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

Table of contents

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[91.] Exemplum 1.
[92.] Exemplum 2.
[93.] De oſcillationibus fluidorum in tubisrecurvis. Caſus II.
[94.] Lemma.
[95.] Solutio.
[96.] Problema.
[97.] Solutio.
[98.] Corollarium 1.
[99.] Corollarium 2.
[100.] Corollarium 3.
[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.
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          <p>
            <s xml:id="echoid-s2280" xml:space="preserve">
              <pb o="83" file="0097" n="97" rhead="SECTIO QUARTA."/>
            ad 1; </s>
            <s xml:id="echoid-s2281" xml:space="preserve">Orificium autem B eratad orificium A proxime ut 25 ad 16; </s>
            <s xml:id="echoid-s2282" xml:space="preserve">tempus eva-
              <lb/>
            cuationis repletis antea cylindris fuit in Fig. </s>
            <s xml:id="echoid-s2283" xml:space="preserve">24, ſex min. </s>
            <s xml:id="echoid-s2284" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s2285" xml:space="preserve">cum dimidio, in
              <lb/>
            altera præterpropter 4 hujuſmodi minutorum cum triente.</s>
            <s xml:id="echoid-s2286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2287" xml:space="preserve">In his caſibus vaſa ſatis ampla ſuere ratione tuborum annexorum, ut
              <lb/>
            veluti infinita cenſeri poſſent; </s>
            <s xml:id="echoid-s2288" xml:space="preserve">debuiſſetque proin per Regulas paſſim à no-
              <lb/>
            bis indicatas aqua effluere per orificia extrema velocitatibus reſpondentibus
              <lb/>
            toti altltudini aquæ, ſi modo excipias prima fluxus momenta, quæ ipſa tam
              <lb/>
            brevia hic ſunt, ut obſervari non poſſint. </s>
            <s xml:id="echoid-s2289" xml:space="preserve">Et cum præterea, ut paſſim mo-
              <lb/>
            nui, quantitas aquæ dato tempore per tubos effluentis ſimpliciter æſtiman-
              <lb/>
            da ſit ex celeritatibus & </s>
            <s xml:id="echoid-s2290" xml:space="preserve">magnitudine orificiorum inveni per regnlam §. </s>
            <s xml:id="echoid-s2291" xml:space="preserve">22.
              <lb/>
            </s>
            <s xml:id="echoid-s2292" xml:space="preserve">exhibitam, tempus evacuationis in primo caſu 4 {1/3} minſec. </s>
            <s xml:id="echoid-s2293" xml:space="preserve">in poſteriori =
              <lb/>
            fere 3. </s>
            <s xml:id="echoid-s2294" xml:space="preserve">m. </s>
            <s xml:id="echoid-s2295" xml:space="preserve">ſec.</s>
            <s xml:id="echoid-s2296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2297" xml:space="preserve">Quod in experimento majora paullo fuerint obſervata in Fig. </s>
            <s xml:id="echoid-s2298" xml:space="preserve">24. </s>
            <s xml:id="echoid-s2299" xml:space="preserve">ma-
              <lb/>
            ximam partem adhæſioni aquæ ad latera tubi, in Fig. </s>
            <s xml:id="echoid-s2300" xml:space="preserve">autem 25. </s>
            <s xml:id="echoid-s2301" xml:space="preserve">alii in ſuper
              <lb/>
            rationi in paragrapho 34. </s>
            <s xml:id="echoid-s2302" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s2303" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">indicatæ eſt tribuendum.</s>
            <s xml:id="echoid-s2305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2306" xml:space="preserve">Phænomena alia in his vaſis ſunt notanda: </s>
            <s xml:id="echoid-s2307" xml:space="preserve">nempe cum vaſa ſunt tan-
              <lb/>
            tum non evacuata, percipitur ſonus quidem ab aëre, qui tunc aquæ in ori-
              <lb/>
            ficio ſuperiori ſe miſcet. </s>
            <s xml:id="echoid-s2308" xml:space="preserve">hunc vero ſonum pro ultimo fluxus momento acce-
              <lb/>
            pi: </s>
            <s xml:id="echoid-s2309" xml:space="preserve">facile fit porro, ut aquæ effluxus concedatur priusquam ad perfectam
              <lb/>
            quietem fuerit reducta (nam ab impletione agitantur & </s>
            <s xml:id="echoid-s2310" xml:space="preserve">in turbinem mo-
              <lb/>
            ventur aquæ); </s>
            <s xml:id="echoid-s2311" xml:space="preserve">tunc autem effluxus admodum retardatur & </s>
            <s xml:id="echoid-s2312" xml:space="preserve">cataractæ ſpecies
              <lb/>
            interne formatur, continueque aër aquæ effluenti ſe permiſcet. </s>
            <s xml:id="echoid-s2313" xml:space="preserve">Ita poteſt
              <lb/>
            pro lubitu retardari effluxus, ſi in vorticem aquæ agantur antequam effluant.</s>
            <s xml:id="echoid-s2314" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div87" type="section" level="1" n="62">
          <head xml:id="echoid-head84" xml:space="preserve">Experimentum 7.</head>
          <p>
            <s xml:id="echoid-s2315" xml:space="preserve">Vaſe uſus ſum Prismatico, cui tubulus infixus erat horizontaliter ut in
              <lb/>
            Fig. </s>
            <s xml:id="echoid-s2316" xml:space="preserve">19. </s>
            <s xml:id="echoid-s2317" xml:space="preserve">Habebat orificium G F in Diametro præciſe quinque lineas; </s>
            <s xml:id="echoid-s2318" xml:space="preserve">alterum
              <lb/>
            N M 6 {1/2} lin. </s>
            <s xml:id="echoid-s2319" xml:space="preserve">Erant proin ipſæ amplitudines orificiorum G F & </s>
            <s xml:id="echoid-s2320" xml:space="preserve">N M ut 100.
              <lb/>
            </s>
            <s xml:id="echoid-s2321" xml:space="preserve">ad 169. </s>
            <s xml:id="echoid-s2322" xml:space="preserve">amplitudo vero vaſis continebat amplitudinem orificii N M ducentis
              <lb/>
            & </s>
            <s xml:id="echoid-s2323" xml:space="preserve">una vicibus. </s>
            <s xml:id="echoid-s2324" xml:space="preserve">Longitudo tubuli G N erat 4. </s>
            <s xml:id="echoid-s2325" xml:space="preserve">poll.</s>
            <s xml:id="echoid-s2326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2327" xml:space="preserve">Denide vas aquâ implevi usque in C D, cujus altitudo ſupra axem tu-
              <lb/>
            bi erat 13. </s>
            <s xml:id="echoid-s2328" xml:space="preserve">poll. </s>
            <s xml:id="echoid-s2329" xml:space="preserve">10, lin. </s>
            <s xml:id="echoid-s2330" xml:space="preserve">Aperto orificio N M effluxerunt aquæ </s>
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