Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO TERTIA.
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vel poſt effluxum guttulæ, G H amplitudinem illam aſſumtam, I L mag-
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nitudinem fundi, P L magnitudinem foraminis, dum adhærens parallelo-
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grammum minimum P N O L reſpondet guttulæ cylindricæ pnol: </
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<
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ſtruatur alia curva T R U, cujus applicatæ ſint rurſus æquales quadrato lineæ
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G H, diviſo per applicatam reſpondentem curvæ C G I, cui curvæ eadem
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conditione annexum eſt parallelogrammulum L O Y X, cujus nempe latus
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L X eſt æquale quadrato lineæ G H diviſo per lineam PL.</
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<
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">Jam igitur apparet aſcenſum potent. </
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<
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xml:space
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">aquæ ante effluxum guttulæ eſſe =
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quartæ proportionali ad ſpatium D C I P L, ſpatium D T U L & </
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<
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nem qs, eundemque poſt effluxum guttulæ eſſe = quartæ proportionali
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ad ſpat. </
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que analogia termini primi (nempe ſpat. </
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<
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xml:space
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">FEIPNOL) in-
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ter ſe æquales, igitur ſi quodvis horum ſpatiorum indicetur per M, ſpa-
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tium D T U L per N, ſpat FWUXYOL per N + dN, altitudo qs per
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v&</
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<
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">qz per v + dv, erit incrementum aſcenſus potentialis durante guttulæ efflu-
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xu = {Ndv + vdN/M}. </
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">Quod ſi nunc ponatur L D = x, F D = - dx, D C
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= y, H G = m, P L = n, erit D T = {mm/y}, L X = {mm/n}, L O = {-ydx/n}
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(quia ſpatium D F E C = ſpatio L O N P), hincque dN = L O Y X -
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D F W T = - {mmydx/nn} + {mmdx/y}, unde nunc incrementum quæſitum
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aſcenſus petentialis eſt = (Ndv - {mmvydx/nn} + {mmvdx/y}): </
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nitè parvum aquæ, dum guttula effluit.</
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<
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">Cum in Figura decima quinta aqua ſitum cdmi mutat cum ſitu efml
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onpi, patet in utroque ſitu centrum gravitatis partis aquæ efmi in eodem
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loco eſſe, poſſeque proin concipi ſolam particulam cdfe, (quæ eſt = - ydx
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dum tota aquæ maſſa eſt = M) deſcendiſſe in lonp. </
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