Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii
page |< < (35) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div51" type="section" level="1" n="36">
          <p>
            <s xml:id="echoid-s967" xml:space="preserve">
              <pb o="35" file="0049" n="49" rhead="SECTIO TERTIA."/>
            patet fore altitudinem, quæ velocitati aquæ effluentis reſpondet = {mm/nn} v,
              <lb/>
            quæ proin, ſi vocetur z, erit nnNdz - mmzydx + {mmnnzdx/y} = mmyxdx.</s>
            <s xml:id="echoid-s968" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div52" type="section" level="1" n="37">
          <head xml:id="echoid-head46" xml:space="preserve">Corollarium 2.</head>
          <p>
            <s xml:id="echoid-s969" xml:space="preserve">§. </s>
            <s xml:id="echoid-s970" xml:space="preserve">10. </s>
            <s xml:id="echoid-s971" xml:space="preserve">Si foramen ſit valde parvum, ratione amplitudinum vaſis,
              <lb/>
            fit n = o, totaque æquatio abit in hanc - mmzydx = - mmyxdx vel
              <lb/>
            z = x; </s>
            <s xml:id="echoid-s972" xml:space="preserve">tunc igitur aqua ea conſtanter effluit velocitate, qua ad altitudinem
              <lb/>
            ſupremæ ſuperficiei usque aſcendere poſſit, quem ſolum caſum Geometræ
              <lb/>
            hactenus fuerunt recte aſſecuti: </s>
            <s xml:id="echoid-s973" xml:space="preserve">valetque hæc propoſitio pro omnibus vaſis
              <lb/>
            utcunque formatis: </s>
            <s xml:id="echoid-s974" xml:space="preserve">at cum foramen non ut infinite parvum conſideratur,
              <lb/>
            nequaquam negligenda eſt vaſis figura. </s>
            <s xml:id="echoid-s975" xml:space="preserve">Notari tamen poteſt, quod niſi fo-
              <lb/>
            ramen ſit ampliſſimum, ſine notabili admodum errore idem ut infinitè par-
              <lb/>
            vum conſiderari poſſit.</s>
            <s xml:id="echoid-s976" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div53" type="section" level="1" n="38">
          <head xml:id="echoid-head47" xml:space="preserve">Corollarium 3.</head>
          <p>
            <s xml:id="echoid-s977" xml:space="preserve">§. </s>
            <s xml:id="echoid-s978" xml:space="preserve">11. </s>
            <s xml:id="echoid-s979" xml:space="preserve">Cum fluidum non eſt ubique idem, ſimili modo inſtituen-
              <lb/>
            dus eſt calculus, inquirendo nimirum tum in incrementum aſcenſus poten-
              <lb/>
            tialis fluidi compoſiti, tum in Deſcenſum actualem, eaque inter ſe æquando.
              <lb/>
            </s>
            <s xml:id="echoid-s980" xml:space="preserve">Quod ſi autem foramen ſit valde parvum, per ſe patet, quod etiam calcu-
              <lb/>
            lus oſtendit, fore ut fluidum velocitate exiliat altitudini debita tali, ut ſi vas
              <lb/>
            ad eandem altitudinem liquore eodem, qui exilit, repletum ſit, eandem
              <lb/>
            preſſionem latera foraminis ſuſtineant.</s>
            <s xml:id="echoid-s981" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div54" type="section" level="1" n="39">
          <head xml:id="echoid-head48" xml:space="preserve">Scholium Generale.</head>
          <p>
            <s xml:id="echoid-s982" xml:space="preserve">§. </s>
            <s xml:id="echoid-s983" xml:space="preserve">12. </s>
            <s xml:id="echoid-s984" xml:space="preserve">Priusquam Corollaria ſpecialiora ex theoria noſtra dedu-
              <lb/>
            camus circa motum fluidorum ex vaſis cylindricis, conveniet hic examina-
              <lb/>
            re, quousque hypotheſes aſſumtæ cum rei natura conſpirent & </s>
            <s xml:id="echoid-s985" xml:space="preserve">quænam aliæ
              <lb/>
            intervenire poſſint cauſæ, quarum in computo nullam rationem habuimus,
              <lb/>
            motum fluidum diminuentes.</s>
            <s xml:id="echoid-s986" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s987" xml:space="preserve">Quod primo attinet ad Principium conſervationis virium vivarum ſeu
              <lb/>
            perpetuæ æqualitatis inter aſcenſum potentialem deſcenſumque actualem nihil hîc vi-
              <lb/>
            deo, quod ei notabili impedimento eſſe poſſit, ſi modo à frictionibus, te-
              <lb/>
            nacitate, aëris reſiſtentia hujuscemodique aliis obſtaculis mentem </s>
          </p>
        </div>
      </text>
    </echo>
Impressum