Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SEXTA.
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<
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<
s
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xml:space
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">Si ponatur canalis c A d ejuſdem amplitudinis cum tubis con-
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junctis, ejuſque longitudo vocetur l, erit maſſa aquæ in eo contentæ, quam
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vocavimus M = gl; </
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<
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">& </
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<
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<
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xml:space
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">aquæ in illo contentæ, quem poſuimus =
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N v, erit = v, ita ut habeatur N = 1. </
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<
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xml:space
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">Subſtitutis autem, iſtis valoribus pro
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litteris M & </
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<
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xml:space
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">N, prodit longitudo penduli tautochroni pro iſto caſu particulari =
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{aaα + aαα + aαl/αb + aβ} = {aα/αb + aβ} X (a + α + l) = {a + α + l/{b/a} + {β/α}</
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<
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">Quia vero a + α + l eſt longitudo totius tractus aqua pleni & </
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<
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ficat rationem ſinus anguli bac ad ſinum totum pariter atque {β/α} denotat ra-
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tionem ſinus anguli efd ad ſinum totum, videmus non differre noſtram ſo-
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lutionem ab illa, quam Pater meus pro iſto caſu dedit, quamque ſupra
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recenſui §. </
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<
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MN = o (per §. </
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<
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">longitudo penduli tantochroni = {a + α/{b/a} + {β/α}}, qua-
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ſi nempe totus canalis intermedius c A d abeſſet, tubique cylindrici inter ſe
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immediate eſſent conjuncti.</
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<
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<
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<
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tochronas faciunt, ubi tubi a c & </
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<
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<
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bus fluidi ſuperficies excurrunt, incurvati ſunt, dantur alii inſuper tanto-
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chronismi caſus, quos facile foret determinare, ſi hiſce diutius immorari
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vellemus. </
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tempora oſcillationbus diverſarum magnitudinum reſpondentia inæqualia,
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& </
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citatem fiuidi in quolibet puncto dedimus.</
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