Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO OCTAVA.
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luſus hydraulicus, venam proſilientem D O videre, quæ æqualibus incre-
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mentis æqualibusque temporum intervallis, quod utrumque fieri poteſt,
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ſubſultim creſcat.</
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<
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">Propoſitum nunc ſit motum fluidi exilientis indagare, cum per
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ſingula foramina alia atque alia fluida transfluunt. </
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<
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">Fluida autem leviora con-
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tinue ponenda eſſe apparet, quo ſunt altius poſita, ne motus turbetur,
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quod fit cum eodem tempore fluidum inferius aſcendit, ſuperiore deſcen-
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dente, per commune foramen. </
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<
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xml:space
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">Innoteſcet hoc modo quisnam ſit motus
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in aquis ex vaſe effluentibus undique clauſo præter foraminulum aliquod ſu-
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perne exiſtens, quod aëri tranſitum concedit. </
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<
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xml:space
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">Hypotheſin vero infinitæ va-
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ſis cylindrici amplitudinis ratione foraminum retinebimus, atque porro
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gravitatem ſpecificam fluidi per D exilientis deſignabimus per A, illiusque
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quod per G transfluit notabimus littera B, ſimiliterque gravitates ſpecificas
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fluidorum per foramina, F, H, &</
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<
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<
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ris C, D, &</
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<
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<
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xml:space
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">Denique cum etiam conſiderandæ hic ſint altitudines diver-
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ſorum fluidorum, quorum quidem, ob figuram vaſis cylindricam ſolum
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infimum effluens altitudinem mutat, vocabimus x altitudinem fluidi infimi
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ſupra foramen D, fluidorum reliquorum, eo quo ſibi ſuperincumbunt or-
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dine, altitudines deſignabimus reſpective per b, c, d &</
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<
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nationes paragraphi undecimi retinebimus; </
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tus inſtituetur ut §. </
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<
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">factum eſt, neque enim quicquam aliud inſuper ob-
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ſervandum eſt, quam ut maſſæ guttularum iisdem tempusculis per diverſa
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foramina transeuntium non ſimpliciter ex mole, ſed etiam ex gravitate ſpe-
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cificia æſtimentur: </
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<
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">deſcenſus autem actualis pro ſingulis fluidis erit ſeorſim ſu-
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mendus: </
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A v + {nn/αα} B v + {nn/ββ} C v + {nn/γγ} D v + &</
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<
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xml:space
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</
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<
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v = (A x + B b + C c + D d + &</
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<
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<
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xml:space
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<
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quam in denominatore ſumendi & </
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<
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ſic porro: </
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<
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cumbat aqua ſtatuanturque gravitates ſpecificæ horum liquorum ut 14. </
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