Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUINTA.
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verticaliter fiat & </
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<
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xml:space
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">cum impetu, tantum abeſſe, ut inde motus acceleretur, quin
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potius retardetur, niſi aquarum affuſio fiat in totam ſuperficiem æquabiliter eo,
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quem §. </
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<
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<
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">expoſui, modo, ſi enim aliter affundantur, motus aquarum in va-
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ſe perturbatur, iſque motus confuſus effluxum retardat.</
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<
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xml:space
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</
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<
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xml:space
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">Joanne Poleno inſtituta, ut refert in libro primo de motu aquæ mixto, p. </
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ſeqq. </
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<
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xml:space
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">quæ ideo hic alleganda eſſe cenſui, quod egregie demonſtrant, ubique
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celeritatem ultimam in vaſis conſtanter plenis eam eſſe, quæ integræ aquæ al-
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titudini conveniat, ſi vaſa non ſint ſubmerſa, aut differentiæ altitudinum aquæ
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internæ & </
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<
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">externæ in vaſis ſubmerſis, quamvis de cætero nihil in illis ſit, quod
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nunc novum adhuc ſit, quia nullæ illic conſiderantur accelerationes.</
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<
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</
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<
s
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">Finge cylindrum, cujus axis habeat ſitum verticalem, amplitudinis ve-
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luti infinitæ; </
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<
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">fundum integrum ſit: </
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<
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xml:space
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">in pariete autem fiſſura ſit axi parallela, fo-
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ramen habens parallelogrammi rectanguli, quæ à fundo ad cylindri uſque ſum-
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mitatem extendatur. </
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<
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xml:space
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">Puta porro aquam in cylindrum affundi æquabiliter, ita,
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ut æqualibus temporibus quantitates injiciantur æquales, effluent aquæ ex cy-
<
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lindro per fiſſuram: </
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<
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">nec tamen ab initio eadem effluent quantitate, qua ſuper-
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ne affunduntur, ſed minori: </
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<
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">igitur aſſurget ſuperficies aquæ in cylindro ad
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certam uſque altitudinem aſſymptoton; </
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<
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">ſi vero is jam intelligatur adeſſe ter-
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minus, immutata manebit altitudo aquæ & </
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<
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">eadem quantitate effluent conſtan-
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ter aquæ, qua affunduntur: </
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<
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">Apparet quoque, altitudinem aquæ in cylindro
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eo majorem fore, quo largius affundantur: </
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<
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">Quæritur itaque auctis quantitati-
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bus aquarum dato tempore affundendis, in quanam ratione creſcere debeant
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altitudines, ad quas aquæ in cylindro aſſurgent.</
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">Sit altitudo aquæ, cum eſt in ſtatu permanente = α:
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</
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">& </
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<
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">abſcindatur à ſuperficie pars quæ ſit = x, una cum differentiali d x: </
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<
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tudo rimæ = n, habebimus veluti foramen amplitudinis = n d x, per quod
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aquæ effluunt velocitate √ x: </
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<
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">igitur quantitas aquæ dato tempore ibi effluen-
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tis eſt ut n d x √ x, cujus integralis eſt {2/3} n x √ x; </
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<
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aquæ dato tempore per rimæ longitudinem abſciſſam x effluentem: </
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titas aquæ eodem tempore per rimam integram effluens exprimetur per {2/3} n α
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√ α: </
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illo tempore affuſæ dicatur q, erit {2/3} n α √ α = q. </
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