Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ.
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xml:space
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xml:space
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">({mmαα - nn/nn})
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= a: </
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xml:space
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<
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quoniam autem {mmαα/nn} eſt numerus infinitus, poterit cenſeri:
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</
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xml:space
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<
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= 1 + (log.</
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xml:space
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xml:space
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cujus rei demonſtratio talis eſt: </
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<
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noſtro exemplo A
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, facile quisque videt eſſe hanc quantitatem paullo majo-
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rem, quam eſt unitas, & </
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<
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">quidem exceſſu infinite parvo, quem vocabimus
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z; </
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<
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= 1 + z, ſumantur utrobique logarithmi & </
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xml:space
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{log. </
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xml:space
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">A/A} = log. </
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<
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xml:space
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">(1 + z) = (ob infinitè parvum valorem ipſius z) z; </
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eſt A
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= 1 + {log. </
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<
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<
s
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xml:space
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">proindeque ſimiliter eſt, ut diximus,
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({mmαα/nn})
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= 1 + (log.</
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<
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xml:space
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<
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xml:space
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</
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<
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">Porro quia quantitas hæc unitati addita eſt infinitè parva, erit
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a:</
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ſeu
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a:</
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<
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">{mmαα/nn}) = a - a (log. </
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xml:space
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</
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<
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">eſt igitur ſpatium per quod ſuperficies aquæ deſcendit, dum à quiete maxi-
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ma oritur velocitas = a (log. </
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<
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xml:space
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<
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xml:space
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<
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<
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">Indicat hæc æquatio deſcenſum aquæ in vaſe infinite amplo infinite par-
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vum eſſe, cum aqua jam maximum velocitatis gradum attigerit: </
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tem hoc non obſtante dubitari, an non interea quantitas aquæ finita effluat,
<
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quandoquidem cylindrus ſuper baſi infinita erectus, utut altitudinis infinite
<
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parvæ magnitudinem poſſit habere infinitam: </
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ne, hanc quoque quantitatem infinite parvam eſſe, & </
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{@nna/mαα}log.</
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<
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">Atque convenit hoc egregie profecto cum phænomenis, quæ in ef-
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fluxu aquarum ex caſtellis per ſimplex foramen toto die experimur. </
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