Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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244
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HYDRODYNAMICÆ
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<
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<
s
xml:id
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xml:space
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">Sit baſis cylindri unius pedis quadrati, altitudo initialis F C duorum
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pedum: </
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<
s
xml:id
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echoid-s6752
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xml:space
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">contineaturque in ſpatio B F aër qualis in ſuperficie terræ medius eſſe
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ſolet, qui ferre poſſit ſuperficie E F 2240 libras: </
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>
<
s
xml:id
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echoid-s6753
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xml:space
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">ponatur x = 1, ut ſic ha-
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beatur vis viva, qua duo pedes cubici aëris naturalis in ſpatium unius pedis
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lb
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cubici coërceri poſſunt in vacuo: </
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>
<
s
xml:id
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echoid-s6754
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xml:space
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">eritque iſta vis viva = 2 X 2240 X log. </
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>
<
s
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echoid-s6755
"
xml:space
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">2
<
lb
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= 3105, id eſt, talis quæ generatur lipſu libero corporis 3105 librarum
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/>
per altitudinem unius pedis. </
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>
<
s
xml:id
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echoid-s6756
"
xml:space
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">Ergo & </
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<
s
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echoid-s6757
"
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">viciſſim, ſi habeatur pes cubicus aëris
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naturali duplo denſioris, poterit illius ope pondus elevari 3105 librarum ad
<
lb
/>
altitudinem unius pedis in vacuo, dum aëris naturalis denſitatèm aſſumit.</
s
>
<
s
xml:id
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echoid-s6758
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</
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<
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<
s
xml:id
="
echoid-s6759
"
xml:space
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">Sit porro ſub iisdem reliquis circumſtantiis idem aër in ſpatium duplum,
<
lb
/>
quam antea fuit, expanſum, occupans nunc in cylindro altitudinem quatuor
<
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/>
pedum, iſque rurſus condenſetur in ſpatium unius pedis cubici, requiretur
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ad hanc compreſſionem vis viva, quæ exprimitur per 4 X 1120 log. </
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>
<
s
xml:id
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echoid-s6760
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xml:space
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">4, quæ
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priore duplo major eſt. </
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<
s
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echoid-s6761
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xml:space
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">Igitur in vacuo ſi habeatur pes cubicus aëris naturali
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duplo denſioris, poterit illius ope pondus elevari 6210 librarum ad altitud.
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</
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<
s
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echoid-s6762
"
xml:space
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">unius pedis, dum aëris naturalis dimidiam denſitatem aſſumit, aut pondus
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9315 lib. </
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<
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echoid-s6763
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xml:space
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">dum aëre naturali fit quadruplo rarior.</
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<
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"/>
</
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<
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<
s
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echoid-s6765
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xml:space
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">Conſequens inde eſt, ſi aër in ſpatium expandere ſe poſſit infinitum & </
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>
<
s
xml:id
="
echoid-s6766
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">
<
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ubique elaſticitatem ſervet denſitati proportionalem, quantitati aëris finitæ
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vim vivam ineſſe infinitam.</
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<
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<
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">§. </
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">41. </
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<
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xml:space
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">Hæc autem pertinent ad æſtimationem vis vivæ, quæ aëri in
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vacuo poſito inſita ſit: </
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<
s
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xml:space
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">paullo alius fit computus pro aëre denſiore, qui in at-
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moſphæra poſitus eſt: </
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<
s
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xml:space
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">hic enim maximus expanſionis gradus non ultra æquili-
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brium cum aëre atmoſphæræ extendi poteſt: </
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<
s
xml:id
="
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xml:space
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">facile hinc eſt in anteceſſum præ-
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videre, ſi v. </
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<
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">gr. </
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>
<
s
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xml:space
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">habeatur pes cubicus aëris naturali duplo denſioris, vim vi-
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vam quæ in atmoſphæra ab hoc aëre compreſſo elici poſſit, minime eſſe in-
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finitam. </
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>
<
s
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xml:space
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">Poterunt autem hujuſmodi vires vivæ hunc in modum determinari.</
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<
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">42. </
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<
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">Sit aër E B C F naturalis & </
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<
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xml:space
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">in æquilibrio cum aëre externo; </
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<
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">in-
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telligatur autem per p preſſio atmoſphæræ, in ſuſtentaculum E F, quæ quidem
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cum preſſione aëris interni nondum condenſati in æquilibrio eſt. </
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>
<
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">Imponatur
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eidem ſuſtentaculo pondus P; </
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<
s
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xml:space
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">fuerit jam aër condenſatus in ſpatium G B C H;
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</
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<
s
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xml:space
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">habeatque ſuſtentaculum pondere P oneratum in ſitu G H velocitatem v, erit
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retentis reliquis </
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