Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO TERTIA.
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{mma/mm - 2nn} X [({nn/mm - nn})
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- ({nn/mm - nn})
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]
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quæ quantitas reducta fit =
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{mma/mm - nn}({nn/mm - nn})
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<
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">Intelligitur ex iſtis formulis tempus, quo velocitas à nihilo in maxi-
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mam vertitur, plane imperceptibile eſſe, quando foramen vel mediocriter
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parvum tubusque non admodum longus eſt: </
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<
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">notabile autem fieri, cum res
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ſecus ſe habet, quod videmus in fontibus ſalientibus, ad quos aquæ per
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longos tractus vehuntur; </
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<
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">hæc vero quæ ad tempora pertinent, magis in
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ſequenti ſectione explicabuntur, atque ſimul oſtendetur, quam parum aquæ
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ex vaſis ampliſſimis ejiciatur, priusquam maxima velocitate effluant.</
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<
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">Natura velocitatum melius intelligitur ex appoſita Figura decima ſepti-
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">Fig. 17.</
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ma, in quâ ſi A B repræſentet totam altitudinem fluidi ſupra foramen ab initio
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fluxus, expriment curvæ A 1 C B, A 2 C B, A 3 C B, A 4 C B, ſcalas altitudi-
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num reſpondentium, ad quas fluidum effluens ſua velocitate aſcendere poſſit in
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diverſis foraminum magnitudinibus: </
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">nempe ſcala accedet ad figuram A 1 C B, ſi
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foramen habeat exiguam rationem ad vaſis amplitudinem & </
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cum aſſumitur fundum majori lumine perforatum; </
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">ſi jam ratio foraminis
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ſit ad amplitudinem vaſis ut 1 ad √ 2, erit ſcala illa ut A 3 C B (quo in caſu
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minor fit maxima velocitas quam in quocunque alio, eſtque nominatim ea
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quæ debetur altitudini {2a/c}, intelligendo per c numerum cujus Logarithmus
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eſt unitas, id eſt, altitudini paulo minori quam {3/4}a) ac denique erit ſcala ut
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A 4 C B cum fere nihil fundi ſupereſt.</
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<
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<
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">indicatum fuit, nempe niſi foramen ſit ampliſſimum, poſſe id ſine valde
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ſenſibili errore in calculo conſiderari ut infinitè parvum, atque adeo aſſumi
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z = x, ut §. </
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">Videtur id tantum apud nonnullos
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Auctores valuiſſe, ut cenſuerint, nullam magnitudinis in foramine rationem
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unquam eſſe habendam, quantumvis magnum ponatur foramen, quæ res
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certe ridicula eſt: </
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">faltem nemo hactenus quod ſciam magnitudinem forami-
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nis pro hoc negotio recte conſideravit. </
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<
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">Ponamus igitur cylindrum, cujus
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diameter quadrupla tantum ſit diametri foraminis, cujusmodi magna </
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