Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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<
s
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xml:space
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">Cum vero amplitudo foraminis rationem habet finitam ad amplitudi-
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nem tubi, aſcenſus fit ultra ſuperficiem R S veluti usque in s t: </
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<
s
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xml:space
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tem ſemper erit Vt quam Vy, niſi cum omne fundum abeſt, tunc enim
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erit V t = V y. </
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<
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">Prouti monuimus §. </
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<
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xml:space
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">in deſcenſu differentiam inter V Y & </
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V y, proportionalem eſſe & </
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<
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xml:space
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">originem debere aſcenſui potentiali aquæ durante
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deſcenſu ejectæ, ita nunc obſervari poteſt in aſcenſu differentiam inter V y
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& </
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<
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">V t originem habere ab illiſione guttularum L o n P in maſſam aquæ ſu-
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perjacentis, quæ quidem illiſio non promovet aſcenſum, ſed in inutilem mo-
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tum inteſtinum impenditur, prouti indicatum fuit §. </
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<
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<
s
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xml:space
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">Ergo cum omne
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fundum I M abeſt, aqua tubum eadem velocitate ingreditur, qua jam gau-
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det aqua tubum antea ingreſſa & </
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<
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">nulla fit colliſio, quæ cauſa eſt cur in iſto
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caſu tantum aſcendat aqua ultra ſuperficiem R S, quantum fuerat infra il-
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lam depreſſa, quod æquatio, uti mox videbimus, indicat.</
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<
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<
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xml:space
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">Determinabitur maximus aſcenſus s t, faciendo v = o. </
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<
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ut motus omnis recte definiatur, alternatim adhibendæ erunt formulæ §. </
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</
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">& </
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<
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<
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">erutæ, quod nunc hoc unico illuſtrabo exemplo, quo nn = 1.</
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<
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">Si proinde nn = 1, fit v = b (1 - {α/ξ} - {1/2} (ξ - {αα/ξ}): </
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<
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v = o, cum ſumitur ξ = 2b - α, id eſt, cum ſumitur V t = V y. </
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<
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tur ſi verbi gratia tubus A B M I aqua plenus, omnique fundo deſtitutus fue-
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rit ad medietatem usque immerſus aquæ exteriori, atque tota ipſius longi-
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tudo dicatur a, aqua ſic agitabitur ut primo infra T V deſcendat, ſpatio
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o, 297a, deinde ſimili ſpatio ſuper eandem T V elevetur, rurſusque infra eam
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deprimatur ſpatio o, 240a, eodemque lineam illam iterum tranſcendat, & </
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ſic porro.</
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<
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<
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xml:space
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">Patet etiam cum α eſt = o, tubo ſcilicet ab omni aqua va-
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cuo, fore generaliter v = {b/nn} - {ξ/nn + 1}: </
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<
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ter fore {nn + 1/nn}b vel aſcenſum ſupra ſuperficiem exteriorem aquæ = {b/nn}.</
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<
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">Venio nunc ad tubos infinite ſubmerſos, in quibus deſcenſum
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cum ſuis affectionibus determinavimus §. </
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<
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<
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methodo ad hunc caſum definiendum quâ ibi uſi ſumus: </
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<
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depreſſio initialis V y(= b - α) = c, aſcenſus inde factus y d (= ξ - α) = z.</
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