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

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        <div xml:id="echoid-div40" type="section" level="1" n="27">
          <pb o="32" file="0046" n="46" rhead="HYDRODYNAMICÆ."/>
        </div>
        <div xml:id="echoid-div41" type="section" level="1" n="28">
          <head xml:id="echoid-head37" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s883" xml:space="preserve">Sit ſpatium A E G B = M, ſpatium A E Z U = N, qs = v, erit
              <lb/>
            aſcenſus potent. </s>
            <s xml:id="echoid-s884" xml:space="preserve">= {Nv/M}: </s>
            <s xml:id="echoid-s885" xml:space="preserve">quia vero quantitas aquæ in canali conſtanter eadem
              <lb/>
            ponitur, erit ſpatium A E G B invariabile, adeoque d M = o ita ut diffe-
              <lb/>
            rentiale aſcenſus potent. </s>
            <s xml:id="echoid-s886" xml:space="preserve">ſit ſimpliciter = {Ndv + vdN/M}, habetur autem d N
              <lb/>
            ex variatione ſitus aquæ. </s>
            <s xml:id="echoid-s887" xml:space="preserve">Patet igitur propoſitum. </s>
            <s xml:id="echoid-s888" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s889" xml:space="preserve">E. </s>
            <s xml:id="echoid-s890" xml:space="preserve">I.</s>
            <s xml:id="echoid-s891" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div42" type="section" level="1" n="29">
          <head xml:id="echoid-head38" xml:space="preserve">Scholion.</head>
          <p>
            <s xml:id="echoid-s892" xml:space="preserve">§. </s>
            <s xml:id="echoid-s893" xml:space="preserve">5. </s>
            <s xml:id="echoid-s894" xml:space="preserve">Poterunt hæ propoſitiones inſervire pro motu |fluidi intra vaſa
              <lb/>
            moti, id eſt, non effluentis definiendo, uti ſuo loco oſtendam: </s>
            <s xml:id="echoid-s895" xml:space="preserve">at ve-
              <lb/>
            ro cum fluidum per foramen effluit, aptius inſtituetur aliter calculus,
              <lb/>
            nempe ut ſequitur.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div43" type="section" level="1" n="30">
          <head xml:id="echoid-head39" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s897" xml:space="preserve">§. </s>
            <s xml:id="echoid-s898" xml:space="preserve">6. </s>
            <s xml:id="echoid-s899" xml:space="preserve">Invenire differentiam aſcenſus potentialis poſtquam guttula
              <lb/>
            per foramen effluxit.</s>
            <s xml:id="echoid-s900" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div44" type="section" level="1" n="31">
          <head xml:id="echoid-head40" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s901" xml:space="preserve">Fingamus aquam effluere ex vaſe aimb (Fig. </s>
            <s xml:id="echoid-s902" xml:space="preserve">15.) </s>
            <s xml:id="echoid-s903" xml:space="preserve">utcunque for-
              <lb/>
            mato, fundum ſit im perforatum foramine pl: </s>
            <s xml:id="echoid-s904" xml:space="preserve">quantitas aquæ, poſtquam
              <lb/>
              <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">Fig. 15.</note>
            jam data ejus quantitas effluxit, reſidua in vaſe ſit cimd; </s>
            <s xml:id="echoid-s905" xml:space="preserve">effluat autem
              <lb/>
            tempusculo infinitè parvo guttula pnol, ſuperficie cd deſcendente in ſitum
              <lb/>
            ef: </s>
            <s xml:id="echoid-s906" xml:space="preserve">concipiatur in medio aquæ ſectio gh parallela ſuperficiebus cd vel ef
              <lb/>
            ipſique fundo im; </s>
            <s xml:id="echoid-s907" xml:space="preserve">ſitque velocitas unius cujusvis particulæ in gh talis,
              <lb/>
            ut poſſit aſcendere ad altitudinem qs ſeu v, cum nondum effluxit guttula
              <lb/>
            & </s>
            <s xml:id="echoid-s908" xml:space="preserve">ad altitudinem qz ſive
              <gap/>
            + dv, poſtquam ea ipſa guttula effluxit.
              <lb/>
            </s>
            <s xml:id="echoid-s909" xml:space="preserve">Omnibus his ita poſitis, quæritur incrementum aſcenſus potentialis aquæ poſt-
              <lb/>
            quam ſitum cimd commutavit cum ſitu eipnolmf, id eſt, poſtquam gut-
              <lb/>
            tula emanavit.</s>
            <s xml:id="echoid-s910" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s911" xml:space="preserve">Fiat, ut antea, curva C G I (Fig. </s>
            <s xml:id="echoid-s912" xml:space="preserve">16.) </s>
            <s xml:id="echoid-s913" xml:space="preserve">ceu ſcala amplitudinum, ubi
              <lb/>
              <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">Fig. 16.</note>
            adeoque C D vel E F repræſentabunt magnitudinem ſuperficiei aqueæ </s>
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