Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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          <pb o="191" file="0205" n="205" rhead="SECTIO NONA."/>
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        <div xml:id="echoid-div229" type="section" level="1" n="181">
          <head xml:id="echoid-head229" xml:space="preserve">Scholium 1.</head>
          <p>
            <s xml:id="echoid-s5518" xml:space="preserve">(XIII.) </s>
            <s xml:id="echoid-s5519" xml:space="preserve">Ut appareat, non differre valorem iſtius potentiæ ab illa, quam
              <lb/>
            pro globo ejusdem ponderis p invenimus articulo V. </s>
            <s xml:id="echoid-s5520" xml:space="preserve">nempe {m N p/M}, demon-
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            ſtranda eſt æqualitas inter {n p (g - f)/Mc} & </s>
            <s xml:id="echoid-s5521" xml:space="preserve">{m N p/M} ſeu inter n (g - f) & </s>
            <s xml:id="echoid-s5522" xml:space="preserve">m N c: </s>
            <s xml:id="echoid-s5523" xml:space="preserve">iſta
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            vero æqualitas deducenda eſt ex eo, quod extremitates aquæ l & </s>
            <s xml:id="echoid-s5524" xml:space="preserve">o in eadem
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            ab horizonte altitudine poſitæ ſint; </s>
            <s xml:id="echoid-s5525" xml:space="preserve">inde enim ſequitur, ut demonſtravi-
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            mus art. </s>
            <s xml:id="echoid-s5526" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s5527" xml:space="preserve">eſſe aggregatum ex arcu a c multiplicato per {m N/M} & </s>
            <s xml:id="echoid-s5528" xml:space="preserve">ex linea M d
              <lb/>
            multiplicata per n = aggregato ex arcu a c M p pariter multiplicato per {m N/M}
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            & </s>
            <s xml:id="echoid-s5529" xml:space="preserve">ex linea M q multiplicata per n. </s>
            <s xml:id="echoid-s5530" xml:space="preserve">Adhibitis itaque denominationibus præ-
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            cedentis articuli, fit M e X {m N/M} + (2 - f) X n = (M e + M c) X {m N/M} +
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            (2 - g) X n, vel n (g - f) = m N c; </s>
            <s xml:id="echoid-s5531" xml:space="preserve">quæ æqualitas demonſtranda erat ad
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            demonſtrandam æqualitatem potentiarum tum pro globo tum pro aqua in
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            f applicandarum.</s>
            <s xml:id="echoid-s5532" xml:space="preserve"/>
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        <div xml:id="echoid-div230" type="section" level="1" n="182">
          <head xml:id="echoid-head230" xml:space="preserve">Scholium 2.</head>
          <p>
            <s xml:id="echoid-s5533" xml:space="preserve">(XIV) Quia potentia {n p (g - f)/M c} non differt ab {m N p/M} & </s>
            <s xml:id="echoid-s5534" xml:space="preserve">quantitas {m N/M}
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            eadem manet, quæcunque aquæ quantitas una revolutione hauriatur aut eji-
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            ciatur, erit potentia iſta proportionalis eidem quantitati aquæ ſingulis revolu-
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            tionibus ejectæ ſeu ponderi p. </s>
            <s xml:id="echoid-s5535" xml:space="preserve">Facile quoque demonſtratu eſt, ſi eadem aqua-
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            rum quantitas, eadem potentia movente eademque velocitate ad parem altitudi-
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            nem verticalem elevetur ſuper ſimplici plano, quod ad hunc finem debite ver-
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            ſus horizontem inclinatum ſit, fore ut tempus elevationis quoque idem ſit.</s>
            <s xml:id="echoid-s5536" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5537" xml:space="preserve">Igitur eadem potentia abſoluta requiritur in cochlea Archimedis, quam
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            ſuper plano inclinato, ad quod omnes machinæ reduci poſſunt, nec ullam
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            habet iſta cochlea prærogativam præ reliquis machinis in theoria ſpectatis.
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            </s>
            <s xml:id="echoid-s5538" xml:space="preserve">Fortaſſe in praxi minus eſt obnoxia incommodis §. </s>
            <s xml:id="echoid-s5539" xml:space="preserve">26. </s>
            <s xml:id="echoid-s5540" xml:space="preserve">indicatis: </s>
            <s xml:id="echoid-s5541" xml:space="preserve">nequaquam
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            improbo ejus uſum, ſed nec eam præfero præ antliis Cteſibianis.</s>
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