Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO DECIMA.
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dv = (P + p - {ap/a - x}) X {dx/v}: </
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<
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xml:space
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">P, vel
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Pvdv = (P - {xp/a - x}) dx, quæ integrata dat
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{1/2} P vv = Px + px - ap log. </
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<
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<
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<
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xml:space
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">Jam vero deſcenſu ponderis P per altitudinem x genita fuit vis viva P x,
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de qua eidem ponderi ceu velocitate v moto ineſt pars {1/2} P v v ſeu P x + p x -
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ap log. </
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<
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xml:space
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<
s
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xml:space
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">pars igitur vis vivæ quæ ad aërem tranſiit, eſt = - p x +
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ap log. </
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<
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<
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">pes cubicus aëris naturali duplo denſioris, inveniètur
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vis viva, quam iſte aër amittit, dum aëris naturalis circumfuſi denſitatem aſſu-
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mit, ea quæ lapſu libero corporis 865. </
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<
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ratur.</
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<
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<
s
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">Pari ſenſu pes cubicus aëris naturali triplo denſioris vim vivam habere
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intelligitur talem quæ reſpondeat lapſui libero corporis 2898 lib. </
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<
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</
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<
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">unius pedis, qui numerus nempe prodit cum ponitur p = 2240, ut §. </
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a = 3. </
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">& </
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">Perſpicuum eſt ex hoc conſenſu inter conſervationem virium vi-
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varum aëri compreſſo & </
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<
s
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">corpori à data altitudine delapſo inſitarum, nullam
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eſſe ad uſum machinarum perficiendum prærogativam ſperandam ex principio
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aëris comprimendi, & </
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<
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">ubique valere regulas in præcedente ſectione exhibi-
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tas. </
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">Quia vero multis modis fit, ut aër non vi ſed natura ſit compreſſus aut
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elaterem naturali majorem acquirat, ſpes certe eſt, poſſe hujuſmodi rebus na-
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turalibus magna ad machinas movendas compendia excogitari, prouti D.
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</
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<
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">Amontons jamjam docuit modum movendarum machinarum vi ignis. </
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perſuadeo ſi omnis vis viva, quæ in carbonum pede cubico latet, ex eodem-
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que combuſtione elicitur, utiliter ad machinam movendam impendatur, quod
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plus inde profici poſſit, quam labore diurno octo aut decem hominum. </
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<
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carbones dum comburuntur aëris elafticitatem nonſolum inſigniter augent, ſed
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& </
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