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

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            luſus hydraulicus, venam proſilientem D O videre, quæ æqualibus incre-
              <lb/>
            mentis æqualibusque temporum intervallis, quod utrumque fieri poteſt,
              <lb/>
            ſubſultim creſcat.</s>
            <s xml:id="echoid-s4312" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4313" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">14. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">Propoſitum nunc ſit motum fluidi exilientis indagare, cum per
              <lb/>
            ſingula foramina alia atque alia fluida transfluunt. </s>
            <s xml:id="echoid-s4316" xml:space="preserve">Fluida autem leviora con-
              <lb/>
            tinue ponenda eſſe apparet, quo ſunt altius poſita, ne motus turbetur,
              <lb/>
            quod fit cum eodem tempore fluidum inferius aſcendit, ſuperiore deſcen-
              <lb/>
            dente, per commune foramen. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">Innoteſcet hoc modo quisnam ſit motus
              <lb/>
            in aquis ex vaſe effluentibus undique clauſo præter foraminulum aliquod ſu-
              <lb/>
            perne exiſtens, quod aëri tranſitum concedit. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">Hypotheſin vero infinitæ va-
              <lb/>
            ſis cylindrici amplitudinis ratione foraminum retinebimus, atque porro
              <lb/>
            gravitatem ſpecificam fluidi per D exilientis deſignabimus per A, illiusque
              <lb/>
            quod per G transfluit notabimus littera B, ſimiliterque gravitates ſpecificas
              <lb/>
            fluidorum per foramina, F, H, &</s>
            <s xml:id="echoid-s4319" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4320" xml:space="preserve">fluentium indicabimus reſpective litte-
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            ris C, D, &</s>
            <s xml:id="echoid-s4321" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4322" xml:space="preserve">Denique cum etiam conſiderandæ hic ſint altitudines diver-
              <lb/>
            ſorum fluidorum, quorum quidem, ob figuram vaſis cylindricam ſolum
              <lb/>
            infimum effluens altitudinem mutat, vocabimus x altitudinem fluidi infimi
              <lb/>
            ſupra foramen D, fluidorum reliquorum, eo quo ſibi ſuperincumbunt or-
              <lb/>
            dine, altitudines deſignabimus reſpective per b, c, d &</s>
            <s xml:id="echoid-s4323" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4324" xml:space="preserve">reliquas denomi-
              <lb/>
            nationes paragraphi undecimi retinebimus; </s>
            <s xml:id="echoid-s4325" xml:space="preserve">quibus ita præparatis compu-
              <lb/>
            tus inſtituetur ut §. </s>
            <s xml:id="echoid-s4326" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4327" xml:space="preserve">factum eſt, neque enim quicquam aliud inſuper ob-
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            ſervandum eſt, quam ut maſſæ guttularum iisdem tempusculis per diverſa
              <lb/>
            foramina transeuntium non ſimpliciter ex mole, ſed etiam ex gravitate ſpe-
              <lb/>
            cificia æſtimentur: </s>
            <s xml:id="echoid-s4328" xml:space="preserve">deſcenſus autem actualis pro ſingulis fluidis erit ſeorſim ſu-
              <lb/>
            mendus: </s>
            <s xml:id="echoid-s4329" xml:space="preserve">Hiſce veſtigiis inſiſtendo reperitur talis primo æquatio
              <lb/>
            A v + {nn/αα} B v + {nn/ββ} C v + {nn/γγ} D v + &</s>
            <s xml:id="echoid-s4330" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4331" xml:space="preserve">= A x + B b + C c + D d, + &</s>
            <s xml:id="echoid-s4332" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4333" xml:space="preserve">quæ reducta dat
              <lb/>
            v = (A x + B b + C c + D d + &</s>
            <s xml:id="echoid-s4334" xml:space="preserve">c.)</s>
            <s xml:id="echoid-s4335" xml:space="preserve">: </s>
            <s xml:id="echoid-s4336" xml:space="preserve">(A + {nn/αα} B + {nn/ββ} C + {nn/γγ} D + &</s>
            <s xml:id="echoid-s4337" xml:space="preserve">c.)</s>
            <s xml:id="echoid-s4338" xml:space="preserve"/>
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            <s xml:id="echoid-s4339" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4340" xml:space="preserve">15. </s>
            <s xml:id="echoid-s4341" xml:space="preserve">Si duo ſint liquores, erunt duo termini tam in numeratore
              <lb/>
            quam in denominatore ſumendi & </s>
            <s xml:id="echoid-s4342" xml:space="preserve">tres termini cum tres fuerint liquores, atque
              <lb/>
            ſic porro: </s>
            <s xml:id="echoid-s4343" xml:space="preserve">Si proinde liquor effluens ſit, v. </s>
            <s xml:id="echoid-s4344" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4345" xml:space="preserve">mercurius, ipſique ſuperin-
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            cumbat aqua ſtatuanturque gravitates ſpecificæ horum liquorum ut 14. </s>
            <s xml:id="echoid-s4346" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s4347" xml:space="preserve"/>
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