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

Table of contents

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[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.
[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.
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            <emph style="bf">HYDRODYNAMICÆ</emph>
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          <head xml:id="echoid-head166" xml:space="preserve">SECTIO OCTAVA.</head>
          <head xml:id="echoid-head167" style="it" xml:space="preserve">De motu fluidorum cum homogeneorum tum hetero-
            <lb/>
          geneorum per vaſa irregularis & præruptæ ſtru-
            <lb/>
          cturæ, ubi ex theoria virium vivarum, quarum pars
            <lb/>
          continue abſorbeatur, explicantur præcipue Phæno-
            <lb/>
          mena ſingularia fluidorum, per plurima foramina trajecto-
            <lb/>
          rum, præmiſsis regulis generalibus pro motibus fluido-
            <lb/>
          rum ubique definiendis.</head>
          <head xml:id="echoid-head168" xml:space="preserve">§. 1.</head>
          <p>
            <s xml:id="echoid-s4147" xml:space="preserve">ALiis adhuc principiis præter quam in ſectione proxime præceden-
              <lb/>
            te uſi non ſumus, quam hiſce duobus quod velocitates fluidorum
              <lb/>
            ſint ubique reciproce proportionales amplitudinibus vaſorum, cujus
              <lb/>
            ope invenitur aſcenſus potentialis totius aquæ ex dato aſcenſu po-
              <lb/>
            tentiali cujusvis particulæ; </s>
            <s xml:id="echoid-s4148" xml:space="preserve">tum quod aſcenſus pot. </s>
            <s xml:id="echoid-s4149" xml:space="preserve">totius aquæ perpetuo æqua-
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            lis maneat deſcenſui actuali. </s>
            <s xml:id="echoid-s4150" xml:space="preserve">Quoties ambo hæc principia locum habent, mi-
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            nime dubitandum eſt, quin methodo à nobis adhibita motus fluidorum
              <lb/>
            recte definiatur. </s>
            <s xml:id="echoid-s4151" xml:space="preserve">Non diffitebor tamen, hujusmodi fieri poſſe ſtructuræ va-
              <lb/>
            ſa, in quibus fluida moventur, ut neutrum iſtorum principiorum recte pro-
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            cedat. </s>
            <s xml:id="echoid-s4152" xml:space="preserve">Prius equidem raro aut nunquam notabiliter à vero abducit, quia
              <lb/>
            ubicunque locum non habet, ibi nullum fere aquæ habere ſolent motum,
              <lb/>
            poſſuntque ſine ſenſibili errore ceu ſtagnantes conſiderari: </s>
            <s xml:id="echoid-s4153" xml:space="preserve">Longe vero ali-
              <lb/>
            ter comparatum eſt alterum principium, quod apparebit exinferioribus ex-
              <lb/>
            emplis, & </s>
            <s xml:id="echoid-s4154" xml:space="preserve">cujus rei luculentum eſſe poſſunt teſtimonium ea, quæ in ſupe-
              <lb/>
            riori ſectione protulimus circa refluxum aquarum; </s>
            <s xml:id="echoid-s4155" xml:space="preserve">tantum enim abeſt, ut
              <lb/>
            aquæ in vaſe ſubmerſo ex data altitudine delapſæ, ad hanc altitudinem re-
              <lb/>
            gredi poſſint, prouti vi iſtius principii deberent, ſublatis impedimentis ex-
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            trinſecis, quin potius plerunque vix ſenſibilis ſit earum aſcenſus præ deſcen-
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            ſu, quem antea fecerunt: </s>
            <s xml:id="echoid-s4156" xml:space="preserve">imo nequidem aſcendere ſuperficies aquæ </s>
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