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

Table of contents

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[61.] Ad Theoriam aquarum per tubos effluentium. Experimentum 6.
[62.] Experimentum 7.
[63.] Experimentum 8.
[64.] Ad theoriam aquarum, quæ ex vaſis ampliſsi-mis à puncto quietis usque ad datum veloci-tatis gradum effluunt. Experimentum 9.
[65.] Experimentum 10.
[66.] Experimentum 11.
[67.] Experimentum 12.
[68.] HYDRODYNAMICÆ SECTIO QUINTA. De motu aquarum ex vaſis conſtanter plenis. §. 1.
[69.] Problema.
[70.] Solutio.
[71.] Caſus 1.
[72.] Caſus II.
[73.] Scholion 1.
[74.] Scholion 2.
[75.] Scholion 3.
[76.] Scholion 4.
[77.] Corollarium 1.
[78.] Corollarium 3.
[79.] Corollarium 4.
[80.] Problema.
[81.] Solutio.
[82.] Scholium.
[83.] Problema.
[84.] Solutio.
[85.] Corollarium 1.
[86.] Corollarium 2.
[87.] Scholium.
[88.] Experimenta quæ ad Sectionem V. pertinent. Ad §. 5.
[89.] HYDRODYNAMICÆ SECTIO SEXTA. De fluidis non effluentibus ſeu intra latera vaſorum motis. §. 1.
[90.] De motu aquarum per canales indefinite longos. Caſus 1.
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            <s xml:id="echoid-s2370" xml:space="preserve">
              <pb o="85" file="0099" n="99" rhead="SECTIO QUARTA."/>
            E H obſervavi effluente aqua per N M, ſimulque amplitudinem jactus exa-
              <lb/>
            minavi.</s>
            <s xml:id="echoid-s2371" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2372" xml:space="preserve">Duo hæc vidi, quæ prima fronte ſibi contradicere fere videntur; </s>
            <s xml:id="echoid-s2373" xml:space="preserve">de-
              <lb/>
            ſcenſus ex C D in E H tardior factus eſt quam in præcedenti experimento
              <lb/>
            fuerat, & </s>
            <s xml:id="echoid-s2374" xml:space="preserve">nunc duravit 10. </s>
            <s xml:id="echoid-s2375" xml:space="preserve">min. </s>
            <s xml:id="echoid-s2376" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s2377" xml:space="preserve">& </s>
            <s xml:id="echoid-s2378" xml:space="preserve">tamen amplior fuit jactus P Q pro ea-
              <lb/>
            dem altitudine o P; </s>
            <s xml:id="echoid-s2379" xml:space="preserve">jam enim erat P Q = 10. </s>
            <s xml:id="echoid-s2380" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s2381" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2382" xml:space="preserve">lin.</s>
            <s xml:id="echoid-s2383" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2384" xml:space="preserve">Ambo Phænomena ita explico: </s>
            <s xml:id="echoid-s2385" xml:space="preserve">ob foramen e, quod fuit factum prope
              <lb/>
            G F quodque aëri liberum tranſitum concedit, ſolvitur nexus, quem alias
              <lb/>
            inter ſe habent aquæ in tubo, nec proin aliter transfluunt aquæ ubi eſt fo-
              <lb/>
            raminulum e, quam ſi eo ipſo in loco eſſet reſciſſus tubus; </s>
            <s xml:id="echoid-s2386" xml:space="preserve">fluerent autem
              <lb/>
            tardius, quod paſſim demonſtravi, ſi tubus G N M F ceu divergens brevior
              <lb/>
            fieret. </s>
            <s xml:id="echoid-s2387" xml:space="preserve">Quod porro aquæ quamvis minori quantitate, tamen majori impetu per
              <lb/>
            orificium N M non mutatum fluere poſſint ſine implicita contradictione, ra-
              <lb/>
            tio eſt permixtio aëris cum aqua; </s>
            <s xml:id="echoid-s2388" xml:space="preserve">nam aër perpetuo irruit in tubum per fo-
              <lb/>
            raminulum e & </s>
            <s xml:id="echoid-s2389" xml:space="preserve">una cum aqua effluit per N M. </s>
            <s xml:id="echoid-s2390" xml:space="preserve">Denique phænomenon illud,
              <lb/>
            quod aquæ actu celerius fluant per M N aperto, quam clauſo foramine e,
              <lb/>
            aliter explicari non poſſe mihi videtur, quam quod impedimenta extrinſeca
              <lb/>
            minus agant in aquam aëre rarefactam quam naturalem.</s>
            <s xml:id="echoid-s2391" xml:space="preserve"/>
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        <div xml:id="echoid-div89" type="section" level="1" n="64">
          <head xml:id="echoid-head86" style="it" xml:space="preserve">Ad theoriam aquarum, quæ ex vaſis ampliſsi-
            <lb/>
          mis à puncto quietis usque ad datum veloci-
            <lb/>
          tatis gradum effluunt.</head>
          <head xml:id="echoid-head87" xml:space="preserve">Experimentum 9.</head>
          <p>
            <s xml:id="echoid-s2392" xml:space="preserve">Quum aquæ per foramen in lamina tenui factum ex vaſe ampliſſimo
              <lb/>
            effluunt, prima ſtatim guttula omni velocitate, quæ altitudini aquæ ſupra fo-
              <lb/>
            ramen debetur, erumpit.</s>
            <s xml:id="echoid-s2393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2394" xml:space="preserve">Conforme hoc eſt cum theoria §. </s>
            <s xml:id="echoid-s2395" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2396" xml:space="preserve">indicata, ſi vas ſit revera
              <lb/>
            infinitum, & </s>
            <s xml:id="echoid-s2397" xml:space="preserve">quamvis etiam non fuerit ſenſu Geometrico infinitum,
              <lb/>
            dummodo ſit valde amplum, nulla pariter guttula ab initio fluxus ob-
              <lb/>
            ſervari poteſt, quæ non maxima velocitate effluxerit: </s>
            <s xml:id="echoid-s2398" xml:space="preserve">Phænomenon hoc
              <lb/>
            explicui §. </s>
            <s xml:id="echoid-s2399" xml:space="preserve">14. </s>
            <s xml:id="echoid-s2400" xml:space="preserve">cum nempe vi theoriæ in caſu particulari aliquo ibidem re-
              <lb/>
            cenſito vix una aut duæ guttulæ ſenſibiliter à jactu maximo deficere </s>
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