Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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(B) ααy + (β√x + γ√y)
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= αα X (a + b).</
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<
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">Subtractâ æquatione (B) ab æquatione (A) prodity = x + b, ex quo
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ſequitur, ſi venæ ambæ verticaliter ſurſum dirigantur, utramque ad eundem lo-
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cum aſſilire. </
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">Deinde ſi in æquatione (A) ſubſtituatur pro y valor ejus x + b,
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erit
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(C) ααx + (β√x + γ√x + b)
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= ααa,
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unde deducitur valor ipſius x æquatione quadrata.</
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<
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ctiones.</
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tudo generans hanc velocitatem = ({β√x + γ√y/α})
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; </
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tiones (A) & </
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</
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<
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= {2a + b - x - y/2} = ob(y = x + b)a - x.</
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β poſſit cenſeri nulla ratione α & </
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">γ, abit æquatio (C) in hanc
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ααx + γγx + γγb = ααa, ſeu
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x = {ααa - γγb/αα + γγ};</
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<
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">Id vero egregie convenit cum paragrapho decimo nono, cum manife-
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ſtum ſit aquam per foramen valde exiguum ad eandem altitudinem aſſilire,
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quam haberet aqua, ſi hæc laminam L Q tantum deorſum premat, quantum
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ab aqua interna ſurſum premitur; </
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</
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ſeu x + b = {ααa + ααb/αα + γγ}
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& </
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">denique altitudo velocitatis aquarum in M, ſeu
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a - x = {γγa + γγb/αα + γγ}; </
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quæ poſteriores æquationes in iſto caſu particulari pariter ex §. </
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colligi aut prævideri potuiſſent.</
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