Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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0045
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SECTIO TERTIA.
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<
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xml:space
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<
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<
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b c f g; </
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<
s
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">aſſumitur, ſi in axe a e accipiatur punctum quodcunque n, per
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& 14.</
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quod planum ad axem perpendiculare p m tranſeat, fore, ut omnes parti-
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culæ aqueæ in illo plano exiſtentes æquali velocitate fluant, & </
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<
s
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xml:space
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li, quæ ſit ubique reciproce proportionalis magnitudini ſectionis p m. </
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<
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autem velocitas aquæ in g f talis, quæ debetur altitudini verticali q s, id eſt,
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ſit aſcenſus potentialis ſtrati aquei in g f æqualis lineæ q s, & </
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<
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modi altitudines ſunt in ratione quadrata velocitatum, ſequitur eſſe aſcen-
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ſum potentialem aquæ in p m æqualem quartæ proportionali ad quadratum
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amplitudinis p m, quadratum amplitudinis g f & </
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<
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">altitudinem q s, nempe
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= {gf
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/pm
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} X qs. </
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<
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">His ita præmonitis ponemus in figura decima quarta eſſe
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curvam B P G, ſcalam amplitudinum canalis, ita ut poſita A N = a n, denotet
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N P amplitudinem in p m: </
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<
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xml:space
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">dein curvam H I K eſſe ſcalam aſcenſuum poten-
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tialium, ita ut ſit N I = {EG
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/NP
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} X qs. </
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<
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xml:space
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">fingatur nunc elementa ſingula curvæ
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H I K habere pondus æquale ponderi ſtrati aquei reſpondentis, & </
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<
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centrum gravitatis iſtius curvæ in punctum L, & </
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<
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laris ad axem A E; </
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<
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">ſic erit L O aſcenſus potentialis totius aquæ quæſitus. </
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<
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mechanicis autem conſtat, fi fiat tertia curva U X Z, cujus applicata N X
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ſit ubique æqualis {EG
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/NP}, fore L O æqualem quartæ proportionali ad ſpa-
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tium A E G B & </
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</
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<
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<
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& </
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<
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">poſterior b c diametros habeant ut m ad n, erit aſcenſus potentialis aquæ
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= {3m3/n(mm + mn + nn)} X qs.</
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locitatis, quæ ſuperficiei aquæ anteriori reſpondent, invenire variationes
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ad aſcenſus potentiales totius aquæ pertinentes.</
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