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

Table of contents

< >
[61.] Ad Theoriam aquarum per tubos effluentium. Experimentum 6.
[62.] Experimentum 7.
[63.] Experimentum 8.
[64.] Ad theoriam aquarum, quæ ex vaſis ampliſsi-mis à puncto quietis usque ad datum veloci-tatis gradum effluunt. Experimentum 9.
[65.] Experimentum 10.
[66.] Experimentum 11.
[67.] Experimentum 12.
[68.] HYDRODYNAMICÆ SECTIO QUINTA. De motu aquarum ex vaſis conſtanter plenis. §. 1.
[69.] Problema.
[70.] Solutio.
[71.] Caſus 1.
[72.] Caſus II.
[73.] Scholion 1.
[74.] Scholion 2.
[75.] Scholion 3.
[76.] Scholion 4.
[77.] Corollarium 1.
[78.] Corollarium 3.
[79.] Corollarium 4.
[80.] Problema.
[81.] Solutio.
[82.] Scholium.
[83.] Problema.
[84.] Solutio.
[85.] Corollarium 1.
[86.] Corollarium 2.
[87.] Scholium.
[88.] Experimenta quæ ad Sectionem V. pertinent. Ad §. 5.
[89.] HYDRODYNAMICÆ SECTIO SEXTA. De fluidis non effluentibus ſeu intra latera vaſorum motis. §. 1.
[90.] De motu aquarum per canales indefinite longos. Caſus 1.
< >
page |< < (49) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div64" type="section" level="1" n="45">
          <p>
            <s xml:id="echoid-s1266" xml:space="preserve">
              <pb o="49" file="0063" n="63" rhead="SECTIO TERTIA."/>
            ubi pro noſtro caſu præſente intelligitur per v altitudo quæſita reſpondens ve-
              <lb/>
            locitati ſuperficiei aqueæ in ſitu F, per ξ longitudo B D E F & </s>
            <s xml:id="echoid-s1267" xml:space="preserve">per x altitudo
              <lb/>
            B G, atque per {m/n} index rationis inter amplitudines tubi & </s>
            <s xml:id="echoid-s1268" xml:space="preserve">foraminis B: </s>
            <s xml:id="echoid-s1269" xml:space="preserve">Quod
              <lb/>
            ſi vero dicatur longitudo B D A = αerit x = {ξ - α/g}, unde nunc habetur
              <lb/>
            v = ξ
              <emph style="super">{mm/nn} - 1}</emph>
            ſ - ({ξ - α/g}) ξ
              <emph style="super">{- mm/nn}</emph>
            dξ</s>
          </p>
          <p>
            <s xml:id="echoid-s1270" xml:space="preserve">Indicetur longitudo totius canalis B D E C per β, & </s>
            <s xml:id="echoid-s1271" xml:space="preserve">erit
              <lb/>
            ſ - ({ξ - α/g} ξ
              <emph style="super">{- mm/nn}</emph>
            dξ = {nnα/g(nn - mm)} (ξ
              <emph style="super">{nn - mm/nn}</emph>
            - β
              <emph style="super">{nn - mm/nn}</emph>
            })
              <lb/>
            {- nn/g(2nn - mm)} (ξ
              <emph style="super">{2nn - mm/nn}</emph>
            - β
              <emph style="super">{2nn - mm/nn}</emph>
            )
              <lb/>
            atque proinde
              <lb/>
            v = {nnα/g(nn - mm)}(1 - ({β/ξ})
              <emph style="super">{nn - mm/nn}</emph>
            )
              <lb/>
            - {nnξ/g(2nn - mm)}(1 - ({β/ξ})
              <emph style="super">{2nn - mm/nn}</emph>
            ). </s>
            <s xml:id="echoid-s1272" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s1273" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1274" xml:space="preserve">I.</s>
            <s xml:id="echoid-s1275" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div65" type="section" level="1" n="46">
          <head xml:id="echoid-head57" xml:space="preserve">
            <emph style="bf">Scholium.</emph>
          </head>
          <p>
            <s xml:id="echoid-s1276" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1277" xml:space="preserve">27. </s>
            <s xml:id="echoid-s1278" xml:space="preserve">Quoniam hæ æquationes ſunt paullo prolixiores @non immora-
              <lb/>
            bimur generali earundem contemplationi, conſideraturi potius caſus iſtos
              <lb/>
            particulares, qui calculum abbreviant, nec ultima iſta æquatione definiri
              <lb/>
            poſſunt.</s>
            <s xml:id="echoid-s1279" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1280" xml:space="preserve">Si operculum in B omne abeſſe ponamus, fit m = n & </s>
            <s xml:id="echoid-s1281" xml:space="preserve">(quod ſeorſim
              <lb/>
            pro hoc pariter atque @altero caſu mox dicendo erui debet)
              <lb/>
            v = {b - ξ + αlog.</s>
            <s xml:id="echoid-s1282" xml:space="preserve">ξ - αlog.</s>
            <s xml:id="echoid-s1283" xml:space="preserve">β/g}
              <lb/>
            tuncque velocitas maxima eſt in A, nominatimquæ talis, quæ reſpondet al-
              <lb/>
            titudini {β - α + αlog.</s>
            <s xml:id="echoid-s1284" xml:space="preserve">α - αlog.</s>
            <s xml:id="echoid-s1285" xml:space="preserve">β.</s>
            <s xml:id="echoid-s1286" xml:space="preserve">/g}</s>
          </p>
        </div>
      </text>
    </echo>