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

Table of contents

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[101.] Corollarium 4.
[102.] Theorema.
[103.] Demonſtratio.
[104.] Problema.
[105.] Solutio.
[106.] Corollarium. 1.
[107.] Corollarium 2.
[108.] Scholion.
[109.] Theorema.
[110.] Demonſtratio.
[111.] Problema.
[112.] Solutio.
[113.] Scholium.
[114.] Corollarium 1.
[115.] Corollarium 2.
[116.] Scholion Generale.
[117.] HYDRODYNAMICÆ SECTIO SEPTIMA. De motu aquarum per vaſa ſubmerſa, ubi exem-plis oſtenditur, quam inſigniter utile ſit princi-pium conſervationis virium vivarum, veliis in caſibus, quibus continue aliquid de illis perdi cenſendum eſt. PARS PRIMA. De deſcenſu aquarum. §. 1.
[118.] PARS SECUNDA. De aſcenſu aquarum.
[119.] Corollarium.
[120.] Scholium Generale.
[121.] EXPERIMENTA Ad ſect. ſept. referenda. Experimentum 1.
[122.] Experimentum 2.
[123.] Experimentum 3.
[124.] De iſto tubo experimentum ita ſumſi:
[125.] Experimentum 4.
[126.] Experimentum 5.
[127.] HYDRODYNAMICÆ SECTIO OCTAVA. De motu fluidorum cum homogeneorum tum hetero-geneorum per vaſa irregularis & præruptæ ſtru-cturæ, ubi ex theoria virium vivarum, quarum pars continue abſorbeatur, explicantur præcipue Phæno-mena ſingularia fluidorum, per plurima foramina trajecto-rum, præmiſsis regulis generalibus pro motibus fluido-rum ubique definiendis. §. 1.
[128.] Regula 1.
[129.] Regula 2.
[130.] Problema.
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            <s xml:id="echoid-s3791" xml:space="preserve">Fuerit v. </s>
            <s xml:id="echoid-s3792" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3793" xml:space="preserve">elevatio indicata per c unius pollicis, immerſio cylindri b
              <lb/>
            80. </s>
            <s xml:id="echoid-s3794" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s3795" xml:space="preserve">ipſaque a 81. </s>
            <s xml:id="echoid-s3796" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s3797" xml:space="preserve">dein ponatur diameter tubi tripla diametri forami-
              <lb/>
            nis, id eſt, nn = 81, erit v = {2 - z - 2α
              <emph style="super">- z</emph>
            /nn}, atque ſi porro ponatur
              <lb/>
            z = c = 1, ut habeatur altitudo velocitatis, cum utraque ſuperficies eſt ad
              <lb/>
            libellam poſita, erit v = {α - 2/nnα}, id eſt, proxime v = {1/307} poll. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">cum ſecundum
              <lb/>
            paragraphum decimum debuiſſet oriri v = {1/162} poll. </s>
            <s xml:id="echoid-s3799" xml:space="preserve">& </s>
            <s xml:id="echoid-s3800" xml:space="preserve">ſecundum paragraphum
              <lb/>
            quartum v = o. </s>
            <s xml:id="echoid-s3801" xml:space="preserve">In eodem exemplo fit ſpatium integrum, quod ſuperficies
              <lb/>
            percurrit non omnino octo quintarum partium unius pollicis, locusque
              <lb/>
            maximæ velocitatis eſt præterpropter ſexaginta novem centeſimarum partium
              <lb/>
            ejusdem menſuræ infra altitudinem initialem.</s>
            <s xml:id="echoid-s3802" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3803" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">12. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">Non difficilius eſſet ad omnes vaſorum figuras extendere, quæ
              <lb/>
            hactenus dicta ſunt, imo etiam ad ſpatia finita, quibus aqua externa deter-
              <lb/>
            minetur: </s>
            <s xml:id="echoid-s3806" xml:space="preserve">fiunt autem formulæ plerumque adeo prolixæ, ut conſultius du-
              <lb/>
            xerim easdem ſilentio præterire, & </s>
            <s xml:id="echoid-s3807" xml:space="preserve">ſpecimine ſaltem aliquo particularem oſten-
              <lb/>
            dere modum, quo theoria ad quoslibet caſus alios eruendos applicanda ſit.</s>
            <s xml:id="echoid-s3808" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3809" xml:space="preserve">Attentionem particulariorem merentur, quæ de motu aquarum in tu-
              <lb/>
            bis inferius largiter apertis, & </s>
            <s xml:id="echoid-s3810" xml:space="preserve">profundiſſime ſubmerſis indicavi, quia in his
              <lb/>
            motus oſcillatorius, ut in pendulis, conſtantis durationis eſt, & </s>
            <s xml:id="echoid-s3811" xml:space="preserve">undarum
              <lb/>
            in mari fluxus illuſtratur ab illis. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">Exiſtimavi autem prius de refluxu aquarum
              <lb/>
            in cylindris ſubmerſis generaliter tractandum eſſe, atque oſtendendum in iſta
              <lb/>
            hypotheſi refluxum non differre à præcedente fluxu, quam motus totus
              <lb/>
            oſcillatorius examinetur. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">Jam igitur de iſto refluxu commentabimur, dein-
              <lb/>
            ceps utrumque motum in diverſis caſibus combinaturi, ne aliquid in argu-
              <lb/>
            mento deſiderari poſſit.</s>
            <s xml:id="echoid-s3814" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div150" type="section" level="1" n="118">
          <head xml:id="echoid-head153" xml:space="preserve">PARS SECUNDA.</head>
          <head xml:id="echoid-head154" style="it" xml:space="preserve">De aſcenſu aquarum.</head>
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            <s xml:id="echoid-s3815" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3816" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">Poſtquam aquæ deſcenderunt in vaſe ſubmerſo, quantum id
              <lb/>
            ipſis natura rei permittit, duo potiſſimum conſideranda ſe offerunt; </s>
            <s xml:id="echoid-s3818" xml:space="preserve">primo
              <lb/>
            exceſſus altitudinis ſuperficiei externæ ſupra internam & </s>
            <s xml:id="echoid-s3819" xml:space="preserve">ſecundo vis viva ſeu
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            productum ex aſcenſu potentiali in maſſam illius aquæ, quæ ex cylindro in </s>
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