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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          <pb o="141" file="0155" n="155" rhead="SECTIO SEPTIMA."/>
          <p>
            <s xml:id="echoid-s4082" xml:space="preserve">Deinde tubum hunc eadem lamina inſtructum admoto ſuperius digi-
              <lb/>
            to aquæ immiſi@ad profunditatem 18. </s>
            <s xml:id="echoid-s4083" xml:space="preserve">lin. </s>
            <s xml:id="echoid-s4084" xml:space="preserve">totum ab aquâ vacuum: </s>
            <s xml:id="echoid-s4085" xml:space="preserve">remoto
              <lb/>
            digito emerſit ſuperficies tubi ſupra aquam ſtagnantem integris octo lineis,
              <lb/>
            cum §. </s>
            <s xml:id="echoid-s4086" xml:space="preserve">17. </s>
            <s xml:id="echoid-s4087" xml:space="preserve">earum novem indicat pro iſto caſu.</s>
            <s xml:id="echoid-s4088" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4089" xml:space="preserve">Quod hic defectus minor admodum fuerit, quam in deſcenſu, ratio-
              <lb/>
            ni adſcripſi, quam prolixe paragrapho decimo tertio indicavi, cum dicerem
              <lb/>
            motum paullo majorem oriturum, cum foramen amplitudinem reſpectu tu-
              <lb/>
            bi notabilem veluti in ratione √ {1/2} ad 1, aut circiter habuerit, quam qui ex
              <lb/>
            hypotheſi ſequitur: </s>
            <s xml:id="echoid-s4090" xml:space="preserve">atque ut ea de re certus plane fierem, tubum adhibui
              <lb/>
            breviorem & </s>
            <s xml:id="echoid-s4091" xml:space="preserve">ampliorem, ut omnis fere impedimentis alienis effectus præri-
              <lb/>
            peretur, & </s>
            <s xml:id="echoid-s4092" xml:space="preserve">experimentum cepi, quod ſequitur.</s>
            <s xml:id="echoid-s4093" xml:space="preserve"/>
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        <div xml:id="echoid-div155" type="section" level="1" n="123">
          <head xml:id="echoid-head161" xml:space="preserve">Experimentum 3.</head>
          <p>
            <s xml:id="echoid-s4094" xml:space="preserve">Tubum adhibui cujus diameter erat plus quam ſeptem linearum, quem
              <lb/>
            ex ferro confieri curavi, quia vitreus bene cylindricus non fuit ad manus:
              <lb/>
            </s>
            <s xml:id="echoid-s4095" xml:space="preserve">longitudo ejus fuit quatuor pollicum cum ſex lineis & </s>
            <s xml:id="echoid-s4096" xml:space="preserve">ſemiſſe: </s>
            <s xml:id="echoid-s4097" xml:space="preserve">amplitudo
              <lb/>
            ejus ratione foraminis indicata per n fuit = 1, 860 & </s>
            <s xml:id="echoid-s4098" xml:space="preserve">nn = 3, 4 5 8.</s>
            <s xml:id="echoid-s4099" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div156" type="section" level="1" n="124">
          <head xml:id="echoid-head162" xml:space="preserve">De iſto tubo experimentum ita ſumſi:</head>
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            <s xml:id="echoid-s4100" xml:space="preserve">Obturato ſcilicet orificio ſuperiori identidem tentavi, ad quam pro-
              <lb/>
            funditatem ſubmergendus eſſet aquæ in arca ampliſſima ſtagnanti, ut re-
              <lb/>
            moto protinus digito, qui orificium obtegebat, aqua ad limbum ejus-
              <lb/>
            dem orificii præciſe aſcenderet, nihilque præterflueret. </s>
            <s xml:id="echoid-s4101" xml:space="preserve">Iſtam vero pro-
              <lb/>
            funditatem expertus ſum 3. </s>
            <s xml:id="echoid-s4102" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s4103" xml:space="preserve">cum tribus lineis; </s>
            <s xml:id="echoid-s4104" xml:space="preserve">fuit igitur aſcenſus ſupra
              <lb/>
            aquam externam unius pollicis & </s>
            <s xml:id="echoid-s4105" xml:space="preserve">trium linearum cum dimidia, cum vel
              <lb/>
            omnibus remotis impedimentis parum ultra undecim lineas aſcenſus fieri
              <lb/>
            debuerit vi paragraphi 17. </s>
            <s xml:id="echoid-s4106" xml:space="preserve">Recte igitur præmonitum fuit §. </s>
            <s xml:id="echoid-s4107" xml:space="preserve">13. </s>
            <s xml:id="echoid-s4108" xml:space="preserve">non poſſe
              <lb/>
            non aſcenſus fieri paullo majores in iſtiusmodi caſibus, quam hypotheſis
              <lb/>
            poſtulat. </s>
            <s xml:id="echoid-s4109" xml:space="preserve">Mox eidem tubo aliud applicui fundum; </s>
            <s xml:id="echoid-s4110" xml:space="preserve">erat jam n = 3, 68,
              <lb/>
            & </s>
            <s xml:id="echoid-s4111" xml:space="preserve">nn = 13, 54: </s>
            <s xml:id="echoid-s4112" xml:space="preserve">difficile fuit experimenti ſucceſſum recte dignoſcere, quia
              <lb/>
            ſuperficies in tubo aſcendens ſemper fuit bullata: </s>
            <s xml:id="echoid-s4113" xml:space="preserve">viſum tamen fuit, tubum
              <lb/>
            nunc immergendum fuiſſe ad altitudinem 4. </s>
            <s xml:id="echoid-s4114" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s4115" xml:space="preserve">cum duabus tribuſue lineis,
              <lb/>
            manentibus ſic extra aquam præterpropter quatuor lineis, prorſus ut theo-
              <lb/>
            ria indicat.</s>
            <s xml:id="echoid-s4116" xml:space="preserve"/>
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