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

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            ertiæ quæ globo ineſt: </s>
            <s xml:id="echoid-s7055" xml:space="preserve">vi iſtius hypotheſeos avolabit aura per utramque aper-
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            turam eadem velocitate, cum alias poſita velocitate in lumine accenſorio
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            = √ A, & </s>
            <s xml:id="echoid-s7056" xml:space="preserve">velocitate globi = v, velocitas auræ in hiatu a
              <unsure/>
            globo ad ſuperfi-
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            ciem animæ relicto dicenda eſſet = √ A - v. </s>
            <s xml:id="echoid-s7057" xml:space="preserve">Venio nunc ad ſolutionem.</s>
            <s xml:id="echoid-s7058" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7059" xml:space="preserve">(VI) Primo notandum eſt, ſi elaſticitates auræ cenſeantur denſitatibus
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            proportionales, fore ut aura
              <unsure/>
            conſtanter eadem velocitate per utramque
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            aperturam avolet, uti vidimus in problemate §. </s>
            <s xml:id="echoid-s7060" xml:space="preserve">34. </s>
            <s xml:id="echoid-s7061" xml:space="preserve">iſtaque velocitas no-
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            minatim talis erit, quæ generetur ab altitudine auræ homogeneæ, cu-
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            jus pondus auram captam coërcere poſſit, ne ſe expandat. </s>
            <s xml:id="echoid-s7062" xml:space="preserve">Igitur deter-
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            minabitur dicta velocitas hoc modo: </s>
            <s xml:id="echoid-s7063" xml:space="preserve">ſit gravitas globi = 1, elaſticitas
              <lb/>
            ſeu pondus quod auram pulveris modo inflammati A C D B in illo com-
              <lb/>
            preſſionis ſtatu coërcere poſſit = P: </s>
            <s xml:id="echoid-s7064" xml:space="preserve">pondus pulveris adhibiti = p;
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            </s>
            <s xml:id="echoid-s7065" xml:space="preserve">erit pondus auræ pulveris modo inflammati etiam = p: </s>
            <s xml:id="echoid-s7066" xml:space="preserve">ſique lon-
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            gitudo A C ponitur = b, patet altitudinem auræ homogeneæ, quæ pondus
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            P habeat, fore = {P/p} b; </s>
            <s xml:id="echoid-s7067" xml:space="preserve">Igitur velocitas quacum aura recens nata per lumen
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            accenſorium avolat eſt = √({P/p} b), eademque velocitate durante tota ex-
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            ploſione ejicietur, idque non ſolum per lumen accenſorium, ſed & </s>
            <s xml:id="echoid-s7068" xml:space="preserve">proxime
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            per hiatum inter globum & </s>
            <s xml:id="echoid-s7069" xml:space="preserve">animam relictum.</s>
            <s xml:id="echoid-s7070" xml:space="preserve"/>
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            <s xml:id="echoid-s7071" xml:space="preserve">(VII) Sit nunc porro amplitudo animæ = F; </s>
            <s xml:id="echoid-s7072" xml:space="preserve">hiatus interceptus inter
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            globum & </s>
            <s xml:id="echoid-s7073" xml:space="preserve">animam = f: </s>
            <s xml:id="echoid-s7074" xml:space="preserve">amplitudo luminis accenſorii = Φ: </s>
            <s xml:id="echoid-s7075" xml:space="preserve">longitudo ani-
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            mæ = a, quantitas auræ ab initio exploſionis = g. </s>
            <s xml:id="echoid-s7076" xml:space="preserve">Intelligatur deinde glo-
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            bus perveniſſe ex E in e, dicaturque A C = x: </s>
            <s xml:id="echoid-s7077" xml:space="preserve">quantitas auræ eo temporis
              <lb/>
            puncto in tormento reſidua = z: </s>
            <s xml:id="echoid-s7078" xml:space="preserve">velocitas globi in iſto ſitu = v, reliquæ de-
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            nominationes fuerunt jam antea explicatæ.</s>
            <s xml:id="echoid-s7079" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s7080" xml:space="preserve">Quoniam elaſticitas per hypotheſin eſt directe ut quantitas & </s>
            <s xml:id="echoid-s7081" xml:space="preserve">recipro-
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            ce ut ſpatium, erit elaſticitas auræ in A c d B reſiduæ = {zb/gx} P: </s>
            <s xml:id="echoid-s7082" xml:space="preserve">quæ quidem
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            non tota in propellendum globum impenditur, ſed tantum pars ejus, quæ
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            ſe habeat ad totam ut F - f ad f. </s>
            <s xml:id="echoid-s7083" xml:space="preserve">Eſt itaque poſito d t pro elemento temporis
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            dv = {F - f/F} X {zb/gx} P X dt.
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            </s>
            <s xml:id="echoid-s7084" xml:space="preserve">Per methodum autem §. </s>
            <s xml:id="echoid-s7085" xml:space="preserve">34. </s>
            <s xml:id="echoid-s7086" xml:space="preserve">exhibitam, ubi quantitas aëris dato tempuſculo
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            effluens ſpecifice definita fuit, </s>
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