Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUARTA.
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dv = o, ſive - {nndz/mm} + {na/mb}√{g/n}:</
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<
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xml:space
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<
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, id eſt,
<
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z = {nb/m}√{n/g}, X log.</
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<
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xml:space
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">({ma/nb}√{g/n})</
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</
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<
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<
s
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xml:space
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">Hæc autem altitudo multiplicata per altitudinem cylindri m dat quan-
<
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titatem aquæ interea effluentis, nempe nb√{n/g} X log.</
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<
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xml:space
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">({ma/nb}√{g/n},) quæ quan-
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titas, ut ſupra §. </
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<
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<
s
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xml:space
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">præmonui, eſt infinita, quamvis tantum logarithmica-
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liter, cujusmodi infinitum minus eſt, quam radix cujuscunque dimenſionis
<
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datæ ex eodem infinito; </
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<
s
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xml:space
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">eſt ſcilicet log. </
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<
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xml:space
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">∞ minor quam ∞ {1/n}, quantuscunque
<
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fuerit numerus n aſſignabilis. </
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<
s
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xml:space
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">Atque hoc ideo moneo, ut ſic intelliga-
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tur, qui fiat, ut, ſi à vero infinito ratiocinamur ad quantitates valde ma-
<
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gnas, quantitas iſta aquæ ſat parva evadat. </
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<
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hæc ſunt.</
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</
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<
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<
s
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">(I) Si tubus annexus eſt cylindricus, fit z = {nb/m}log.</
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<
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xml:space
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">{ma/nb}:
<
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</
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<
s
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xml:space
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">Igitur cæteris paribus hæc quantitas ſe habet, ut longitudo tubi annexi, quod
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generaliter etiam verum eſt: </
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<
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xml:space
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">nam à mutato valore ipſius b cenſenda eſt non
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mutari quantitas log.</
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<
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xml:space
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">{ma/nb}√{g/n} ob valorem infinitum numeri {m/n}.</
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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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">(II) Pro eodem orificio g cæterisque etiam paribus, ſequitur quantitas z
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ſesquiplicatam rationem orificii extremi: </
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<
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xml:space
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">atque ſi idem tubus modo orifi-
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cio ſtrictiori modo ampliori vaſi applicetur, erit quantitas aquæ in caſu prio-
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ri ad ſimilem quantitatem in poſteriori, ut quadratum orificii amplioris, ad
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quadratum orificii minoris.</
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<
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xml:space
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">(III) Denique obſervandum eſt valere totum ratiocinium pro omnibus
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directionibus tubi, quod quivis perſpiciet qui §. </
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<
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</
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<
s
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xml:space
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">Poterit igitur tubus adhiberi etiam horizontalis aut ſub quâcunque alia di-
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rectione & </
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<
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xml:space
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">utcunque incurvus, ad quod præſertim in inſtituendis experimen-
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tis animus erit advertendus. </
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<
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xml:space
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">Semper autem intelligetur per b longitudo tu-
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bi, per a vero altitudo aquæ verticalis ſupra orificium extremum.</
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<
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