Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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aquæ in c A d per C A, aggregatumque horum productorum dividendo per
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ſummam harum maſſarum. </
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xml:space
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<
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xml:space
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"> A F = {ga X (f + {1/2}
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) + γα X (φ + {1/2}
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) + Mm/ga + γα + M}</
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xml:space
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">Determinare ubique velocitates aquæ oſcillantis, poſito oſcilla-
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tiones ultra terminos tuborum cylindricorum non divagari.</
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xml:space
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xml:space
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">Sit aqua oſcillationem inchoans in ſitu a c A d f perveneritque poſtmo-
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dum in ſitum o c A d p, retentiſque denominationibus |in præcedente paragra-
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pho factis, ponatur a o = x; </
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<
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xml:space
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">erit f p = {gx/γ}: </
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<
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xml:space
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">unde (ſi nempe centrum gravita-
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tis omnis aquæ deſcendiſſe putetur ex F in O) erit vi præcedentis paragraphi
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A O = {g X (a - x) X (f + {1/2}
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- {bx/2a}) + γ X (a + {gx/γ}) X (φ + {1/2}
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+ {βgx/2αγ}) + Mm/ga + γα + M}</
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<
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<
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">Inde deducitur deſcenſus centri gravitatis ſeu deſcenſus actualis
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F O = {(b - β + f - φ)gx - ({bg/2a} + {bgg/2αγ}) xx/ga + γα + M}</
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</
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<
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<
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">Sit nunc velocitas aquæ in tubo a c (cum nempe ſuperficies eſt in o) ta-
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lis quæ reſpondeat altitudini v, & </
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<
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">aquæ in altero tubo
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= {gg/γγ} v: </
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<
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<
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xml:space
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">aquæ c A d, erit proportionalis altitudini v,
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eamque proinde ponemus = N v (ubi N pendet à figura utris c A d & </
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minari poteſt per §. </
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">Jam vero ſi multiplicatis ubique aſcenſibus po-
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tentialibus per ſuas maſſas producta dividantur per ſummam maſſarum, habebi-
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tur aſcenſ{us} potent. </
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<
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xml:space
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">omnis aquæ o c A d p =
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{(ga - gx + {αgg/γ} + {g
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x/γγ} + MN)v/ga + γα + M}</
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<
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<
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xml:space
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">Et quia hic aſcenſus potentialis eſt æqualis deſcenſui actuali F O paullo ante
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invento, </
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