Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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re, ſi canalis C E abſit: </
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<
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xml:space
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">Sed tunc eſt vis ſuſpenſorra = Ma - √(aa + ab),
<
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quia pondus aquæ A B C eſt = Ma & </
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<
s
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xml:space
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">vis repellens per hypotheſin eſt ſimplex
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cylindrus foramini C ad altitudinem a ſuperinſtructus. </
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<
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xml:space
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">Deberet igitur in hâc
<
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hypotheſi ſemper eſſe Ma + a + b - 2√(aa + ab) = Ma - √(aa + ab)
<
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ſeu a + b = √(aa + ab), quod eſt abſurdum. </
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<
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xml:space
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">Similis abſurditas demonſtra-
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ri poſſet, ſi vena ſurſum verticaliter aſcendere putetur: </
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<
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xml:space
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">& </
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<
s
xml:id
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"
xml:space
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">fruſtra hic excipe-
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retur pro communi ſententia firmanda, venam effluentem C E fingi non poſſe
<
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tanquam continuam, niſi aliqua aquæ tenacitas fingatur ſimul (aliàs enim ve-
<
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nam mox præ orificio in guttulas abruptum iri) & </
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<
s
xml:id
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xml:space
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">tenacitatem rei ſtatum per-
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mutare: </
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<
s
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xml:space
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">nam profecto nec velocitates aquæ à cohæſione mutua aquæ in C E
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mutantur nec latera canalis C E preſſionem ullam ſentiunt, ſicut demonſtravi
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Sect. </
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<
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<
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">§. </
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<
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xml:space
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">13. </
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<
s
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xml:space
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">ut taceam cohæſionem aquæ non oriri à tenacitate ſed ab ali-
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qua virtute magnetica ſeu à mutua attractione, à qua virtute centrum gravita-
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tis in nullo ſyſtemate nec majorem nec minorem velocitatem acquirere poteſt.
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</
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<
s
xml:id
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xml:space
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">Sed hæc porro adverſariorum exceptio in venis verticaliter aſcendentibus nul-
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lum plane locum habet, cum aquæ ibi continuè maneant, ſi vel nulla aquisin-
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ſit tenacitas aut mutua attractio.</
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<
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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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">At poſſem infinitis aliis modis & </
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<
s
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xml:space
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">exemplis particularibus ſententiam
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noſtram confirmare, ſi hiſce diutius inſiſtere vellem. </
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<
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<
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</
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<
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xml:space
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">deſcripta, ſi ſit altitudo N S = 1, orificium L M = 1, & </
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<
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">orificium
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R S = 2, erit P B = {1/3}, vis repellens, quæ oritur ab effluxu aquæ per R S
<
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= 2 X {2/3} = {4/3}, & </
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<
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xml:space
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">demonſtrare poſſum vim repellentem, quæ prodit ab ef-
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fluxu aquæ ex ſimplici cylindro R N per L M eſſe etiam = {4/3}, & </
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<
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xml:space
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">ſic vim re-
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pellentem totalem eſſe = {8/3}, quæ præciſe facit duplum cylindrum aqueum fo-
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ramini L M ad altitudinem N S + P B inſiſtentem. </
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<
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">Talis autem conſenſus ex
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aliis theoriis falſo receptis minime prodit, ita ut de noſtra amplius non poſ-
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ſint dubitare, niſi harum rerum penitus ignari: </
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<
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xml:space
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">Id vero, quod dixi, vim re-
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pellentem aquæ ex ſimplici cylindro R N per L M effluentis eſſe = {4/3}, ſi de-
<
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monſtrare velim, poſtulat ut vis repellens definiatur, cum aquæ ex vaſe non
<
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infinito data velocitate quacunque non variata fluunt: </
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<
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">Ne vero prolixior ſim
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in hâc re, id aliis efficiendum relinquo; </
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<
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ceſſet operam; </
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