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

Table of Notes

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            concipe foramen D, priori C æquale, & </s>
            <s xml:id="echoid-s5615" xml:space="preserve">in eadem altitudine poſitum, ita ut
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            tanta aquarum copia effluat per D, quanta fuperius injicitur, ipſumque vas
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            E D F conſtanter plenum ſervetur. </s>
            <s xml:id="echoid-s5616" xml:space="preserve">Porro puta aquas per D effluentes perpe-
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            tuo impingere in alas alicujus rotæ, quæ hoc modo circumacta aquas alias ele-
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            vet: </s>
            <s xml:id="echoid-s5617" xml:space="preserve">Loco iſtius machinæ deſcribitur in figura ſimplex vectis volubilis circa H,
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            ponendo talem vectem continue alium atque alium adeſſe præ foramine D,
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            qui aquas excipiat, atque altera ſua extremitate aquas hauriat, eaſdemque ad
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            datam altitudinem elevet.</s>
            <s xml:id="echoid-s5618" xml:space="preserve"/>
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            <s xml:id="echoid-s5619" xml:space="preserve">His ita poſitis inquiram primo in potentiam abſolutam, quæ aquas per fo-
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            ramen C ad altitudinem C E elevat; </s>
            <s xml:id="echoid-s5620" xml:space="preserve">deinde quoque in potentiam abſolutam, quæ
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            requiritur in G ad vectem eadem velocitate movendum, quâ movetur ab im-
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            pulſu aquarum D G.</s>
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            <s xml:id="echoid-s5622" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5623" xml:space="preserve">33. </s>
            <s xml:id="echoid-s5624" xml:space="preserve">Sit amplitudo foraminis C vel D = n, amplitudo A B = m, ve-
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            locitas aquarum in C vel D = v, pondus cylindri ſuper foramine C aut D ad
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            altitudinem C E extructi = p: </s>
            <s xml:id="echoid-s5625" xml:space="preserve">tempus fluxus = t; </s>
            <s xml:id="echoid-s5626" xml:space="preserve">erit pondus P = {m/n} p: </s>
            <s xml:id="echoid-s5627" xml:space="preserve">ve-
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            locitas, qua pondus dum aquæ expelluntur deſcendit = {n/m} v: </s>
            <s xml:id="echoid-s5628" xml:space="preserve">eſt igitur (per
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            §. </s>
            <s xml:id="echoid-s5629" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s5630" xml:space="preserve">potentia abſoluta in aquas per C ejectas impenſa = {m/n} p X {n/m} v X t = p v t.</s>
            <s xml:id="echoid-s5631" xml:space="preserve"/>
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            <s xml:id="echoid-s5632" xml:space="preserve">§. </s>
            <s xml:id="echoid-s5633" xml:space="preserve">34. </s>
            <s xml:id="echoid-s5634" xml:space="preserve">Ut jam potentia abſoluta in gyrationem vectis G L circa punctum
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            Himpenfa determinetur, notandum eſt illam minime ſibimet conſtare; </s>
            <s xml:id="echoid-s5635" xml:space="preserve">mutari
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            enim à mutata velocitate, quacum vectis circumagitur. </s>
            <s xml:id="echoid-s5636" xml:space="preserve">Igitur faciemus ve-
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            locitatem qua extremitas ejus in G movetur = V. </s>
            <s xml:id="echoid-s5637" xml:space="preserve">Hoc autem modo aquæ
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            impingere cenſendæ ſunt in G velocitate v - V, atque ſic preſſionem exerce-
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            re, quæ fit = ({v - V/v})
              <emph style="super">2</emph>
            p: </s>
            <s xml:id="echoid-s5638" xml:space="preserve">(ſunt enim preſſiones in ratione quadrata velo-
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            citatum fluidi impingentis atque pro velocitate v ponitur preſſio = p). </s>
            <s xml:id="echoid-s5639" xml:space="preserve">Iſta
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            vero preſſio eſt loco potentiæ moventis; </s>
            <s xml:id="echoid-s5640" xml:space="preserve">poſſumus nempe loco preſſionis fluidi
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            ponere pondus vecti ſuperincumbens in G, quod ſit = ({v - V/v})
              <emph style="super">2</emph>
            p. </s>
            <s xml:id="echoid-s5641" xml:space="preserve">Iſtud
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            vero pondus eadem velocitate movebitur quâ punctum G, nempe velocitate V,
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            agitque durante tempore t: </s>
            <s xml:id="echoid-s5642" xml:space="preserve">Eſt igitur potentia abſoluta ad rotationem vectis du-
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            rante tempore t & </s>
            <s xml:id="echoid-s5643" xml:space="preserve">velocitate V requiſita = ({v - V/v})
              <emph style="super">2</emph>
            p X V X t.</s>
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