Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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rhead
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HYDRODYNAMICÆ
"/>
(M X {Nv/M} + ndx X o): </
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>
<
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xml:id
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xml:space
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">(M + ndx) = {Nv/M + ndx}. </
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<
s
xml:id
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xml:space
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">Poſtquam vero particula
<
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n d x ſuperne jam affuſa eſt, communem acquiſivit motum cum aqua proxi-
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me inferiori, ſicque fit aſcenſus potentialis ejusdem aquæ in ſitu c d m l o n p i c
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æqualis tertiæ proportionali ad ſpatium C D L O N P I C (M + ndx), ſpa-
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tium D t u x y O L D (N + ndx) & </
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<
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xml:space
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">altitudinem v + dv, id eſt, =
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{(N + ndx) x (v + dv)/M + ndx}, cujus exceſſus ſupra priorem aſcenſum potentialem eſt =
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{Ndv + nvdx + ndxdv/M + dx} =, rejectis differentialibus ſecundi ordinis, {Ndv + nvdx/M}.
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</
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<
s
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xml:space
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">Habetur igitur talis æquatio {Ndv + nvdx/M} = {nadx/M}, quæ ut prior per tra-
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ctata & </
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<
s
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xml:space
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">ad finem deducta dat
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x = {N/n} log. </
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<
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xml:space
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">{a/a - v}, vel
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v = a X (1 - c {-nx/N})
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quæ ſolutio valet pro affuſione laterali.</
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<
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<
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xml:space
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">Scholion 1.</
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xml:space
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">Sunt hæ æquationes inter ſe admodum diverſæ; </
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<
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xml:space
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">diverſitas au-
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tem eo major quo minoris eſt amplitudinis vas; </
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xml:space
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">& </
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<
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xml:space
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">ſi quidem amplitudo va-
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ſis ſuprema in cd quaſi infinita ſit præ amplitudine foraminis, evaneſcit n
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præ m fitque in priori caſu ſicut in poſteriori.
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</
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<
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xml:space
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">v = a X (1 - c
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)
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Eſt igitur hâc in hypotheſi motus utrobique idem quod haud difficulter
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quisque prævidere potuerit. </
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<
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xml:space
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">Celerior autem ſemper eſt cæteris paribus mo-
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tus in priori affuſione, quam in altera.</
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<
s
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">Conveniet hic rem etiam phyſice explicare, ut eam diſtinctius in omni-
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bus phænomenis percipere poſſimus.</
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<
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">quamcunque directionem habentis bre-
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vioris delineationis gratia cylindrus verticalis cum foramine in fundo, nempe
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G H N D (Fig. </
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xml:space
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<
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cia RS & </
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