Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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vorticum commendare hypotheſin, ſed quasdam tantum inde concluſiones
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facere, ſine quibus ipſam hypotheſin ſubſiſtere non poſſe crediderim.</
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<
s
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xml:space
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">Venio jam ad alteram ſectionis partem, qua breviter conſiderabimus
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ſtatum fluidorum, quæ intra vaſa mota continentur: </
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<
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xml:space
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">Argumentum eſt fertiliſ-
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ſimum infinitiſque modis variabile: </
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<
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xml:space
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">Sed pauca attingemus, ceu exempla, ad
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quæ multa alia revocari poterunt.</
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<
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xml:space
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">Si aqua in vaſe perforato contineatur ipſumque vas libere ca-
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dat, ex ſe patet, nihil aquæ durante vaſis lapſu eſſe effluxurum, quia nem-
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pe particulæ ſuperiores non gravitant in inferiores: </
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<
s
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xml:space
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">Si vas motu quidem acce-
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lerato deſcendat ſed tardiore quam quo corpora naturaliter in vacuo accele-
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rantur, effluet aqua, ſed minori velocitate ac ſi vas quiescat: </
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<
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xml:space
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">Contrarium erit,
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ſi vas motu accelerato ſurſum trahatur: </
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<
s
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xml:space
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">Denique ſi vas horizontaliter accele-
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rato motu feratur (jam enim ad reliquas non attendemus directiones) fieri po-
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teſt, ut velocitas aquæ effluentis major ſit vel minor velocitate ordinaria pro
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ratione ſitus foraminis: </
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<
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">Velocitates autem aquæ ſic determinabuntur.</
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<
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">aqua plenus usque in A B,
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<
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cujus fundum C D foramen habeat in E valde parvum per quod aquæ effluant,
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dum interea totum vas ſurſum trahaturà pondere P deſcendente mediante funi-
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culo ſuper duabus trochleis H & </
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<
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xml:space
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">Denique conſtanter tantum
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aquæ ſuperius affundi ponatur, quantum effluit per foramen E: </
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<
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cylindri & </
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<
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<
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xml:space
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">lta apparet quamlibet gut-
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tam aquæ in vaſe veluti ſtagnantis vi animari ad aſcenſum quæ ſe habeat ad vim
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gravitatis naturalem ut {P - p/P + p} ad 1: </
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<
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xml:space
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">Quia vero reactio guttulæ in fundum æqua-
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lis eſt vi, qua ad aſcenſum animatur quævis guttula, præter preſſionem natu-
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ralem aliam exeret in fundum, quæ exprimenda erit per {P - p/P + p}. </
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<
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xml:space
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">Utraquè vero
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preſſio ſimul ſumta erit ad preſſionem ſolam naturalem ut {2P/P + p} ad 1, adeo
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ut fundum haud ſecus ab incumbente aqua prematur, quam ſi cylindrus quieſ-
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ceret eſſetque altitudo aquæ = {2P/P + p} X A C, ex quo ipſo ſequitur altitudinem
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velocitati aquæ uniformiter effluentis debitam eſſe = {2P/P + p} X A C.</
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