Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SEPTIMA.
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expertus ſum cylindrum eodem tempore evacuari, ſive aquæ in aërem eji-
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ciantur, ſive fundum aquæ ſtagnanti tantillum ſubmergatur. </
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<
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xml:space
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">Docet hæc ex-
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perientia parum aut nihil obſtare aërem externum effluxui, cum reſiſtentia
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plus quam octingenties major notabiliorem effectum non exerat. </
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<
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xml:space
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">Quia adeo-
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que iſte caſus nihil particulare habet, quod non loco citato monitum fuerit,
<
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huic non ulterius immorabimur: </
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<
s
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xml:space
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">Inquiremus potius, quid fieri debeat, cum
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elevatio aquæ internæ ſuper externam, quanta ab initio deſcenſus eſt, ſumi-
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tur valde parva & </
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<
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xml:space
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">negligenda præ immerſione cylindri; </
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<
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xml:space
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">cui hypotheſi ſatisfit,
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cum exceſſus altitudinis a ſuper altitudinem b (quem exceſſum rurſus vocabi-
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mus (ut §. </
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<
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">7.) </
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">c) eſt admodum parvus.</
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<
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<
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xml:space
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">Cum itaque ponitur a - b = c, ponendum etiam erit a - x = z,
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tumque utraque quantitas, nempe c & </
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<
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xml:space
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">z, erunt negligendæ præ quantitatibus
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a & </
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<
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xml:space
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">b, ſed ſi a - x = z, erit x = a - z & </
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<
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xml:space
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">x
<
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= (a - z)
<
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">nn - 1</
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=
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a
<
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- (nn - 1)a
<
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z + ({
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">nn - 1. nn -2</
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>
/2})a
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">nn - 3</
emph
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zz
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- ({
<
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/2. </
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<
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xml:space
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">3.</
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<
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z
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+ &</
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<
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<
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">Hæc ſeries quantum ad inſtitutum noſtrum ſufficit eſt continuanda;
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<
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dedimus §. </
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x
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= a
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- (nn - 1)a
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z + ({
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/2})a
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zz & </
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ſic erit
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v = {1/nn -2} [a - z - a + (nn - 1) z - ({
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/2}){zz/a}]
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- {b/nn - 1}[1 - 1 + (nn - 1){z/a} - ({
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/2}){zz/aa}]</
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<
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">In qua æquatione ſi termini ſe deſtruentes deleantur, atque ponatur a - c
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pro b, rejiciaturque terminus qui affectatur quantitate {czz/aa}, prodit ſimpliciter
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v = {2cz - zz/2a}.
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<
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">ex quâ formula, cum littera n evanuerit, indicium habemus, nihil </
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