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

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        <div xml:id="echoid-div125" type="section" level="1" n="95">
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            <s xml:id="echoid-s3339" xml:space="preserve">
              <pb o="116" file="0130" n="130" rhead="HYDRODYNAMICÆ"/>
            aquæ in c A d per C A, aggregatumque horum productorum dividendo per
              <lb/>
            ſummam harum maſſarum. </s>
            <s xml:id="echoid-s3340" xml:space="preserve">Unde invenitur.</s>
            <s xml:id="echoid-s3341" xml:space="preserve"> A F = {ga X (f + {1/2}
              <emph style="super">b</emph>
            ) + γα X (φ + {1/2}
              <emph style="super">β</emph>
            ) + Mm/ga + γα + M}</s>
          </p>
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        <div xml:id="echoid-div126" type="section" level="1" n="96">
          <head xml:id="echoid-head126" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s3342" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">Determinare ubique velocitates aquæ oſcillantis, poſito oſcilla-
              <lb/>
            tiones ultra terminos tuborum cylindricorum non divagari.</s>
            <s xml:id="echoid-s3345" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div127" type="section" level="1" n="97">
          <head xml:id="echoid-head127" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s3346" xml:space="preserve">Sit aqua oſcillationem inchoans in ſitu a c A d f perveneritque poſtmo-
              <lb/>
            dum in ſitum o c A d p, retentiſque denominationibus |in præcedente paragra-
              <lb/>
            pho factis, ponatur a o = x; </s>
            <s xml:id="echoid-s3347" xml:space="preserve">erit f p = {gx/γ}: </s>
            <s xml:id="echoid-s3348" xml:space="preserve">unde (ſi nempe centrum gravita-
              <lb/>
            tis omnis aquæ deſcendiſſe putetur ex F in O) erit vi præcedentis paragraphi
              <lb/>
            A O = {g X (a - x) X (f + {1/2}
              <emph style="super">b</emph>
            - {bx/2a}) + γ X (a + {gx/γ}) X (φ + {1/2}
              <emph style="super">β</emph>
            + {βgx/2αγ}) + Mm/ga + γα + M}</s>
          </p>
          <p>
            <s xml:id="echoid-s3349" xml:space="preserve">Inde deducitur deſcenſus centri gravitatis ſeu deſcenſus actualis
              <lb/>
            F O = {(b - β + f - φ)gx - ({bg/2a} + {bgg/2αγ}) xx/ga + γα + M}</s>
          </p>
          <p>
            <s xml:id="echoid-s3350" xml:space="preserve">Sit nunc velocitas aquæ in tubo a c (cum nempe ſuperficies eſt in o) ta-
              <lb/>
            lis quæ reſpondeat altitudini v, & </s>
            <s xml:id="echoid-s3351" xml:space="preserve">erit tunc aſcenſus potent. </s>
            <s xml:id="echoid-s3352" xml:space="preserve">aquæ in altero tubo
              <lb/>
            = {gg/γγ} v: </s>
            <s xml:id="echoid-s3353" xml:space="preserve">pariterque aſcenſus potent. </s>
            <s xml:id="echoid-s3354" xml:space="preserve">aquæ c A d, erit proportionalis altitudini v,
              <lb/>
            eamque proinde ponemus = N v (ubi N pendet à figura utris c A d & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">deter-
              <lb/>
            minari poteſt per §. </s>
            <s xml:id="echoid-s3356" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s3358" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s3359" xml:space="preserve">Jam vero ſi multiplicatis ubique aſcenſibus po-
              <lb/>
            tentialibus per ſuas maſſas producta dividantur per ſummam maſſarum, habebi-
              <lb/>
            tur aſcenſ{us} potent. </s>
            <s xml:id="echoid-s3360" xml:space="preserve">omnis aquæ o c A d p =
              <lb/>
            {(ga - gx + {αgg/γ} + {g
              <emph style="super">3</emph>
            x/γγ} + MN)v/ga + γα + M}</s>
          </p>
          <p>
            <s xml:id="echoid-s3361" xml:space="preserve">Et quia hic aſcenſus potentialis eſt æqualis deſcenſui actuali F O paullo ante
              <lb/>
            invento, </s>
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