Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO TERTIA.
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(1 - {mm/nn})vdξ + ξdv = - xdξ
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cujus integralis, quod patet multiplicatis terminis per ξ - {mm/nn} hæc eſt
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v = ξ
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ſ - xξ
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dξ.
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">ita inclinatus verſus horizontem, ut ſinus anguli
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intercepti inter utrumque ſit ad ſinum totum ut 1 ad g, erit ξ = gx; </
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v = {nna/2nn - mm} (({a/x})
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- {x/a})
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quæ æquatio cum non differat ab æquatione §. </
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data, ſequitur in utroque caſu velocitates aquæ easdem eſſe, poſtquam deſ-
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cenſus verticales ſuperficiei aquæ iidem ſunt: </
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">Igitur accelerationes in locis
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homologis utrobique ſimiles ſunt ratione altitudinum verticalium, & </
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tum diſcriminis intercedit, quod in canali inclinato lentius fiant, idque in
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ratione ut 1 ad g: </
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">facile igitur ſenſibus percipi poterunt hæ accelerationes in
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canalibus valde inclinatis, quæ in verticalibus ob nimiam mutationum celeri-
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tatem non poſſunt. </
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">Cœterum patet per ſe ex eo, quod frictiones à longitu-
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dine tubi augeantur, non poſſe non velocitates inde diminui, ad quod ani-
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mum advertent ii, quibus experimenta hâc de re inſtituere animus erit.</
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