Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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272
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HYDRODYNAMICÆ
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gpv:</
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xml:space
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">[pv + m√(a - {ppvv/nn})].</
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<
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xml:space
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">Si hæ partes multiplicentur reſpective per quadrata ſuarum velocitatum,
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habebuntur earundem vires vivæ, quarum aggregatum æquandum eſt
<
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cum g X a, id eſt, cum deſcenſu actuali guttulæ g per altitudinem a. </
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<
s
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tinetur talis æquatio, ſi reducatur
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n
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vv - n
<
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a = mpv√(nna - ppvv) ſive
<
lb
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vv = {2n
<
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emph
>
+ mmnnpp + nnmp√4n
<
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style
="
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">4</
emph
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+ mmpp - 4nnpp)/2n
<
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style
="
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+ 2mmp
<
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style
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.</
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<
s
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xml:space
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">}a,
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hæcque quantitas exprimit altitudinem pro velocitate aquæ in o effluentis, qua
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cognita habetur quoque altitudo ſimilis pro altero foramine ac, quæ nempe
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eſt = a - {ppvv/nn}.</
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<
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">Si p = n, fit vv = a; </
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<
s
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xml:space
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">ergo tunc aquæ tota velocitate exiliunt
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ſolita per foramen o, & </
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<
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">per alterum foramen a c nihil effluit. </
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<
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">In utroque
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porro foramine velocitas reſpondet integræ altitudini a, ſi p eſt veluti infini-
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te parva: </
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<
s
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xml:space
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">Si vero m eſt infinite parva, fit quidem v v = a, ſed altitudo ve-
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locitatis pro foraminulo ac eſt = a - {pp/nn}a, ut §. </
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</
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<
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xml:id
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xml:space
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">Si m = p, fit vv = {n
<
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a/n
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- nnpp + p
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}; </
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<
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">& </
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<
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xml:space
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">a - {ppvv/nn} = {(nn - pp)
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a/n
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- nnpp + p
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}.</
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<
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">Denique obſervari poteſt, aquas per foramen o ſemper majori velo-
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citate ejici, quam quæ altitudini a reſpondet, quod utique fit, quia aquæ
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in E d veluti impetum faciunt in aquas d F.</
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<
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">Interim quamvis omnia hæc Corollaria egregie cum indole argumenti
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conſentiunt, non poteſt tamen ſolutio iſtius problematis aliter quam proxi-
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me vera cenſeri.</
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