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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">(γ) Videbitur forta@@e rem non ſatis perluſtrantibus fore, ut omni-
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bus in ſtatu permanente jam poſitis, nullisque præſentibus obſtaculis alienis,
<
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aqua per foramen E velocitate exiliat, qua aſcendere poſſit ad altitudinem co-
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lumnæ aqueæ in æquilibrio poſitam cum preſſione emboli: </
s
>
<
s
xml:id
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xml:space
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preserve
">atque ita ſane fo-
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ret, ſi preſſio emboli ſine interr uptione adeſſet, nullusque in aqua aſcenſus po-
<
lb
/>
tentialis perderetur: </
s
>
<
s
xml:id
="
echoid-s5049
"
xml:space
="
preserve
">quia vero in utroque res aliter ſe habet, non poteſt non
<
lb
/>
alia oriri in jactu aqueo velocitatis æſtimatio: </
s
>
<
s
xml:id
="
echoid-s5050
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xml:space
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">Hinc quiſque non obſcure videt
<
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animum advertendum eſſe ad temporum rationem, quibus embolus deprimi-
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tur, retrahiturque, tum etiam ad rationem amplitudinum in canaliculo D & </
s
>
<
s
xml:id
="
echoid-s5051
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xml:space
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<
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orificio E.</
s
>
<
s
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xml:space
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</
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<
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<
s
xml:id
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xml:space
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">(δ) Ponamus igitur tempus quo embolus deprimitur = θ tempus
<
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unius integræ agitationis = t, amplitudinem orificii E = μ, & </
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>
<
s
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xml:space
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">diabetes D = m:
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</
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<
s
xml:id
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echoid-s5055
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xml:space
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">deinde comparata potentia embolum detrudente cum ſuperincumbente colum-
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lb
/>
na aquea, faciamus hujus columnæ altitudinem = a, altitudinem vero aquæ
<
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exilientis velocitati debitam = x. </
s
>
<
s
xml:id
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echoid-s5056
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xml:space
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preserve
">His ita ad calculum præparatis licebit duo-
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bus indagare modis rationem quæ futura ſit inter velocitates aquarum in
<
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orificio E & </
s
>
<
s
xml:id
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xml:space
="
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">diabete D, atque hinc valorem incognitæ x; </
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<
s
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xml:space
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">elicere. </
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>
<
s
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xml:space
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">Primò enim
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patet tempore θ (quo ſcilicet embolus detruditur) tantum aquæ fluere per
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diabeten D, quantum tempore t (quo embolus deprimitur retrahiturque) ef-
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fluit per E. </
s
>
<
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xml:space
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">Eſt igitur velocitas in D ad velocitatem in E ut {1/mθ} ad {1/μt}: </
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xml:space
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">& </
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quum poſterior hæc velocitas ſit = √ x, erit altera = {μt/mθ} √ x. </
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>
<
s
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xml:space
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preserve
">Secundò quia
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velocitas aquæ effluentis debetur preſſioni aëris in catino, ſequitur hanc preſ-
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ſionem æquivalere ponderi columnæ aqueæ altitudinis x; </
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>
<
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xml:space
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">ſed ſi à preſſione
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emboli auferas preſſionem aëris, habebis preſſionem, quæ velocitatem aquæ
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in D generet; </
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>
<
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xml:space
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">hinc quia differentia preſſionum exprimitur per a - x, repræ-
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ſentabitur velocitas aquæ in D per √ (a - x); </
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<
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xml:space
="
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">Igitur nunc eſt velocitas aquæ
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in D ad velocitatem aquæ in orificio E ut √ (a - x) ad √ x. </
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>
<
s
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xml:space
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">Combinatis ratio-
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nibus utroque modo inventis, fit
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√ (a - x):</
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<
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xml:space
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">√x = {1/mθ}: </
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>
<
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xml:space
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">{1/μt}, ſive
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x = {mmθθ/mmθθ + μμtt} X a.</
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