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

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              <pb o="69" file="0083" n="83" rhead="SECTIO QUARTA."/>
            enim foramen digito obturamus, moxque remoto digito aquas horizontali-
              <lb/>
            ter effluere ſinimus, nullam guttulam in terram delapſam obſervamus me-
              <lb/>
            diam inter jactum longiſſimum & </s>
            <s xml:id="echoid-s1880" xml:space="preserve">locum, qui foramini ad perpendiculum
              <lb/>
            reſpondeat.</s>
            <s xml:id="echoid-s1881" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1882" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">12. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">Prouti in proximo paragrapho determinavimus quantitates ut-
              <lb/>
            ut infinite parvas, deſcenſus aquæ internæ uti & </s>
            <s xml:id="echoid-s1885" xml:space="preserve">effluentis aquæ dum maxi-
              <lb/>
            ximum velocitatis gradum aqua attingit, ita nunc idem præſtabimus ratione
              <lb/>
            tempusculi. </s>
            <s xml:id="echoid-s1886" xml:space="preserve">Dico eutem ſufficere in æquatione §. </s>
            <s xml:id="echoid-s1887" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1888" xml:space="preserve">tempus exprimente,
              <lb/>
            ut in utraque ſerie unicus accipiatur terminus primus, quod apparebit cum
              <lb/>
            quis calculum ad duos extenderit terminos: </s>
            <s xml:id="echoid-s1889" xml:space="preserve">eſt igitur tempuſculum quæſi-
              <lb/>
            tum ſive
              <lb/>
            t = (2 - 2√{x/a}) X {√(mmαα - 2nn).</s>
            <s xml:id="echoid-s1890" xml:space="preserve">a/n}
              <lb/>
            hinc poſito pro x valore huc pertinente, qui in præcedente paragrapho fuit
              <lb/>
            definitus, fit
              <lb/>
            t = [2 - 2√1 - (log.</s>
            <s xml:id="echoid-s1891" xml:space="preserve">{mmαα/nn}): </s>
            <s xml:id="echoid-s1892" xml:space="preserve">{mmαα/nn}] X √({mmαα - 2 nn/nn})·a
              <lb/>
            vel poſito 1 - (log. </s>
            <s xml:id="echoid-s1893" xml:space="preserve">{mmαα/nn}): </s>
            <s xml:id="echoid-s1894" xml:space="preserve">{2mmαα/nn} pro reſpondente quantitate ſigno ra-
              <lb/>
            dicali involuta prodit
              <lb/>
            t = [(log.</s>
            <s xml:id="echoid-s1895" xml:space="preserve">{mmαα/nn}): </s>
            <s xml:id="echoid-s1896" xml:space="preserve">{mmαα/nn}] X √({mmαα - 2nn/nn})·a}
              <lb/>
            aut denique rejecta quantitate 2 nn in ſigno radicali, oritur t = {2n√a/mα}.</s>
            <s xml:id="echoid-s1897" xml:space="preserve">log.</s>
            <s xml:id="echoid-s1898" xml:space="preserve">{mα/n}.</s>
            <s xml:id="echoid-s1899" xml:space="preserve"/>
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            <s xml:id="echoid-s1900" xml:space="preserve">Eſt autem hoc tempusculum infinite parvum, quia, ut notum eſt, lo-
              <lb/>
            garithmus quantitatis infinitæ infinities minor eſt ipsâ quantitate. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">At vero
              <lb/>
            cum ſic ſtatim ab initio fluxus, aqua maxima ſua velocitate expellitur, mi-
              <lb/>
            rum prima fronte videbitur fortaſſe aliquibus, motum in inſtanti generari
              <lb/>
            finitum: </s>
            <s xml:id="echoid-s1902" xml:space="preserve">nemo tamen abſurdum putabit, maſſam infinitam, cujusmodi
              <lb/>
            eſt quantitas aquæ in vaſe infinito contentæ, poſſe tempuſculo infinitè parvo
              <lb/>
            motum producere finitum, idque ſolâ gravitatis actione.</s>
            <s xml:id="echoid-s1903" xml:space="preserve"/>
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            <s xml:id="echoid-s1904" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1905" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1906" xml:space="preserve">Si præterea in iſta vaſis infinite ampli poſitione tempus deple-
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            tionis, quod utique infinitum erit, exprimere velimus, erit, ut ſupra </s>
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