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-head148" xml:space="preserve">SECTIO SEPTIMA.</head>
          <head xml:id="echoid-head149" style="it" xml:space="preserve">De motu aquarum per vaſa ſubmerſa, ubi exem-
            <lb/>
          plis oſtenditur, quam inſigniter utile ſit princi-
            <lb/>
          pium conſervationis virium vivarum, veliis in caſibus, quibus continue
            <lb/>
          aliquid de illis perdi cenſendum eſt.</head>
          <head xml:id="echoid-head150" xml:space="preserve">PARS PRIMA.</head>
          <head xml:id="echoid-head151" style="it" xml:space="preserve">De deſcenſu aquarum.</head>
          <head xml:id="echoid-head152" xml:space="preserve">§. 1.</head>
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            <s xml:id="echoid-s3565" xml:space="preserve">FInge cylindrum aquâ plenum, cujus fundum perforatum ſit, illudque
              <lb/>
            ad certam altitudinem aquæ ſtagnanti veluti infinitæ ſubmerſum, & </s>
            <s xml:id="echoid-s3566" xml:space="preserve">
              <lb/>
            facile intelliges ſuperficiem aquæ in cylindro contentæ deſcenſuram,
              <lb/>
            & </s>
            <s xml:id="echoid-s3567" xml:space="preserve">quidem infra ſuperficiem aquæ exterioris, dein rurſus aſcenſuram
              <lb/>
            & </s>
            <s xml:id="echoid-s3568" xml:space="preserve">ſic porro. </s>
            <s xml:id="echoid-s3569" xml:space="preserve">Hæ vero oſcillationes admodum differunt ab oſcillationibus in præ-
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            cedente ſectione conſideratis, in quibus nempe motus reciproci ſemper ſunt
              <lb/>
            inverſo ordine iidem cum motibus, qui præceſſerunt. </s>
            <s xml:id="echoid-s3570" xml:space="preserve">Quis autem hic præſumat
              <lb/>
            refluxum aquarum ſeu aſcenſum eundem fore, qui fuerat deſcenſus. </s>
            <s xml:id="echoid-s3571" xml:space="preserve">Talia
              <lb/>
            ſi quis ſtatueret, is certe vehementer falleretur, etiamſi vel nihil motus di-
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            minuatur ab adhæſione aquarum ad latera vaſis hujuscemodique aliis impe-
              <lb/>
            dimentis, non ſecus atque regulæ motuum à percuſſione pro corporibus
              <lb/>
            elaſticis valde diverſæ ſunt ab iis, quæ pro corporibus mollibus valent, utut
              <lb/>
            in utroque caſu corpora liberrime moveri cenſeantur. </s>
            <s xml:id="echoid-s3572" xml:space="preserve">Utor hoc ſimili, quod
              <lb/>
            argumentum noſtrum egregie illuſtrat: </s>
            <s xml:id="echoid-s3573" xml:space="preserve">Prouti enim regulæ motuum in cor-
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            poribus mollibus recte determinatur, ſi poſt colliſionem ea vis vivæ
              <lb/>
            pars deperdita cenſeatur quæ in compreſſionem corporum impenſa fuit
              <lb/>
            (neque enim hæc ut in corporibus elaſticis reſtituitur motui progreſſivo) ita
              <lb/>
            aſcenſus fluidi non minus recte definietur, ſi accurate examinetur, quantum vis
              <lb/>
            vivæ ſingulis momentis motui particularum aquearum inteſtino communi-
              <lb/>
            cetur, nunquam rediturum ad motum progreſſivum, de quo ſermo eſt.</s>
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            <s xml:id="echoid-s3575" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3576" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3577" xml:space="preserve">Cum itaque res eo deducta ſit, ut exploretur, quantum vis vivæ
              <lb/>
            in motibus iſtis reciprocis continue perdatur, diſquiſitionem ab hoc incipie-
              <lb/>
            mus.</s>
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