Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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mmθθ + μμtt ad m m θ θ, ex qua ratione artifices judicabunt de firmitate
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laterum, quæ pro utroque requiritur.</
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">Quando embolus in antliis retrahitur & </
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">aqua in modiolum in-
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fluit, non ſolum proprio pondere ſolicitata ſed maximam partem ab embo-
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lo attracta, tunc omnis potentia abſoluta in hanc attractionem impenſa caſu
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ſupervenit, quia antlia, ſub aquis, ut fit, poſita, ſua ſponte impleretur ſi ſuf-
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ficiens huic impletioni tempus concederetur; </
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<
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xml:space
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">nec adeoque attractio illa ita
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pertinet ad ejiciendas aquas certa cum velocitate, quin tota vitari poſſit, hoc-
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que nomine labor in illam impenſus mihi inutilis dicitur.</
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<
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">Quia vero influxus aquarum partim proprio pondere fit, partim
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etiam elevatione emboli, non poteſt diſpendium potentiæ abſolutæ ab effectu
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æſtimari: </
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<
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">Quin potius calculus ita eſt ponendus, ut poſitis potentia embo-
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lum in certo ſitu elevante = π, velocitate emboli = v, tempuſculoque
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quantitatibus π & </
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<
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">v reſpondente d t, dicatur omnis potentia abſoluta in eleva-
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tionem emboli impenſa = ſ π v d t vel = ſ π d x, ſi per d x intelligatur ele-
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mentum ſpatioli tempuſculo d t percurſi. </
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<
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">Sequitur inde, ſi conſtantis mag-
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nitudinis ſit, uti fere eſt conatus, quo embolus elevatur, fore potentiam abſo-
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lutam æqualem potentiæ moventi ductæ in ſpatium percurſum: </
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<
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tiocinium cum valeat etiam pro depreſſione emboli ſimulque tantum eleve-
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tur embolus quantum deprimitur, apparet potenti{as} abſolut{as}, quæ in attrahen-
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das expellendaſque alternatim aquas impenduntur, proxime eſſe ut potentiæ
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utrobique moventes; </
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<
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">unde diſpendium oritur quod eſt = {π/π + p} X P, factis ſci-
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licet potentia elevante = π, potentia deprimente = p & </
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<
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">potentia abſoluta in
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elevationem depreſſionemque emboli impenſa = P.</
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<
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">Poteſt aliter diſpendium potentiœ abſolutæ proxime æſtimari ex eo, quod
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omnis aſcenſ{us} potentialis aquæ in antliam influentis inutiliter generatus cenſeri
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debeat. </
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<
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">Sed ſi iiſdem temporibus, ſive eadem velocitate embolus ſurſum de-
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orſumque movetur, erit velocitas quâ aquæ admittuntur ad velocitatem quâ
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ejiciuntur reciproce ut foramina reſpondentia, ipſique aſcenſus potentiales utro-
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bique erunt in ratione quadrata inverſa foraminum reſpondentium. </
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