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

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        <div xml:id="echoid-div189" type="section" level="1" n="147">
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              <pb o="168" file="0182" n="182" rhead="HYDRODYNAMICÆ"/>
            pe omnis motus qui aquis reſiduus eſt poſtquam altitudinem G attigerunt in
              <lb/>
            noſtro caſu ſuperfluus eſt dicendus.</s>
            <s xml:id="echoid-s4873" xml:space="preserve"/>
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        <div xml:id="echoid-div190" type="section" level="1" n="148">
          <head xml:id="echoid-head195" xml:space="preserve">Regula 4.</head>
          <p>
            <s xml:id="echoid-s4874" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4875" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4876" xml:space="preserve">Cum aquæ expelluntur per canalem D F (Fig. </s>
            <s xml:id="echoid-s4877" xml:space="preserve">48.) </s>
            <s xml:id="echoid-s4878" xml:space="preserve">habentque
              <lb/>
              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">Fig. 48.</note>
            in orificio F velocitatem quæ debeatur altitudini verticali G F, eſt potentia abſo-
              <lb/>
            luta eodem tempore impenſa proportionalis velocitati aquæ in F ductæ in alti-
              <lb/>
            tudinem G ſupra A B.</s>
            <s xml:id="echoid-s4879" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div192" type="section" level="1" n="149">
          <head xml:id="echoid-head196" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s4880" xml:space="preserve">Eſt enim potentia movens P proportionalis præfatæ altitudini & </s>
            <s xml:id="echoid-s4881" xml:space="preserve">velo-
              <lb/>
            citas iſtius potentiæ eſt ut velocitas aquæ in F.</s>
            <s xml:id="echoid-s4882" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div193" type="section" level="1" n="150">
          <head xml:id="echoid-head197" xml:space="preserve">Scholium.</head>
          <p>
            <s xml:id="echoid-s4883" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4884" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4885" xml:space="preserve">Pòtentiæ abſolutæ majori ratione creſcunt quam velocitates
              <lb/>
            aquarum effluentium, id eſt, quam quantitates eodem tempore ejectæ: </s>
            <s xml:id="echoid-s4886" xml:space="preserve">atta-
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            men differentia rationum fere inſenſibilis eſt, cum altitudo F G parva admo-
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            dum eſt ratione altitudinis canalis F D: </s>
            <s xml:id="echoid-s4887" xml:space="preserve">Sit ex. </s>
            <s xml:id="echoid-s4888" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4889" xml:space="preserve">F G æqualis {1/4} F D (negli-
              <lb/>
            gendo altitudinem B D) mox vero ejiciantur aquæ velocitate dupla, ita, ut
              <lb/>
            nunc ſit F D = F G; </s>
            <s xml:id="echoid-s4890" xml:space="preserve">ſic erunt potentiæ abſolutæ ut 1 X {@/4} ad 2 X 2 ſeu ut 5 ad 16
              <lb/>
            ſic ut ad ejiciendam duplam aquæ quantitatem potentia abſoluta requiratur pluſ-
              <lb/>
            quam tripla: </s>
            <s xml:id="echoid-s4891" xml:space="preserve">Si vero F G ſtatuatur prius = {1/100} F D, & </s>
            <s xml:id="echoid-s4892" xml:space="preserve">deinde aquæ rurſus
              <lb/>
            dupla velocitate exprimi ponantur, erunt nunc potentiæ abſolutæ ut 1 X 101
              <lb/>
            ad 2 X 204 ſeu ut 101 ad 208, quæ ratio à ſubdupla parum deficit. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">Sequitur
              <lb/>
            inde, quo minori velocitate aquæ hauriantur, eo majori cum fructu potentiam
              <lb/>
            abſolutam impendi, & </s>
            <s xml:id="echoid-s4894" xml:space="preserve">tunc demum eam propemodum omnem utiliter impen-
              <lb/>
            di, cum fere inſenſibili velocitate aquæ per orificium F effluunt: </s>
            <s xml:id="echoid-s4895" xml:space="preserve">poterit au-
              <lb/>
            tem magnitudo orificii compenſare velocitatis exiguitatem, ut dato tempore
              <lb/>
            notabilis aquarum quantitas hauriri poſſit. </s>
            <s xml:id="echoid-s4896" xml:space="preserve">Diſpendium potentiæ abſolutæ ſic de-
              <lb/>
            finietur.</s>
            <s xml:id="echoid-s4897" xml:space="preserve"/>
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        <div xml:id="echoid-div194" type="section" level="1" n="151">
          <head xml:id="echoid-head198" xml:space="preserve">Regula 5.</head>
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            <s xml:id="echoid-s4898" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4900" xml:space="preserve">Conſtitutum fuerit ope antliæ A B D F, valvula in fundo in-
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            ſtructæ & </s>
            <s xml:id="echoid-s4901" xml:space="preserve">aquæ impoſitæ, aquas ex loco humiliori A D in altiorem F trans-
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            fundere, fueritque velocitas media aquæ in F effluentis debita altitudini F </s>
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