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

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        <div xml:id="echoid-div307" type="section" level="1" n="231">
          <pb o="298" file="0312" n="312" rhead="HYDRODYNAMICÆ"/>
          <p>
            <s xml:id="echoid-s8873" xml:space="preserve">B = 2 MC X (A - √AB).</s>
            <s xml:id="echoid-s8874" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8875" xml:space="preserve">Exinde fit preſſio navem urgens = {B/C}, atque adeo’ proportionalis
              <lb/>
            altitudini B, quia C eſt quantitas conſtans: </s>
            <s xml:id="echoid-s8876" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s8877" xml:space="preserve">preſſio navem promo-
              <lb/>
            vens & </s>
            <s xml:id="echoid-s8878" xml:space="preserve">altitudo navis velocitati reſpondens ſimul fiunt maximæ: </s>
            <s xml:id="echoid-s8879" xml:space="preserve">Igitur ſi pro
              <lb/>
            præſenti inſtituto differentietur quantitas 2MA - 2M√AB, quæ preſſionem
              <lb/>
            navem propellentem exprimit, poterit poni d B = o. </s>
            <s xml:id="echoid-s8880" xml:space="preserve">Prius vero quam dif-
              <lb/>
            ferentiatio inſtituatur oportet pro M ſubſtituere valorem ejus §. </s>
            <s xml:id="echoid-s8881" xml:space="preserve">25. </s>
            <s xml:id="echoid-s8882" xml:space="preserve">& </s>
            <s xml:id="echoid-s8883" xml:space="preserve">tunc
              <lb/>
            fit preſſio navem promovens = {N/4√A} - {N√B/4A}, in qua littera N eſt con-
              <lb/>
            ſtans, litteræ vero B & </s>
            <s xml:id="echoid-s8884" xml:space="preserve">A variabiles. </s>
            <s xml:id="echoid-s8885" xml:space="preserve">Sumatur nunc ejus differentiale, facien-
              <lb/>
            do d B = o, idque fiat = o; </s>
            <s xml:id="echoid-s8886" xml:space="preserve">atque ſic reperietur A = 4B.</s>
            <s xml:id="echoid-s8887" xml:space="preserve"/>
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            <s xml:id="echoid-s8888" xml:space="preserve">Eſt igitur vis navem promovens maxima cum altitudo, ad quam aquæ
              <lb/>
            elevantur, eſt quadrupla altitudinis velocitati navis debitæ.</s>
            <s xml:id="echoid-s8889" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s8890" xml:space="preserve">Ponatur in æquatione B = 2 M C X (A - √AB) ſuperius inventa
              <lb/>
            A = 4B & </s>
            <s xml:id="echoid-s8891" xml:space="preserve">reperietur
              <lb/>
            M = {1/4C},
              <lb/>
            & </s>
            <s xml:id="echoid-s8892" xml:space="preserve">quia (per §. </s>
            <s xml:id="echoid-s8893" xml:space="preserve">25.) </s>
            <s xml:id="echoid-s8894" xml:space="preserve">eſt M = {N/8A√A}, fit tunc
              <lb/>
            A = ({1/2} NC)
              <emph style="super">{2/3}</emph>
            , atque
              <lb/>
            B = {1/4}({1/2} NC)
              <emph style="super">{2/3}</emph>
            .</s>
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        <div xml:id="echoid-div308" type="section" level="1" n="232">
          <head xml:id="echoid-head294" xml:space="preserve">Corollarium.</head>
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            <s xml:id="echoid-s8896" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8897" xml:space="preserve">28. </s>
            <s xml:id="echoid-s8898" xml:space="preserve">Si ad præceptum præcedentis paragraphi orificio, per quod
              <lb/>
            aquæ inferius ex canali verſus puppim effluunt, concilietur amplitudo {1/4C},
              <lb/>
            id eſt, talis, quæ ſe habeat ad amplitudinem unius pedis quadrati, ſicuti men-
              <lb/>
            ſura unius pedis, ad altitudinem quadruplam velocitati navis, vi 72. </s>
            <s xml:id="echoid-s8899" xml:space="preserve">libra-
              <lb/>
            rum animatæ, debitam, fiet tunc ut navis dimidia velocitate feratur ejus qua
              <lb/>
            aquæ effluunt & </s>
            <s xml:id="echoid-s8900" xml:space="preserve">erit vis repellens aquarum effluentium
              <lb/>
            2MA = {1/2C} X ({1/2} NC)
              <emph style="super">{2/3}</emph>
            </s>
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