Full text: Bernoulli, Daniel: Hydrodynamica s. de viribus et motibus fluidorum commentarii

181. Scholium 1.

(XIII.) Ut appareat, non differre valorem iſtius potentiæ ab illa, quam
pro globo ejusdem ponderis p invenimus articulo V. nempe {m N p/M}, demon-
ſtranda eſt æqualitas inter {n p (g - f)/Mc} & {m N p/M} ſeu inter n (g - f) & m N c: iſta
vero æqualitas deducenda eſt ex eo, quod extremitates aquæ l & o in eadem
ab horizonte altitudine poſitæ ſint; inde enim ſequitur, ut demonſtravi-
mus art. IV. eſſe aggregatum ex arcu a c multiplicato per {m N/M} & ex linea M d
multiplicata per n = aggregato ex arcu a c M p pariter multiplicato per {m N/M}
& ex linea M q multiplicata per n. Adhibitis itaque denominationibus præ-
cedentis articuli, fit M e X {m N/M} + (2 - f) X n = (M e + M c) X {m N/M} +
(2 - g) X n, vel n (g - f) = m N c; quæ æqualitas demonſtranda erat ad
demonſtrandam æqualitatem potentiarum tum pro globo tum pro aqua in
f applicandarum.

182. Scholium 2.

(XIV) Quia potentia {n p (g - f)/M c} non differt ab {m N p/M} & quantitas {m N/M}
eadem manet, quæcunque aquæ quantitas una revolutione hauriatur aut eji-
ciatur, erit potentia iſta proportionalis eidem quantitati aquæ ſingulis revolu-
tionibus ejectæ ſeu ponderi p. Facile quoque demonſtratu eſt, ſi eadem aqua-
rum quantitas, eadem potentia movente eademque velocitate ad parem altitudi-
nem verticalem elevetur ſuper ſimplici plano, quod ad hunc finem debite ver-
ſus horizontem inclinatum ſit, fore ut tempus elevationis quoque idem ſit.

Igitur eadem potentia abſoluta requiritur in cochlea Archimedis, quam
ſuper plano inclinato, ad quod omnes machinæ reduci poſſunt, nec ullam
habet iſta cochlea prærogativam præ reliquis machinis in theoria ſpectatis. Fortaſſe in praxi minus eſt obnoxia incommodis §. 26. indicatis: nequaquam
improbo ejus uſum, ſed nec eam præfero præ antliis Cteſibianis.

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