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

Table of contents

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[31.] Solutio.
[32.] Problema.
[33.] Solutio.
[34.] Problema.
[35.] Solutio.
[36.] Corollarium 1.
[37.] Corollarium 2.
[38.] Corollarium 3.
[39.] Scholium Generale.
[40.] De his quæ pertinent ad effluxum aquarum ex Cy-lindris verticaliter poſitis, per Lumen quod-cunque, quod eſt in fundo horizontali. §. 13.
[41.] De Effluxu Aquarum ex Cylindris verticaliter po-ſitis, qui in alios tubos ſtrictiores pariter verticales deſinunt. §. 21.
[42.] Problema.
[43.] Solutio.
[44.] Problema.
[45.] Solutio.
[46.] Scholium.
[47.] Experimenta quæ ad Sect. 3. pertinent. Prænotanda.
[48.] Lemma.
[49.] De Velocitatibus maximis fluidorum per foramina valde ampla effluentium. Ad §. 16. & 20. Experimentum Primum.
[50.] De velocitate aquæ ex vaſe ampliſſimo erumpentis. Ad §. 17.
[51.] De vaſis quæ ſunt Tubis verticalibus inſtructa. Ad §. 22. & 23.
[52.] De iisdem vaſis, quibus tubi horizontales inſeruntur. Ad §. 24.
[53.] De canalibus recurvis. Ad §. 27.
[54.] HYDRODYNAMICÆ SECTIO QUARTA. De variis temporibus, quæ in effluxu aquarum deſiderari poſſunt. §. 1.
[55.] Experimenta quœ ad Sect. IV. pertinent.
[56.] Ad Theoriam Contractionis Venarum aquearum Experimentum 1.
[57.] Experimentum 2.
[58.] Experimentum 3.
[59.] Experimentum 4.
[60.] Experimentum 5.
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            <emph style="bf">HYDRODYNAMICÆ
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            SECTIO QUARTA.</emph>
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          <head xml:id="echoid-head73" style="it" xml:space="preserve">De variis temporibus, quæ in effluxu aquarum
            <lb/>
          deſiderari poſſunt.</head>
          <head xml:id="echoid-head74" xml:space="preserve">§. 1.</head>
          <p>
            <s xml:id="echoid-s1664" xml:space="preserve">REs videbitur multis omnino Geometrica, quæ ſcilicet nulla conſide-
              <lb/>
            ratione phyſica opus habeat, ut, cum aquæ ex dato vaſe per lumen co-
              <lb/>
            gnitum velocitatibus in omniſitu determinatis effluunt, tempus de-
              <lb/>
            finiatur, quo data effluat aquæ quantitas. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">Attamen experientia contra-
              <lb/>
            rium docet; </s>
            <s xml:id="echoid-s1666" xml:space="preserve">nam multo minori quantitate aquæ effluunt perforamina, quæ ſunt
              <lb/>
            in lamina tenui, quam ex ſimplici velocitatum conſideratione ſequeretur, idque
              <lb/>
            plerumque (nec enim res ſibi conſtat in diverſis circumſtantiis) in ratione ut
              <lb/>
            1 ad √ 2; </s>
            <s xml:id="echoid-s1667" xml:space="preserve">movit hoc Newtonum, ut affirmaret in prima Princ. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">math. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">editio-
              <lb/>
            ne aquam ex vaſe ea effluere velocitate, quæ generetur altitudine dimidia aquæ
              <lb/>
            ſupra foramen, cui opinioni omnia experimenta de velocitatibus immediate
              <lb/>
            ſumta, contradicunt. </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Explorans poſtmodum ipſe magnus Vir hujus contra-
              <lb/>
            dictionis originem, eam poſitam eſſe obſervavit in contractione venæ aqueæ,
              <lb/>
            quæ contractio mox præ foramine fieri ſolet. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">Alia quoque mihi obſervata fuit
              <lb/>
            venæ mutatio priori nunc ſimilis nunc contraria. </s>
            <s xml:id="echoid-s1672" xml:space="preserve">Nempe cum aquæ non per
              <lb/>
            fimplex foramen, verum per tubulum effluunt, rurſus contrahitur vena, ſi
              <lb/>
            tubus exteriora verſus convergit, ſed dilatatur ſi idem divergit. </s>
            <s xml:id="echoid-s1673" xml:space="preserve">De contra-
              <lb/>
            ctione venæ aqueæ per tubos convergentes effluentis accuratiſſima ſumſit ex-
              <lb/>
            perimenta Joh. </s>
            <s xml:id="echoid-s1674" xml:space="preserve">Polenus in libro de caſtellis p. </s>
            <s xml:id="echoid-s1675" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">& </s>
            <s xml:id="echoid-s1677" xml:space="preserve">ſeqq. </s>
            <s xml:id="echoid-s1678" xml:space="preserve">contractio venæ eo
              <lb/>
            major à Viro Celeberrimo obſervata fuit, quo amplius erat orificium tubi co-
              <lb/>
            nici internum manentibus orificio externo atque longitudine tubi, quæ ratio eſt,
              <lb/>
            quod ſimilis aquæ quantitas ceteris paribus eò tardius effluxerit, quò amplius
              <lb/>
            fuerit orificium internum, quamvis impedimenta ab adhæſione aquæ ad </s>
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