Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO DECIMA.
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poteſt ejus ope pondus 865 librarum ad altitudinem unius pedis elevari, ſi
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modo machina adhibeatur perfectiſſima.</
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<
s
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">Ab auctis autem aëris tum denſitate tum calore pendent omnium re-
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rum hic expoſitarum effectus.</
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<
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<
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<
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xml:space
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">Interim non ſolum ab aëre condenſato calefactove vis viva pro
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machinis movendis impendenda obtineri poteſt, ſed & </
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<
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frigidiore. </
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<
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">Ubicunque enim æquilibrium ſublatum eſt, vis viva adeſt, quæ
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impendi poteſt, ſi debita machina excogitetur, ad onera elevanda machina-
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mentaque circumagenda. </
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<
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">Methodus autem determinans vim vivam, quæ ab
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aëre datæ denſitatis datique caloris ſpatium datum occupante elici poteſt,
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mutatis mutandis eadem eſt cum illa quam §. </
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<
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<
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">Fuerit nempe rurſus cylindrus verticalis A B C D (Fig. </
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<
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phragmate mobili E F: </
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<
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brio cum aëre externo: </
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<
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: </
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<
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dein pondus P, quod mediante fune trans duas trochleas M & </
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diaphragmate cohæreat, idemque verſus A D trahat, perveneritque ſic dia-
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phragma ex ſitu E F in G H: </
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">Denique ponatur rurſus F C = a, F H = x:
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<
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">velocitas diaphragmatis in ſitu G H ſeu ponderis in ſitu P = v; </
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<
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ſi conferantur §. </
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dv = (P + {ap/a + x} - p) X {dx/v}: </
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Pvdv = (P - {px/a + x}) dx, quæ integrata dat
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{1/2}Pvv = Px - px + ap log.</
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xml:space
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<
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">At rurſus deſcenſus ponderis P per altitudinem x producta fuit vis viva
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P x, dum ipſi interim ponderi velocitate v moto ineſt tantum vis viva {1/2} P v v
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ſeu Px - px + ap log.</
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<
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xml:space
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">{a + x/a}, Igitur vis viva, quæ reſidua eſt, nempe p x -
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a p log.</
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<
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">{a + x/a}, ad aërem tranſiit rurſusque reſtitutione æquilibrii inter aërem
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internum & </
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">externum, illa vis viva ad alia corpora pro lubitu transfundi po-
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terit: </
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">Igitur ſi habeas ſpatium G B C H aëre plenum cujus denſitas ſit ad
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denſitatem aëris externi ut C F ad C H, in poteſtate erit vis viva p x -
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a p log.</
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