Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO OCTAVA.
"/>
<
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<
s
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xml:space
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">III. </
s
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<
s
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echoid-s4625
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xml:space
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">Si vero nunc alterum foramen N admodum exiguum præ ambo-
<
lb
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bus reliquis ponatur, erit facto γ = o
<
lb
/>
x = {ααa/αα + ββ}; </
s
>
<
s
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="
echoid-s4626
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xml:space
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">deinde
<
lb
/>
x + b = {ααa + ααb + ββb/αα + ββ}, & </
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>
<
s
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="
echoid-s4627
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xml:space
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">
<
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a - x = {ββa/αα + ββ}.</
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>
<
s
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echoid-s4628
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</
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<
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<
s
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xml:space
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">IV. </
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<
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xml:space
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">Si γγb = ααa, fit x = o. </
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<
s
xml:id
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echoid-s4631
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xml:space
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">Nullam igitur in hoc caſu preſſionem
<
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ſuſtinent partes laminæ L Q: </
s
>
<
s
xml:id
="
echoid-s4632
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xml:space
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">imo inferiora verſus premitur, ſi γ ſit majus
<
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quam {ααa/b}, & </
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>
<
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xml:id
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">lamina nullibi ſit perforata.</
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<
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</
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<
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<
s
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xml:space
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">Iſta vero omnia ſimiliter ex §. </
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<
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">19. </
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<
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">facile colliguntur.</
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<
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</
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<
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<
s
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xml:space
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">V. </
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>
<
s
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xml:space
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">Ita quoque ope ejusdem paragraphi ſine calculo novo prævideri po-
<
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tuiſſet, quid fieri debeat, cum poſitis foraminibus H & </
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>
<
s
xml:id
="
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xml:space
="
preserve
">N in eadem altitudi-
<
lb
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ne ſumma foraminum eorum, ceu unicum amplitudinis β + γ conſiderari
<
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poteſt: </
s
>
<
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xml:space
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">Indicant nempe tam §. </
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<
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">19. </
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<
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">quam §. </
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<
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">26. </
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<
s
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">eſſe
<
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/>
x = {ααa/αα + (β + γ)
<
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style
="
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">2</
emph
>
},</
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>
</
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<
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<
s
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">VI. </
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<
s
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xml:space
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">Notari etiam poteſt, cum valor ipſius x fit imaginarius, id pro-
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venire ex eo, quod aquæ non ſolum non effluant, in aliquibus caſibus per
<
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H, ſed quod ſuperficies L Q etiam deſcendat; </
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<
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xml:space
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">unde fieri poteſt, ut infra
<
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orificium M deſcendat, quo ipſo ceſſat aqua@um contiguitas contra hypothe-
<
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/>
ſin propoſitionis. </
s
>
<
s
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xml:space
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">Si autem valor x eſt realis, tum dupliciter exprimitur,
<
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ſed alter valor inutilis eſt reputandus; </
s
>
<
s
xml:id
="
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xml:space
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">ſic igitur cavendum ne præpoſtera
<
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radix ceu utilis aſſumatur.</
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>
<
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</
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<
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<
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echoid-s4653
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xml:space
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">VII. </
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>
<
s
xml:id
="
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xml:space
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">Denique ut caſum ſpecialiſſimum attingamus, ponemus om-
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nia foramina inter ſe æqualia, & </
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>
<
s
xml:id
="
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xml:space
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">prodibit 5xx + (2b - 6a) x = - aa +
<
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2ab - bb, ſeu x = {3a - b - 2√ (aa + ab - bb)/5}; </
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>
<
s
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xml:space
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">atque ſi fuerit præterea
<
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a = 3b, erit x = (proxime) {4/15} b, deinde altitudo velocitatis in forami-
<
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/>
ne N ſeu x + b = {19/15}b atque altitudo velocitati in M debita ſeu a - x = {41/15}b.
<
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</
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>
<
s
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">Sunt itaque velocitates ſeu etiam, quia foramina æqualia ſunt, </
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