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

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        <div xml:id="echoid-div93" type="section" level="1" n="68">
          <head xml:id="echoid-head91" xml:space="preserve">HYDRODYNAMICÆ
            <lb/>
          SECTIO QUINTA.</head>
          <head xml:id="echoid-head92" style="it" xml:space="preserve">De motu aquarum ex vaſis conſtanter plenis.</head>
          <head xml:id="echoid-head93" xml:space="preserve">§. 1.</head>
          <p>
            <s xml:id="echoid-s2540" xml:space="preserve">VAſa plena ſervantur, cum continue totidem affunduntur aquæ,
              <lb/>
            quot effluunt; </s>
            <s xml:id="echoid-s2541" xml:space="preserve">affuſio autem eſſe poteſt vel in eadem cum mo-
              <lb/>
            tus ſuperficiei aqueæ directione eademque ſingulis momentis
              <lb/>
            velocitate, quaſi ſcilicet nova continue crearetur ſuperficies,
              <lb/>
            cui velocitas aquæ proximæ jam inſit, vel lateralis & </s>
            <s xml:id="echoid-s2542" xml:space="preserve">ſine im-
              <lb/>
            petu, veluti ſi ſuperficies, quæ continue nova creari fingitur, nullo motu
              <lb/>
            prædita ſit & </s>
            <s xml:id="echoid-s2543" xml:space="preserve">demum ab aqua inferiore ad motum cienda. </s>
            <s xml:id="echoid-s2544" xml:space="preserve">Reliquos affun-
              <lb/>
            dendi novas aquas, qui infiniti ſunt, modos præteribo.</s>
            <s xml:id="echoid-s2545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2546" xml:space="preserve">Regula interim circa hunc motum, præſertim poſteriorem, recepta eſt,
              <lb/>
            aquam effluere velocitate conveniente altitudini ſuperficiei ſupra lumen: </s>
            <s xml:id="echoid-s2547" xml:space="preserve">fa-
              <lb/>
            cile tamen eſt prævidere illam valere non poſſe, niſi pro vaſe ubique infini-
              <lb/>
            te amplo, in reliquis autem fore, ut motus à quiete incipiens ſenſim ſenſim-
              <lb/>
            que per aliqua temporis intervalla augeatur, & </s>
            <s xml:id="echoid-s2548" xml:space="preserve">poſt infinitum demum tem-
              <lb/>
            pus omnem velocitatem acquirat. </s>
            <s xml:id="echoid-s2549" xml:space="preserve">Attamen, ſi dicendum, quod res eſt,
              <lb/>
            fiunt iſtæ accelerationes plerunque tam celeriter, ut minimo tempusculo tan-
              <lb/>
            tum non tota velocitas adſit: </s>
            <s xml:id="echoid-s2550" xml:space="preserve">Verum res ſecus ſe habet in prælongis aquæ
              <lb/>
            ductibus, in quibus velocitatum augmenta oculos non effugiunt & </s>
            <s xml:id="echoid-s2551" xml:space="preserve">cum
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            diſtinctis menſuris obſervari poſſunt.</s>
            <s xml:id="echoid-s2552" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2553" xml:space="preserve">Quicquid autem ejus rei ſit, cum nullibi diſplicere poſſit accuratio
              <lb/>
            mathematica, conſtitui motum aquarum à principio ad quemvis datum ter-
              <lb/>
            minum conſiderare & </s>
            <s xml:id="echoid-s2554" xml:space="preserve">proſequi.</s>
            <s xml:id="echoid-s2555" xml:space="preserve"/>
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            <s xml:id="echoid-s2556" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2557" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2558" xml:space="preserve">Omnes hujus motus proprietates ad tres præcipue æquationes ſe
              <lb/>
            reduci patiuntur 1⁰. </s>
            <s xml:id="echoid-s2559" xml:space="preserve">inter quantitatem aquæ ejectæ reſpondentisque velocitatis;
              <lb/>
            </s>
            <s xml:id="echoid-s2560" xml:space="preserve">2⁰. </s>
            <s xml:id="echoid-s2561" xml:space="preserve">inter tempus & </s>
            <s xml:id="echoid-s2562" xml:space="preserve">velocitatem & </s>
            <s xml:id="echoid-s2563" xml:space="preserve">3⁰. </s>
            <s xml:id="echoid-s2564" xml:space="preserve">inter quantitatem aquæ & </s>
            <s xml:id="echoid-s2565" xml:space="preserve">tempus. </s>
            <s xml:id="echoid-s2566" xml:space="preserve">
              <lb/>
            Harum æquationum ſi una habeatur reliquæ inde ſua ſponte fluunt.</s>
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