Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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ctum in motum aquarum exerere debeat, quiſque videt ex eo, quod in utro-
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que modo omnis aquæ tubum ingredientis inertia ſit ab aqua inferiore ſupe-
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randa. </
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<
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">Sed idem etiam à priori demonſtrari poterit inquirendo in motum, qui
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inde oriri debeat, ſecundum æquationem paragraphi octavi Sect. </
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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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">Ndv - {mmvydx/nn} + {mmvdx/y} = - yxdx; </
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accommodabitur autem ad præſentem caſum, ſi pro m, x & </
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<
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ſpective n, a, & </
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<
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">{ndx/y}, (cujus rei ratio patebit, ſi hæc cum illis contuleris) ſi-
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mulque y infinitum ponas; </
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<
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">tunc enim evaneſcit tertius æquationis terminus,
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fitque omnino, ut pro præſenti negotio ſupra invenimus,
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Ndv + nvdx = nadx.</
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">Poſtquam in his ſcholiis motus utriuſque indolem, quantum ſimplexrei
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conſideratio phyſica permittit, eorumque differentiam oſtendimus, ſimulque
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modum illos producendi ad legem hypotheſeos mechanicum tradidimus, ſu-
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pereſt, ut reliqua phænomena notabiliora etiam indicentur, quod nunc faciam.</
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">Si in vaſe R S N H omnè fundum abſit, erit orificium L M =
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orificio R S; </
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<
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">poteſt etiam hoc ab illo ſuperari, ſi nempe vaſis divergant late-
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ra. </
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<
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">In his autem caſibus nullum habet terminum altitudo v in æquatione
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v = {mma/mm - nn} X (1 - c{n
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- nmm/mmN} x)
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& </
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<
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">fit infinita, ſi quantitas aquæ ejectæ indicata per n x eſt infinita.</
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<
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">Id quidem per ſe patet ex æquatione, cum n eſt major quam m; </
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cum amplitudines orificiorum ſunt æquales, recurrendum eſt ad æquationem
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differentialem paragraphi tertii, ex qua iſta æquatio proxima deducta fuit, nempe
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{N/M}dv - {n
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/mmM}vdx + {n/M}vdx = {n/M}adx,
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quæ poſito n = m dat N d v = n a d x, id eſt, v = {nax/N}, ubi v fit manifeſte in-
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finita ſi x eſt infinita.</
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<
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