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

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            <s xml:id="echoid-s1906" xml:space="preserve">
              <pb o="70" file="0084" n="84" rhead="HYDRODYNAMICÆ."/>
            catum fuit, in æquatione paragraphi decimi ponendum x = o, ſint
              <unsure/>
            ulque
              <lb/>
            ſolus primus ſeriei terminus adhibendus rurſusque ponendum m α pro
              <lb/>
            √(mmαα - 2nn); </s>
            <s xml:id="echoid-s1907" xml:space="preserve">atque ſic fit
              <lb/>
            t = {2mα/n}√a.</s>
            <s xml:id="echoid-s1908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1909" xml:space="preserve">Tum denique tempus, quod impenditur in deſcenſum ſuperficiei per
              <lb/>
            altitudinem a - c exprimetur in ſimili hypotheſi hac æquatione
              <lb/>
            t = {2ma/n} (√a - √c).</s>
            <s xml:id="echoid-s1910" xml:space="preserve">}</s>
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          <p>
            <s xml:id="echoid-s1911" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1912" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1913" xml:space="preserve">Præmiſſæ æquationes non accurate quidem, proxime tamen
              <lb/>
            ſatisfacient, cum vas non infinitæ, permagnæ tamen amplitudinis eſt: </s>
            <s xml:id="echoid-s1914" xml:space="preserve">imo
              <lb/>
            non multum admodum defie
              <unsure/>
            ient, cum numerus m vel mediocriter ſuperat
              <lb/>
            numerum n. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">Liceat quædam hic verba adjicere circa experimentum quod in
              <lb/>
            fine paragraphi undecimi indicavi, deturque hæc venia inſtituto noſtro,
              <lb/>
            quod in phænomenis motuum experientia cognitis potiſſimum verſatur il-
              <lb/>
            luſtrandis examinandisque. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">Dixi autem in citato paragrapho cum aqua ho-
              <lb/>
            rizontaliter effluit, primam guttulam totam ſtatim obtinere amplitudinem
              <lb/>
            jactus; </s>
            <s xml:id="echoid-s1917" xml:space="preserve">atque idem hoc quidem indicat theoria pro vaſis ampliſſimis; </s>
            <s xml:id="echoid-s1918" xml:space="preserve">at ve-
              <lb/>
            ro in vaſis mediocriter amplis, quædam guttulæ minori impetu effluere de-
              <lb/>
            berent, priusquam punctum maximæ velocitatis adſit, hæque guttulæ in-
              <lb/>
            cidere deberent in locum aliquem medium inter maximum jactum & </s>
            <s xml:id="echoid-s1919" xml:space="preserve">pun-
              <lb/>
            ctum, quod foramini verticaliter reſpondet; </s>
            <s xml:id="echoid-s1920" xml:space="preserve">atque hoc etiam ita fieri ob-
              <lb/>
            ſervavi, ex vaſis amplitudinis veluti decies foramine majoris. </s>
            <s xml:id="echoid-s1921" xml:space="preserve">Verum cum
              <lb/>
            experimentum aliquando ſumerem de vaſe pedem dimidium alto, quod am-
              <lb/>
            plitudinem præter propter centuplam haberet foraminis, ne minima quidem
              <lb/>
            particula aquæ, quantum videre potui, notabiliter à jactu aquæ pleno de-
              <lb/>
            fecit. </s>
            <s xml:id="echoid-s1922" xml:space="preserve">Videamus itaque quænam aquæ quantitas in hoc caſu effluere deberet
              <lb/>
            ante punctum maximæ velocitatis; </s>
            <s xml:id="echoid-s1923" xml:space="preserve">erit autem tanta, quantam continet cy-
              <lb/>
            lindrus ejusdem amplitudinis in altitudine
              <lb/>
            a - a: </s>
            <s xml:id="echoid-s1924" xml:space="preserve">({mmαα - nn/nn})
              <emph style="super">nn: (mmαα - 2nn)</emph>
              <lb/>
            (vid. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1926" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">ſub. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">fin.)</s>
            <s xml:id="echoid-s1929" xml:space="preserve">; </s>
            <s xml:id="echoid-s1930" xml:space="preserve">nec differt fere hæc minima altitudo ab hac multo com-
              <lb/>
            pendioſiori, nempe {2nna/mmαα} log. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">{mα/n} (vid. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">11.) </s>
            <s xml:id="echoid-s1934" xml:space="preserve">ubi nunc per {n/m} </s>
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