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

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        <div xml:id="echoid-div48" type="section" level="1" n="33">
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              <pb o="34" file="0048" n="48" rhead="HYDRODYNAMICÆ."/>
            ticulæ aqueæ cdfe ſupra guttulam lonp = x, altitudo centri gravitatis aquæ
              <lb/>
            efmi a fundo = b, erit altitudo centri gravitatis omnis aquæ in ſitu cdmi
              <lb/>
            ſupra fundum = b - {ydx/M} X (x - b) & </s>
            <s xml:id="echoid-s940" xml:space="preserve">in ſitu efmlonpi erit eadem
              <lb/>
            altitudo = ({M + ydx/M}) X b; </s>
            <s xml:id="echoid-s941" xml:space="preserve">unde differentia altitudinum ſeu deſcenſus actualis
              <lb/>
            quæſitus = - {ydx/M} X x, quæ æquatio indicat, guttulam quæ effluxerit
              <lb/>
            multiplicandam eſſe per altitudinem aquæ ſupra foramen, productumque
              <lb/>
            dividendum per quantitatem aquæ, ut habeatur deſcenſus actualis, qui fit
              <lb/>
            dum guttula effluit, Q. </s>
            <s xml:id="echoid-s942" xml:space="preserve">E. </s>
            <s xml:id="echoid-s943" xml:space="preserve">I.</s>
            <s xml:id="echoid-s944" xml:space="preserve"/>
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        <div xml:id="echoid-div49" type="section" level="1" n="34">
          <head xml:id="echoid-head43" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s945" xml:space="preserve">§. </s>
            <s xml:id="echoid-s946" xml:space="preserve">8. </s>
            <s xml:id="echoid-s947" xml:space="preserve">Determinare motum fluidi homogenei ex vaſe dato per fo-
              <lb/>
            ramen datum effluentis.</s>
            <s xml:id="echoid-s948" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div50" type="section" level="1" n="35">
          <head xml:id="echoid-head44" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s949" xml:space="preserve">Quoniam per hypotheſin noſtram aſcenſus potentialis ſingulis mo-
              <lb/>
            mentis æqualis eſt Deſcenſui actuali, erit incrementum prioris dum guttula
              <lb/>
            effluit æquale incremento poſterioris, quod ſimili tempuſculo oritur. </s>
            <s xml:id="echoid-s950" xml:space="preserve">Igi-
              <lb/>
            tur ſi rurfus ſuperficies aquæ, poſtquam data ejus quantitas effluxit, pona-
              <lb/>
            tur = y, amplitudo vaſis quocunque in loco ad libitum aſſumta = m, am-
              <lb/>
            plitudo foraminis = n, altitudo aquæ ſupra foramen = x; </s>
            <s xml:id="echoid-s951" xml:space="preserve">ſi præterea
              <lb/>
            quantitas N ea lege conſtruatur, quæ §. </s>
            <s xml:id="echoid-s952" xml:space="preserve">6. </s>
            <s xml:id="echoid-s953" xml:space="preserve">indicata fuit, atque per v in-
              <lb/>
            telligatur altitudo debita velocitati aquæ in loco aſſumto, ubi nempe am-
              <lb/>
            plitudo vaſis eſt = m, erit per §. </s>
            <s xml:id="echoid-s954" xml:space="preserve">6. </s>
            <s xml:id="echoid-s955" xml:space="preserve">incrementum aſcenſus potentialis =
              <lb/>
            (Ndv - {mmvydx/nn} + {mmvdx/y}): </s>
            <s xml:id="echoid-s956" xml:space="preserve">M, minimusque deſcenſus actualis = {- yxdx/M}
              <lb/>
            (per præced.</s>
            <s xml:id="echoid-s957" xml:space="preserve">§.)</s>
            <s xml:id="echoid-s958" xml:space="preserve">; </s>
            <s xml:id="echoid-s959" xml:space="preserve">unde habetur (Ndv - {mmvydx/nn} + {mmvdx/y}): </s>
            <s xml:id="echoid-s960" xml:space="preserve">M =
              <lb/>
            - yxdx: </s>
            <s xml:id="echoid-s961" xml:space="preserve">MſeuNdv - {mmvydx/nn} + {mmvdx/y} = - yxdx, quæ æquatio ge-
              <lb/>
            neraliter integrari poteſt, quandoquidem litteræ N & </s>
            <s xml:id="echoid-s962" xml:space="preserve">y ſunt functiones datæ
              <lb/>
            ipſius x & </s>
            <s xml:id="echoid-s963" xml:space="preserve">litera v unius tantum dimenſionis eſt.</s>
            <s xml:id="echoid-s964" xml:space="preserve"/>
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        <div xml:id="echoid-div51" type="section" level="1" n="36">
          <head xml:id="echoid-head45" xml:space="preserve">Corollarium 1.</head>
          <p>
            <s xml:id="echoid-s965" xml:space="preserve">§. </s>
            <s xml:id="echoid-s966" xml:space="preserve">9. </s>
            <s xml:id="echoid-s967" xml:space="preserve">Quum velocitates ſint in ratione reciproca </s>
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