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

Table of contents

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[131.] Solutio.
[132.] Scholium 1.
[133.] Scholium 2.
[134.] Corollarium.
[135.] EXPERIMENTA Ad ſectionem octavam pertinentia. Experimentum 1.
[136.] Experimentum 2.
[137.] HYDRODYNAMICÆ SECTIO NONA. De motu fluidorum, quæ non proprio pondere, ſed potentia aliena ejiciuntur, ubi præſertim de Machinis Hydraulicis earundemque ultimo qui da-ri poteſt perfectionis gradu, & quomodo mecha-nica tam ſolidorum quam fluidorum ulterius perſici poſsit. §. 1.
[138.] Definitiones.
[139.] (A) De machinis aquas cum impetu in altum projicientibus. Regula 1.
[140.] Demonſtratio.
[141.] Scholium.
[142.] Regula 2.
[143.] Demonſtratio.
[144.] Scholium.
[145.] Regula 3.
[146.] Demonſtratio.
[147.] Scholium.
[148.] Regula 4.
[149.] Demonſtratio.
[150.] Scholium.
[151.] Regula 5.
[152.] Demonſtratio.
[153.] Regula 6.
[154.] Demonſtratio.
[155.] Scholium.
[156.] Regula 7.
[157.] Scholium.
[158.] Exemplum 1.
[159.] Exemplum 2.
[160.] Digreſſus continens aliquas commentationes in Ma-chinam Hydraulicam quam repræſent at figura 51.
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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"/>
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          <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"/>
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            <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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