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

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            <s xml:id="echoid-s2047" xml:space="preserve">
              <pb o="75" file="0089" n="89" rhead="SECTIO QUARTA."/>
            dv = o, ſive - {nndz/mm} + {na/mb}√{g/n}:</s>
            <s xml:id="echoid-s2048" xml:space="preserve">c
              <emph style="super">{mz/nb}√{g/n} = o</emph>
            , id eſt,
              <lb/>
            z = {nb/m}√{n/g}, X log.</s>
            <s xml:id="echoid-s2049" xml:space="preserve">({ma/nb}√{g/n})</s>
          </p>
          <p>
            <s xml:id="echoid-s2050" xml:space="preserve">Hæc autem altitudo multiplicata per altitudinem cylindri m dat quan-
              <lb/>
            titatem aquæ interea effluentis, nempe nb√{n/g} X log.</s>
            <s xml:id="echoid-s2051" xml:space="preserve">({ma/nb}√{g/n},) quæ quan-
              <lb/>
            titas, ut ſupra §. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2053" xml:space="preserve">præmonui, eſt infinita, quamvis tantum logarithmica-
              <lb/>
            liter, cujusmodi infinitum minus eſt, quam radix cujuscunque dimenſionis
              <lb/>
            datæ ex eodem infinito; </s>
            <s xml:id="echoid-s2054" xml:space="preserve">eſt ſcilicet log. </s>
            <s xml:id="echoid-s2055" xml:space="preserve">∞ minor quam ∞ {1/n}, quantuscunque
              <lb/>
            fuerit numerus n aſſignabilis. </s>
            <s xml:id="echoid-s2056" xml:space="preserve">Atque hoc ideo moneo, ut ſic intelliga-
              <lb/>
            tur, qui fiat, ut, ſi à vero infinito ratiocinamur ad quantitates valde ma-
              <lb/>
            gnas, quantitas iſta aquæ ſat parva evadat. </s>
            <s xml:id="echoid-s2057" xml:space="preserve">Cæterum corollaria formulæ
              <lb/>
            hæc ſunt.</s>
            <s xml:id="echoid-s2058" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2059" xml:space="preserve">(I) Si tubus annexus eſt cylindricus, fit z = {nb/m}log.</s>
            <s xml:id="echoid-s2060" xml:space="preserve">{ma/nb}:
              <lb/>
            </s>
            <s xml:id="echoid-s2061" xml:space="preserve">Igitur cæteris paribus hæc quantitas ſe habet, ut longitudo tubi annexi, quod
              <lb/>
            generaliter etiam verum eſt: </s>
            <s xml:id="echoid-s2062" xml:space="preserve">nam à mutato valore ipſius b cenſenda eſt non
              <lb/>
            mutari quantitas log.</s>
            <s xml:id="echoid-s2063" xml:space="preserve">{ma/nb}√{g/n} ob valorem infinitum numeri {m/n}.</s>
            <s xml:id="echoid-s2064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2065" xml:space="preserve">(II) Pro eodem orificio g cæterisque etiam paribus, ſequitur quantitas z
              <lb/>
            ſesquiplicatam rationem orificii extremi: </s>
            <s xml:id="echoid-s2066" xml:space="preserve">atque ſi idem tubus modo orifi-
              <lb/>
            cio ſtrictiori modo ampliori vaſi applicetur, erit quantitas aquæ in caſu prio-
              <lb/>
            ri ad ſimilem quantitatem in poſteriori, ut quadratum orificii amplioris, ad
              <lb/>
            quadratum orificii minoris.</s>
            <s xml:id="echoid-s2067" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2068" xml:space="preserve">(III) Denique obſervandum eſt valere totum ratiocinium pro omnibus
              <lb/>
            directionibus tubi, quod quivis perſpiciet qui §. </s>
            <s xml:id="echoid-s2069" xml:space="preserve">22. </s>
            <s xml:id="echoid-s2070" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s2071" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2072" xml:space="preserve">recte examinabit.
              <lb/>
            </s>
            <s xml:id="echoid-s2073" xml:space="preserve">Poterit igitur tubus adhiberi etiam horizontalis aut ſub quâcunque alia di-
              <lb/>
            rectione & </s>
            <s xml:id="echoid-s2074" xml:space="preserve">utcunque incurvus, ad quod præſertim in inſtituendis experimen-
              <lb/>
            tis animus erit advertendus. </s>
            <s xml:id="echoid-s2075" xml:space="preserve">Semper autem intelligetur per b longitudo tu-
              <lb/>
            bi, per a vero altitudo aquæ verticalis ſupra orificium extremum.</s>
            <s xml:id="echoid-s2076" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2077" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">Venio nunc ad tempus, quo iſtæ mutationes à quiete ad </s>
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