Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO DECIMA.
"/>
plitudinis, cujus altitudo ſit plusquam 10000 vicibus major altitudine com-
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muni barometri, invenimus autem ſupra art. </
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<
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xml:space
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">IV. </
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<
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xml:space
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">numerum n ( qui idem ſi-
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gnificabat) = 6004. </
s
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<
s
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"
xml:space
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preserve
">Ergo jam tuto affirmabimus ( ubique enim quæ negle-
<
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ximus majorem vim pulveri arguunt) ineſſe pulveri pyrio vim elaſticam,
<
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minimum decies millies majorem vi elaſtica aëris ordinarii. </
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>
<
s
xml:id
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xml:space
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">Apparet autem
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ſimul ex comparatione numerorum 10000 & </
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>
<
s
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xml:space
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">6004, quantum circiter vi pul-
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veris decedat ab hiatibus ſæpe dictis. </
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<
s
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xml:space
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">Equidem iſtud decrementum majus pu-
<
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taſſem: </
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<
s
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xml:space
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">Confirmatus autem ſum hoc calculo in re de qua aliquando me cer-
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tiorem voluit vir harum rerum gnarus, nullum nempe ſe in tormentis nota-
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bile obſervaſſe decrementum, cum lumen accenſorium diuturno uſu ſupra
<
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modum amplificatum eſſet in obſidio.</
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>
<
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xml:space
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</
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<
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<
s
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xml:space
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">(IX) Verum ut ex æquatione noſtra quædam corollaria deduci poſ-
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ſint faciliora quam vis proxime tantum vera, mutabimus quantitatem lo-
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garithmicalem in ſeriem. </
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>
<
s
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xml:space
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">Eſt autem
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- log. </
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<
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xml:space
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">(1 - {(f + φ)v/(F - f)√(bPp)}) = {(f + φ)v/(F - f)√(b P p)}
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+ {(f + φ)
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vv/2(F - f)
<
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X b P p} + {(f + φ)
<
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v
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/3(F - f)
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X b P p√(b P p)} + &</
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">c.
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</
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<
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xml:space
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">Iſtoque valore ſubſtituto in æquatione ultima art. </
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<
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xml:space
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">(VII) fit
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log. </
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<
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xml:space
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">{a/b} = {Fvv/2(F - f). </
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<
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xml:space
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">b P} + {F.</
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<
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xml:space
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">(f + φ)v
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/3.</
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">(F - f)
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bP√(bPp)} + &</
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Notabimus hic iſtam æquationem perfecte convenire cum æquatione ultima
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art. </
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<
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">(II) ſi aperturæ f & </
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<
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xml:space
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">φ ponantur = 0: </
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<
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">quod enim hic indicatur per {1/2} vv
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& </
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<
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">n P ibi eſt α & </
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<
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xml:space
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">P, convenientibus denominationibus reliquis.</
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<
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xml:space
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">(X) Ut appareat, quantum proxime altitudo jactus ab aperturis dimi-
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nuatur, ſi iſtæ aperturæ ſint minimæ, inſerviet hæc æquatio. </
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<
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xml:space
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">Intelligatur per
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α altitudo ad quam globus pervenire poſſit in vacuo, ſi nulla auræ quantitas
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per aperturas avolare ponatur, & </
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<
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xml:space
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">erit decrementum iſtius altitudinis ab erup-
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tione auræ per easdem aperturas oriundum proxime hoc
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[(2α)
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X (f + φ)]: </
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