Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUARTA.
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poſteriorem per regulas ſolitas reſolvemus in hanc ſeriem
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1 + {1/2} ({x/a})
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+ {1. </
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- 4 + {1.</
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+ &</
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<
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">unde nunc habetur mutata paullulum æquationis forma:
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</
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xml:space
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">dt = - {dx√mmαα - 2nn}/n√a} X [({x/a})
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+ {1/2} ({x/a})
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+ {1.</
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+ {1.</
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+ &</
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Hæc æquatio ita eſt integranda, ut poſita x = a fiat t = 0; </
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t = [2 + {nn/2mmαα - 3nn} + {3nn/16mmαα - 28nn} + &</
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- [2{(x/a)}
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+ {nn/2mmαα - 3nn} ({x/a})
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+ {3nn/16mmαα - 28nn} ({x/a})
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+ &</
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X {√(mmαα - 2nn).</
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ubi 2 √ a exprimit tempus quod corpus impendit dum libere delabitur per
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altitudinem a. </
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x = a:</
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quæ eſt altitudo aquæ cum velocitas maxima eſt (per §. 16. </
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4.)</
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locitatis usque præterit; </
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<
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">cum ponitur x = o, oritur tempus, quo vas to-
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tum depletur, ac denique ſi ponatur x = cuicunque quantitati c, exprimet t
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tempus quod ſuperficies inſumit in deſcenſum per altitudinem a - c; </
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mus autem pro his caſibus, quid fieri debeat, cum vas eſt valde amplum,
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numerusque m alterum n ſic pluries continet.</
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<
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, erit altitudo aquæ puncto
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maximæ velocitatis reſpondens ſeu</
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