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

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              <pb o="92" file="0106" n="106" rhead="HYDRODYNAMICÆ"/>
            altitudinem ſupra foramen, exprimat H G amplitudinem vaſis in illo loco.
              <lb/>
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            <s xml:id="echoid-s2607" xml:space="preserve">Deinde fiat tertia curva t r u, cujus applicata H r ſit ubique æqualis tertiæ con-
              <lb/>
            tinue proportionali ad G H & </s>
            <s xml:id="echoid-s2608" xml:space="preserve">P L ſeu cujus applicata H rſit = P L
              <emph style="super">2</emph>
            : </s>
            <s xml:id="echoid-s2609" xml:space="preserve">G H.</s>
            <s xml:id="echoid-s2610" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2611" xml:space="preserve">Dicatur ſpatium D C I L = M, ſpatium D t u L = N, & </s>
            <s xml:id="echoid-s2612" xml:space="preserve">erit aſcen-
              <lb/>
            ſus potentialis aquæ in vaſe contentæ, poſtquam prædicta quantitas jam efflu-
              <lb/>
            xit (per §. </s>
            <s xml:id="echoid-s2613" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2614" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s2615" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s2616" xml:space="preserve">= {N/M}v. </s>
            <s xml:id="echoid-s2617" xml:space="preserve">Effluere porro intelligatur particula p l o n, ſu-
              <lb/>
            perficiesque c d deſcendere in e f, erit jam velocitatis altitudo pro particula p l o n
              <lb/>
            = v + d v; </s>
            <s xml:id="echoid-s2618" xml:space="preserve">atque ſi nunc conſtruatur parallelogrammum L x y O, cujus latus
              <lb/>
            L O ſit = l o & </s>
            <s xml:id="echoid-s2619" xml:space="preserve">alterum L x = P L, erit aſcenſus potentialis ejusdem aquæ
              <lb/>
            in ſitu e f m l o n p i e æqualis tertiæ proportionali ad ſpatium E F L O N P I E,
              <lb/>
            (quod rurſus eſt = M, quia P L O N exprimit magnitudinem guttulæ p l o n,
              <lb/>
            dum C D F E exprimit quantitatem minimam c d f e iſti guttulæ æqualem)
              <lb/>
            ſpatium w u x y O L F (quod eſt = ſpatio N - D t w F + L x yO, unde ſi
              <lb/>
            P L ſeu L x ponatur = n, C D = m, L O = lo = dx, erit D t = {nn/m},
              <lb/>
            D F = {n/m} dx, hinc ſpatiolum D tw F = {n
              <emph style="super">3</emph>
            /mm} dx & </s>
            <s xml:id="echoid-s2620" xml:space="preserve">ſpatium L xy O =
              <lb/>
            ndx & </s>
            <s xml:id="echoid-s2621" xml:space="preserve">denique ſpatium w uxy O L F = N - {n
              <emph style="super">3</emph>
            /mm} dx + ndx) & </s>
            <s xml:id="echoid-s2622" xml:space="preserve">altitudi-
              <lb/>
            nem v + dv. </s>
            <s xml:id="echoid-s2623" xml:space="preserve">Eſt igitur aſcenſus potentialis modo dictus = (N - {n
              <emph style="super">3</emph>
            /mm} dx + ndx) X
              <lb/>
            (v + dv): </s>
            <s xml:id="echoid-s2624" xml:space="preserve">M = rejectis differentialibus ſecundi ordinis {N/M} v + {N/M} dv
              <lb/>
            - {n
              <emph style="super">3</emph>
            /mmM} vdx + {n/M}vdx, ſic ut incrementum aſcenſus potentialis, quod aquæ
              <lb/>
            acceſſit dum guttula plon effluxit, ſit = {N/M}dv - {n
              <emph style="super">3</emph>
            /mmM}vdx + {n/M}vdx, ubi
              <lb/>
            ſpatia N & </s>
            <s xml:id="echoid-s2625" xml:space="preserve">M ſunt conſtantis magnitudinis ob aquæ continuam affuſionem. </s>
            <s xml:id="echoid-s2626" xml:space="preserve">Non
              <lb/>
            conſideramus in hoc caſu primo aſcenſum potentialem guttulæ cdfe, quæ af-
              <lb/>
            funditur dum altera æqualis plon effluit, quia iſte aſcenſus non generatur vi
              <lb/>
            interna, neque enim aqua inferior poſt ſe trahere ponitur particulam cdfe,
              <lb/>
            quin potius hanc vi quadam extrinſeca continue affundi conſideramus, idque
              <lb/>
            nec ma
              <unsure/>
            jori nec minore velocitate quam quæ eſt ſuperficiei ef. </s>
            <s xml:id="echoid-s2627" xml:space="preserve">Ergo omne
              <lb/>
            incrementum hic conſiderandum, eſt ut diximus
              <lb/>
            {N/M}dv - {n
              <emph style="super">3</emph>
            /mmM}vdx + {n/M} vdx.</s>
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