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

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            <s xml:id="echoid-s3609" xml:space="preserve">
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            altitudini v, & </s>
            <s xml:id="echoid-s3610" xml:space="preserve">in ſitu infinite propinquo E F reſpondebit eadem velocitas
              <lb/>
            altitudini v - d v; </s>
            <s xml:id="echoid-s3611" xml:space="preserve">Et cum aſcenſus potentialis aquæ C D M L P I C ſit v, obti-
              <lb/>
            nebitur aſcenſus potent. </s>
            <s xml:id="echoid-s3612" xml:space="preserve">ejusdem aquæ in ſitu proximo E F M L O N P I E, ſi
              <lb/>
            multiplicetur maſſa E F M L P I E (n x - n d x) per ſuum aſcenſum potent.
              <lb/>
            </s>
            <s xml:id="echoid-s3613" xml:space="preserve">(v - d v) ut etiam guttula L O N P (n d x) per ſuum itidem aſcenſum poten-
              <lb/>
            tialem n n v, aggregatumque productorum dividatur per ſummam maſſarum
              <lb/>
            (n x): </s>
            <s xml:id="echoid-s3614" xml:space="preserve">habetur itaque iste aſcenſus potentialis = {(n x - n d x) x (v - d v) + n d x x n n v/nx}
              <lb/>
            ſeu {xv - vdx - xdv + nnvdx/x}.</s>
            <s xml:id="echoid-s3615" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3616" xml:space="preserve">Eſt proinde incrementum aſcenſus potent. </s>
            <s xml:id="echoid-s3617" xml:space="preserve">= {- vdx - xdv + nnvdx/x}.
              <lb/>
            </s>
            <s xml:id="echoid-s3618" xml:space="preserve">(conf. </s>
            <s xml:id="echoid-s3619" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3620" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s3622" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s3623" xml:space="preserve">Iſtud vero incrementum æquale cenſendum eſt cum de-
              <lb/>
            ſcenſu actuali infinitè parvo, qui (per §. </s>
            <s xml:id="echoid-s3624" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3625" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s3626" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3627" xml:space="preserve">& </s>
            <s xml:id="echoid-s3628" xml:space="preserve">per annotationem modo
              <lb/>
            datam) eſt = {(x - b)dx/x}. </s>
            <s xml:id="echoid-s3629" xml:space="preserve">Habetur itaque talis æquatio
              <lb/>
            - vdx - xdv + nnvdx = (x - b)dx,
              <lb/>
            quæ debito modo integrata mutatur in hanc
              <lb/>
            v = {1/nn - 2} X (x - {x
              <emph style="super">nn - 1</emph>
            /a
              <emph style="super">nn - 2</emph>
            }) - {b/nn - 1} X (1 - {x
              <emph style="super">nn - 1</emph>
            /a
              <emph style="super">nn - 1</emph>
            }).</s>
            <s xml:id="echoid-s3630" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3631" xml:space="preserve">Ex iſta vero æquatione talia ſequuntur corollaria.</s>
            <s xml:id="echoid-s3632" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3633" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3634" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">Fuerit amplitudo cylindri veluti infinita ratione foraminis, & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">
              <lb/>
            erit cènſendum v = {x - b/nn}; </s>
            <s xml:id="echoid-s3637" xml:space="preserve">ipſaque altitudo pro velocitate aquæ, dum
              <lb/>
            effluit, eſt = x - b. </s>
            <s xml:id="echoid-s3638" xml:space="preserve">Unde conſequens eſt, aquam effluere velocitate,
              <lb/>
            quam grave acquirit cadendo ex altitudine ſuperficiei internæ ſupra externam,
              <lb/>
            & </s>
            <s xml:id="echoid-s3639" xml:space="preserve">eo usque effluet, donec ambæ ſuperficies ſint ad libellam poſitæ, tunc-
              <lb/>
            que omnis motus ceſſabit: </s>
            <s xml:id="echoid-s3640" xml:space="preserve">adeoque eadem lege aquæ effluunt, quaſi fun-
              <lb/>
            dum ſitum I M mutaret cum T V.</s>
            <s xml:id="echoid-s3641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3642" xml:space="preserve">Cum vero foramen non poteſt ceu infinite parvum conſiderari, deſcen-
              <lb/>
            dit ſuperficies aquæ internæ infra externam; </s>
            <s xml:id="echoid-s3643" xml:space="preserve">atque ut innoteſcatad quamnam
              <lb/>
            profunditatem x y ſit deſcenſura ſuperficies C D, facienda eſt v = o, ſeu
              <lb/>
            (nn - 1)(a
              <emph style="super">nn - 1</emph>
            x - x
              <emph style="super">nn - 1</emph>
            a) = (nn - 2) X (a
              <emph style="super">nn - 1</emph>
            b - x
              <emph style="super">nn - 1</emph>
            b),
              <lb/>
            nunquam autem ſuperficies interna tantum deſcendet infra ſuperficiem </s>
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