Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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tiæ paragrapho ſecundo: </
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ſiduum eſt: </
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<
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attuliſſe.</
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<
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<
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telligatur pars ejus B G F C fluido plena moto verſus g f; </
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<
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culæ fluidi in G F velocitatem debitam altitudini v; </
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<
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fluidum in ſitum b g f c: </
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<
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bo autem altitudinem velocitati aquæ in g f debitam = V; </
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in H; </
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<
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">diameter in B C = n; </
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">diameter in G F = m: </
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</
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<
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">Gg = b, erit diameter g f = {m a - m b + n b/a}. </
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<
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eſt æquale ſolido b g f c erit B C
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X B H - G F
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X G H = b c
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X b H
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- g f
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X g H: </
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X b H = B C
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X B H - G F
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X G H
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+ g f
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X g H: </
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">igitur b c
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= B C
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-. </
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{GF
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X GH X BC/BH} + {gf
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X gH X BC/BH} = B C
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- G F
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+ g f
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, ſeu
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b c = √Cub.</
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- m
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+ ({m a - m b + n b/a})
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},</
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= {3 m
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v/n(mm + mn + nn)}; </
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<
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reperitur = {3 α
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v;</
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">/β(αα + αβ + ββ)}, poſito brevitatis ergo α & </
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ribus diametrorum g f & </
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<
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<
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V = {m
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X (αα + αβ + ββ) X β X v/α
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X (mm + mn + nn) n}.</
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particulas anteriores, minori poſteriores, & </
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ſeatur infinite parvum, fiat velocitas aquæ in g f infinita & </
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