="echoid-s2671" xml:space="preserve">29.) </s>
            <s xml:id="echoid-s2672" xml:space="preserve">ſitque dein vas E F P Q perforatum in R S; </s>
            <s xml:id="echoid-s2673" xml:space="preserve">fingantur orifi-
              <lb/>
              <note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">Fig. 29,</note>
            cia RS & </s>
            <s xml:id="echoid-s2674" xml:space="preserve">GD perfecte æqualia, & </s>
            <s xml:id="echoid-s2675" xml:space="preserve">ad minimam diſtantiam ſibi perfecte </s>
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