Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SEPTIMA.
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<
s
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<
s
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">Conſideretur ſcilicet guttulæ L O N P quaſi nullam velocitatem fuiſſe,
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priuſquam influere inciperet, eandem vero ſtatim atque influere incipiat, ac-
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quirere aſcenſum potentialem, qui ſit = n n v, quamvis mox poſt ſui influxum
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(per annot. </
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<
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<
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<
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<
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">cenſenda ſit motum continuare velocitate communi
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√ v. </
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<
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">Ante influxum guttulæ, eſt aſcenſus
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potent. </
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<
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">aquæ c d M L P I c (cujus maſſa = n ξ) = v. </
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<
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L O N P (cujus maſſa = n d ξ) = o; </
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<
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">ergo aſcenſus potentialis omnis aquæ
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c d M L O N P I c = {nξv/nξ = ndξ} = {ξv/ξ + dξ}.</
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<
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">At vero poſtquam guttula L O N P influxit ſitumque aſſumſit L on P,
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eſt ejus aſcenſ. </
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<
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<
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">= n n v, reliquæ autem aquæ e f M L o n P I e (cujus
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quidem maſſa rurſus = n ξ) aſcenſus potent. </
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<
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">eſt = v + d v; </
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<
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">igitur aſcenſus
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potent. </
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<
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">omnis aquæ hic conſideratæ poſt influxum guttulæ eſt
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= {ndξ x nnv + nξx(v + dv)/nξ + ndξ} = {ξv + ξdv + nnvdξ/ξ + dξ}, cum ante eundem influ-
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xum fuerit {ξv/ξ + dξ}: </
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<
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">cepit igitur incrementum {ξdv + nnvdξ/ξ + dξ}, vel ſimplicius
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{ξdv + nnvdξ/ξ}. </
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<
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quem aqua facit mutando ſitum c d M L O N P I c ſitu e f M L O N P I e, qui
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deſcenſus æqualis eſt quartæ proportionali ad maſſam aquæ internæ n ξ, ad
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guttulam n d ξ & </
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<
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">altitudinem V f vel b - ξ, ſic ut præfatus deſcenſus ſit =
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{(b - ξ)dξ/ξ}: </
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<
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">unde iterum habetur talis æquatio
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ξdv + nnvdξ = (b - ξ)dξ;</
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<
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">Hujus vero integralis poſt debitæ conſtantis additionem talis fit
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v = {b/nn} (1 - ({α/ξ})
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) - {1/nn + 1} (ξ - ({α/ξ})
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α),
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quam nunc pro diverſis ejus circumſtantiis perpendemus.</
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<
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<
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amplitudo foraminis; </
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<
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<
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citate quæ debeatur altitudini ſuperficiei externæ fuper internam, neque
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tunc ultra ſuperficiem aquæ externæ fiet aſcenſus.</
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