Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ.
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titudinem velocitati debitam, quam ſuperficies mn habet, cum pervenit in
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ſitum fg; </
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<
s
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echoid-s1341
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xml:space
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">ſit iſta altitudo = v, erit aſcenſus potent. </
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<
s
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echoid-s1342
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xml:space
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">omnis aquæ eo ipſo mo-
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mento pariter = v: </
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<
s
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echoid-s1343
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">Deſcenſus actualis autem eſt per §. </
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<
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xml:space
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">7. </
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<
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echoid-s1345
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xml:space
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">= tertiæ propor-
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tionali ad totam maſſam aquæ, particulam aquæ mngf & </
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<
s
xml:id
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echoid-s1346
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xml:space
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">altitudinem verti-
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calem HB, id eſt, = {δ/β}a; </
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<
s
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echoid-s1347
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xml:space
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">eſt igitur v = {δ/β}a. </
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<
s
xml:id
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echoid-s1348
"
xml:space
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">Hæc quidem altitudo dicto
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citius minuitur ſtatim atque aqua per orificium B fluere cogitur, quod de-
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monſtravi §. </
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<
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">18. </
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<
s
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echoid-s1350
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xml:space
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">ſed primo tamen temporis puncto aqua ſervabit motum
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quem acquiſivit, & </
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<
s
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="
echoid-s1351
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xml:space
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">ſic guttula orificio proxima ejicietur velocitate, quæ de-
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beatur altitudini{mmδ/nnß} a. </
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<
s
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xml:space
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">Poteſt autem hæc altitudo non ſolum eſſe tripla
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aut quadrupla ipſius a, ſed & </
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<
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">quantumcunque magna: </
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<
s
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echoid-s1354
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">ego certe cum tubis
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vitreis pro lubitu jactus feci decies aut vigeſies altiores ipſius a; </
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<
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">fuerit v. </
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">gr.
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</
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<
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xml:space
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">δ = 100 pedum, β = uni pollici, diameter autem tubi decupla diametri,
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quam orificium habet; </
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<
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">& </
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<
s
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xml:space
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">erit {mmδ/nnß} = {10000/1200} a, ita ut in his circumſtan-
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tiis prima guttula aſſilire demta aëris reſiſtentia debeat ad altitudinem plus-
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quam octies majorem altitudine ſolita a. </
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<
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xml:space
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">Sunt cœterum multa impedimenta
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eaque maximi momenti, quæ jactus enormes cohibeant; </
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<
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">perditur nempe ali-
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quid de motu ab impulſu ſuperficiei aqueæ mn in latera fg, dein etiam ab
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ingenti attritu quem aqua per foraminulum, quod parvulum eſſe debet,
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tam celeriter lata patitur: </
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<
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">multum etiam abeſt, quominus aqua C A D m
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omni ſua celeritate moveatur ob adhæſionem aquæ ad latera tubi, quæ ad-
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hæſio in tam longo tractu valde notabilis eſt.</
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<
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">Interim veram hanc eſſe ſolutionem phænomeni nullum poteſt eſſe
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dubium, iſtique ſolutioni experimenta quæ feci in omni extenſione ſatisfa-
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ciunt. </
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<
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xml:space
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">Dein hâc theoria etiam recte ſolvitur alterum phænomeni momen-
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tum, quod nempe jactus iſte ſit quaſi momentaneus, poſtque breviſſimum
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tempusculum ad ſenſus non major ſolito: </
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<
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">ita in præſenti, quem modo
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finximus, caſu ſi per regulam §. </
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<
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">18, paullo mutatam (ibi enim de vaſis
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verticaliter poſitis tantum dicitur) exploremus, quantum aquæ effluere de-
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beat ut jactus non amplius milleſimâ parte (quæ utique obſervari in hujus-
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modi experimentis minimè poteſt) ſuperet jactum ſolitum, cum ab initio
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fuerit eodem octies major, invenimus tam parvam eſſe illam quantitatem, ut
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tempus, quo tota ejicitur, nullo modo percipi poſſit.</
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