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

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            <s xml:id="echoid-s7112" xml:space="preserve">
              <pb o="241" file="0255" n="255" rhead="SECTIO DECIMA."/>
            plitudinis, cujus altitudo ſit plusquam 10000 vicibus major altitudine com-
              <lb/>
            muni barometri, invenimus autem ſupra art. </s>
            <s xml:id="echoid-s7113" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s7114" xml:space="preserve">numerum n ( qui idem ſi-
              <lb/>
            gnificabat) = 6004. </s>
            <s xml:id="echoid-s7115" xml:space="preserve">Ergo jam tuto affirmabimus ( ubique enim quæ negle-
              <lb/>
            ximus majorem vim pulveri arguunt) ineſſe pulveri pyrio vim elaſticam,
              <lb/>
            minimum decies millies majorem vi elaſtica aëris ordinarii. </s>
            <s xml:id="echoid-s7116" xml:space="preserve">Apparet autem
              <lb/>
            ſimul ex comparatione numerorum 10000 & </s>
            <s xml:id="echoid-s7117" xml:space="preserve">6004, quantum circiter vi pul-
              <lb/>
            veris decedat ab hiatibus ſæpe dictis. </s>
            <s xml:id="echoid-s7118" xml:space="preserve">Equidem iſtud decrementum majus pu-
              <lb/>
            taſſem: </s>
            <s xml:id="echoid-s7119" xml:space="preserve">Confirmatus autem ſum hoc calculo in re de qua aliquando me cer-
              <lb/>
            tiorem voluit vir harum rerum gnarus, nullum nempe ſe in tormentis nota-
              <lb/>
            bile obſervaſſe decrementum, cum lumen accenſorium diuturno uſu ſupra
              <lb/>
            modum amplificatum eſſet in obſidio.</s>
            <s xml:id="echoid-s7120" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7121" xml:space="preserve">(IX) Verum ut ex æquatione noſtra quædam corollaria deduci poſ-
              <lb/>
            ſint faciliora quam vis proxime tantum vera, mutabimus quantitatem lo-
              <lb/>
            garithmicalem in ſeriem. </s>
            <s xml:id="echoid-s7122" xml:space="preserve">Eſt autem
              <lb/>
            - log. </s>
            <s xml:id="echoid-s7123" xml:space="preserve">(1 - {(f + φ)v/(F - f)√(bPp)}) = {(f + φ)v/(F - f)√(b P p)}
              <lb/>
            + {(f + φ)
              <emph style="super">2</emph>
            vv/2(F - f)
              <emph style="super">2</emph>
            X b P p} + {(f + φ)
              <emph style="super">3</emph>
            v
              <emph style="super">3</emph>
            /3(F - f)
              <emph style="super">3</emph>
            X b P p√(b P p)} + &</s>
            <s xml:id="echoid-s7124" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7125" xml:space="preserve">Iſtoque valore ſubſtituto in æquatione ultima art. </s>
            <s xml:id="echoid-s7126" xml:space="preserve">(VII) fit
              <lb/>
            log. </s>
            <s xml:id="echoid-s7127" xml:space="preserve">{a/b} = {Fvv/2(F - f). </s>
            <s xml:id="echoid-s7128" xml:space="preserve">b P} + {F.</s>
            <s xml:id="echoid-s7129" xml:space="preserve">(f + φ)v
              <emph style="super">3</emph>
            /3.</s>
            <s xml:id="echoid-s7130" xml:space="preserve">(F - f)
              <emph style="super">2</emph>
            bP√(bPp)} + &</s>
            <s xml:id="echoid-s7131" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7132" xml:space="preserve">
              <lb/>
            Notabimus hic iſtam æquationem perfecte convenire cum æquatione ultima
              <lb/>
            art. </s>
            <s xml:id="echoid-s7133" xml:space="preserve">(II) ſi aperturæ f & </s>
            <s xml:id="echoid-s7134" xml:space="preserve">φ ponantur = 0: </s>
            <s xml:id="echoid-s7135" xml:space="preserve">quod enim hic indicatur per {1/2} vv
              <lb/>
            & </s>
            <s xml:id="echoid-s7136" xml:space="preserve">n P ibi eſt α & </s>
            <s xml:id="echoid-s7137" xml:space="preserve">P, convenientibus denominationibus reliquis.</s>
            <s xml:id="echoid-s7138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7139" xml:space="preserve">(X) Ut appareat, quantum proxime altitudo jactus ab aperturis dimi-
              <lb/>
            nuatur, ſi iſtæ aperturæ ſint minimæ, inſerviet hæc æquatio. </s>
            <s xml:id="echoid-s7140" xml:space="preserve">Intelligatur per
              <lb/>
            α altitudo ad quam globus pervenire poſſit in vacuo, ſi nulla auræ quantitas
              <lb/>
            per aperturas avolare ponatur, & </s>
            <s xml:id="echoid-s7141" xml:space="preserve">erit decrementum iſtius altitudinis ab erup-
              <lb/>
            tione auræ per easdem aperturas oriundum proxime hoc
              <lb/>
            [(2α)
              <emph style="super">{3/2}</emph>
            X (f + φ)]: </s>
            <s xml:id="echoid-s7142" xml:space="preserve">[3F X √ (bPp].</s>
            <s xml:id="echoid-s7143" xml:space="preserve"/>
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