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

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            dv = (P + p - {ap/a - x}) X {dx/v}: </s>
            <s xml:id="echoid-s6786" xml:space="preserve">P, vel
              <lb/>
            Pvdv = (P - {xp/a - x}) dx, quæ integrata dat
              <lb/>
            {1/2} P vv = Px + px - ap log. </s>
            <s xml:id="echoid-s6787" xml:space="preserve">{a/a - x}.</s>
            <s xml:id="echoid-s6788" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6789" xml:space="preserve">Jam vero deſcenſu ponderis P per altitudinem x genita fuit vis viva P x,
              <lb/>
            de qua eidem ponderi ceu velocitate v moto ineſt pars {1/2} P v v ſeu P x + p x -
              <lb/>
            ap log. </s>
            <s xml:id="echoid-s6790" xml:space="preserve">{a/a - x}; </s>
            <s xml:id="echoid-s6791" xml:space="preserve">pars igitur vis vivæ quæ ad aërem tranſiit, eſt = - p x +
              <lb/>
            ap log. </s>
            <s xml:id="echoid-s6792" xml:space="preserve">{a/a - x}, quæ minor eſt altera §. </s>
            <s xml:id="echoid-s6793" xml:space="preserve">40. </s>
            <s xml:id="echoid-s6794" xml:space="preserve">definita.</s>
            <s xml:id="echoid-s6795" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6796" xml:space="preserve">Habeatur v. </s>
            <s xml:id="echoid-s6797" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s6798" xml:space="preserve">pes cubicus aëris naturali duplo denſioris, inveniètur
              <lb/>
            vis viva, quam iſte aër amittit, dum aëris naturalis circumfuſi denſitatem aſſu-
              <lb/>
            mit, ea quæ lapſu libero corporis 865. </s>
            <s xml:id="echoid-s6799" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6800" xml:space="preserve">per altitudinem unius pedis gene-
              <lb/>
            ratur.</s>
            <s xml:id="echoid-s6801" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6802" xml:space="preserve">Pari ſenſu pes cubicus aëris naturali triplo denſioris vim vivam habere
              <lb/>
            intelligitur talem quæ reſpondeat lapſui libero corporis 2898 lib. </s>
            <s xml:id="echoid-s6803" xml:space="preserve">per altitud.
              <lb/>
            </s>
            <s xml:id="echoid-s6804" xml:space="preserve">unius pedis, qui numerus nempe prodit cum ponitur p = 2240, ut §. </s>
            <s xml:id="echoid-s6805" xml:space="preserve">40; </s>
            <s xml:id="echoid-s6806" xml:space="preserve">
              <lb/>
            a = 3. </s>
            <s xml:id="echoid-s6807" xml:space="preserve">& </s>
            <s xml:id="echoid-s6808" xml:space="preserve">x = 2.</s>
            <s xml:id="echoid-s6809" xml:space="preserve"/>
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            <s xml:id="echoid-s6810" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6811" xml:space="preserve">43. </s>
            <s xml:id="echoid-s6812" xml:space="preserve">Perſpicuum eſt ex hoc conſenſu inter conſervationem virium vi-
              <lb/>
            varum aëri compreſſo & </s>
            <s xml:id="echoid-s6813" xml:space="preserve">corpori à data altitudine delapſo inſitarum, nullam
              <lb/>
            eſſe ad uſum machinarum perficiendum prærogativam ſperandam ex principio
              <lb/>
            aëris comprimendi, & </s>
            <s xml:id="echoid-s6814" xml:space="preserve">ubique valere regulas in præcedente ſectione exhibi-
              <lb/>
            tas. </s>
            <s xml:id="echoid-s6815" xml:space="preserve">Quia vero multis modis fit, ut aër non vi ſed natura ſit compreſſus aut
              <lb/>
            elaterem naturali majorem acquirat, ſpes certe eſt, poſſe hujuſmodi rebus na-
              <lb/>
            turalibus magna ad machinas movendas compendia excogitari, prouti D.
              <lb/>
            </s>
            <s xml:id="echoid-s6816" xml:space="preserve">Amontons jamjam docuit modum movendarum machinarum vi ignis. </s>
            <s xml:id="echoid-s6817" xml:space="preserve">Mihi
              <lb/>
            perſuadeo ſi omnis vis viva, quæ in carbonum pede cubico latet, ex eodem-
              <lb/>
            que combuſtione elicitur, utiliter ad machinam movendam impendatur, quod
              <lb/>
            plus inde profici poſſit, quam labore diurno octo aut decem hominum. </s>
            <s xml:id="echoid-s6818" xml:space="preserve">Etenim
              <lb/>
            carbones dum comburuntur aëris elafticitatem nonſolum inſigniter augent, ſed
              <lb/>
            & </s>
            <s xml:id="echoid-s6819" xml:space="preserve">ingentem aëris novi quantitatem generant.</s>
            <s xml:id="echoid-s6820" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s6821" xml:space="preserve">Ita Haleſius in veget. </s>
            <s xml:id="echoid-s6822" xml:space="preserve">ſtatiks deprehendit ex ſemipollice carbonis 180.</s>
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