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

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              <pb o="98" file="0112" n="112" rhead="HYDRODYNAMICÆ"/>
            ctum in motum aquarum exerere debeat, quiſque videt ex eo, quod in utro-
              <lb/>
            que modo omnis aquæ tubum ingredientis inertia ſit ab aqua inferiore ſupe-
              <lb/>
            randa. </s>
            <s xml:id="echoid-s2761" xml:space="preserve">Sed idem etiam à priori demonſtrari poterit inquirendo in motum, qui
              <lb/>
            inde oriri debeat, ſecundum æquationem paragraphi octavi Sect. </s>
            <s xml:id="echoid-s2762" xml:space="preserve">III. </s>
            <s xml:id="echoid-s2763" xml:space="preserve">quæ hæc eſt:
              <lb/>
            </s>
            <s xml:id="echoid-s2764" xml:space="preserve">Ndv - {mmvydx/nn} + {mmvdx/y} = - yxdx; </s>
            <s xml:id="echoid-s2765" xml:space="preserve">
              <lb/>
            accommodabitur autem ad præſentem caſum, ſi pro m, x & </s>
            <s xml:id="echoid-s2766" xml:space="preserve">- d x ſubſtituas re-
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            ſpective n, a, & </s>
            <s xml:id="echoid-s2767" xml:space="preserve">{ndx/y}, (cujus rei ratio patebit, ſi hæc cum illis contuleris) ſi-
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            mulque y infinitum ponas; </s>
            <s xml:id="echoid-s2768" xml:space="preserve">tunc enim evaneſcit tertius æquationis terminus,
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            fitque omnino, ut pro præſenti negotio ſupra invenimus,
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            Ndv + nvdx = nadx.</s>
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            <s xml:id="echoid-s2770" xml:space="preserve">Poſtquam in his ſcholiis motus utriuſque indolem, quantum ſimplexrei
              <lb/>
            conſideratio phyſica permittit, eorumque differentiam oſtendimus, ſimulque
              <lb/>
            modum illos producendi ad legem hypotheſeos mechanicum tradidimus, ſu-
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            pereſt, ut reliqua phænomena notabiliora etiam indicentur, quod nunc faciam.</s>
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          <head xml:id="echoid-head102" xml:space="preserve">Corollarium 1.</head>
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            <s xml:id="echoid-s2772" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2773" xml:space="preserve">8. </s>
            <s xml:id="echoid-s2774" xml:space="preserve">Si in vaſe R S N H omnè fundum abſit, erit orificium L M =
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            orificio R S; </s>
            <s xml:id="echoid-s2775" xml:space="preserve">poteſt etiam hoc ab illo ſuperari, ſi nempe vaſis divergant late-
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            ra. </s>
            <s xml:id="echoid-s2776" xml:space="preserve">In his autem caſibus nullum habet terminum altitudo v in æquatione
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            v = {mma/mm - nn} X (1 - c{n
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            - nmm/mmN} x)
              <lb/>
            & </s>
            <s xml:id="echoid-s2777" xml:space="preserve">fit infinita, ſi quantitas aquæ ejectæ indicata per n x eſt infinita.</s>
            <s xml:id="echoid-s2778" xml:space="preserve"/>
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            <s xml:id="echoid-s2779" xml:space="preserve">Id quidem per ſe patet ex æquatione, cum n eſt major quam m; </s>
            <s xml:id="echoid-s2780" xml:space="preserve">at
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            cum amplitudines orificiorum ſunt æquales, recurrendum eſt ad æquationem
              <lb/>
            differentialem paragraphi tertii, ex qua iſta æquatio proxima deducta fuit, nempe
              <lb/>
            {N/M}dv - {n
              <emph style="super">3</emph>
            /mmM}vdx + {n/M}vdx = {n/M}adx,
              <lb/>
            quæ poſito n = m dat N d v = n a d x, id eſt, v = {nax/N}, ubi v fit manifeſte in-
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            finita ſi x eſt infinita.</s>
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            <s xml:id="echoid-s2782" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2783" xml:space="preserve">9. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">Sin autem vaſi propoſito fundum ſit, atque in eo foramen, </s>
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