Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUINTA.
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log. </
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xml:space
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- nmm/mmN} x)] = log.</
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- nmm/mmN} x = {n
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- nmm/mmN} x - log. </
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<
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">Hæ ſubſtitutiones ſi recte fiant, erit pro primo quem finximus affuſio-
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nis modo
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(I) t = {γmN/n√(mm - nn) a} X (2 log. </
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/mmN} x)
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quæ poſito rurſus m = ∞ dat pro altero caſu
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(II) t = {γN/n√a} X (2. </
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<
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<
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">Sequitur ex iſtis formulis, minori quidem quantitate transfluere aquas,
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ac ſi ſtatim ab initio omni velocitate, quam in utroque caſu poſt tempus
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infinitum acquirunt, effluerent: </
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gredi terminum & </
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(I) x = {2mmN/mmn - n
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} - [log. </
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<
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}) - log. </
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(II) x = {2N/n} X [log. </
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) - log. </
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ubi α, ut ſupra, = {-γmN/n√(mm - nn)a} & </
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">Si præterea, ut in proximo Corollario, ponatur t = ∞, evaneſcit
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unitas præ quantitatibus, exponentialibus, quæ ſupra omnem ordinem infinitæ
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ſunt, & </
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xml:space
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<
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) = -{t/α} atque log. </
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xml:space
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<
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) = -{t/β}:
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</
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(I) x = {mt√a/γ√(mm - nn)} - {2mmN/mmn - n
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} log. </
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(II) x = {t√a/γ} - {2N/n} log. </
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