Bernoulli, Daniel - Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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4733SECTIO TERTIA. vel poſt effluxum guttulæ, G H amplitudinem illam aſſumtam, I L mag-
nitudinem fundi, P L magnitudinem foraminis, dum adhærens parallelo-
grammum minimum P N O L reſpondet guttulæ cylindricæ pnol: dein con-
ſtruatur alia curva T R U, cujus applicatæ ſint rurſus æquales quadrato lineæ
G H, diviſo per applicatam reſpondentem curvæ C G I, cui curvæ eadem
conditione annexum eſt parallelogrammulum L O Y X, cujus nempe latus
L X eſt æquale quadrato lineæ G H diviſo per lineam PL.

Jam igitur apparet aſcenſum potent. aquæ ante effluxum guttulæ eſſe =
quartæ proportionali ad ſpatium D C I P L, ſpatium D T U L & altitudi-
nem qs, eundemque poſt effluxum guttulæ eſſe = quartæ proportionali
ad ſpat. FEIPNOL, ſpat. FWUXYOL & altit. qz: ſunt autem in utra-
que analogia termini primi (nempe ſpat. DCIPL & ſpat. FEIPNOL) in-
ter ſe æquales, igitur ſi quodvis horum ſpatiorum indicetur per M, ſpa-
tium D T U L per N, ſpat FWUXYOL per N + dN, altitudo qs per
v& qz per v + dv, erit incrementum aſcenſus potentialis durante guttulæ efflu-
xu = {Ndv + vdN/M}. Quod ſi nunc ponatur L D = x, F D = - dx, D C
= y, H G = m, P L = n, erit D T = {mm/y}, L X = {mm/n}, L O = {-ydx/n}
(quia ſpatium D F E C = ſpatio L O N P), hincque dN = L O Y X -
D F W T = - {mmydx/nn} + {mmdx/y}, unde nunc incrementum quæſitum
aſcenſus petentialis eſt = (Ndv - {mmvydx/nn} + {mmvdx/y}): M. Q. E. I.

Problema.

§. 7. Retentis iisdem poſitionibus inven@re deſcenſum actualem infi-
nitè parvum aquæ, dum guttula effluit.

Solutio.

Cum in Figura decima quinta aqua ſitum cdmi mutat cum ſitu efml
onpi, patet in utroque ſitu centrum gravitatis partis aquæ efmi in eodem
loco eſſe, poſſeque proin concipi ſolam particulam cdfe, (quæ eſt = - ydx
dum tota aquæ maſſa eſt = M) deſcendiſſe in lonp. Sit jam altitudo

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