Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ
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<
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<
s
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xml:space
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">B = 2 MC X (A - √AB).</
s
>
<
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</
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<
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<
s
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xml:space
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">Exinde fit preſſio navem urgens = {B/C}, atque adeo’ proportionalis
<
lb
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altitudini B, quia C eſt quantitas conſtans: </
s
>
<
s
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xml:space
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>
<
s
xml:id
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xml:space
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">preſſio navem promo-
<
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vens & </
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>
<
s
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xml:space
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">altitudo navis velocitati reſpondens ſimul fiunt maximæ: </
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>
<
s
xml:id
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xml:space
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">Igitur ſi pro
<
lb
/>
præſenti inſtituto differentietur quantitas 2MA - 2M√AB, quæ preſſionem
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navem propellentem exprimit, poterit poni d B = o. </
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>
<
s
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xml:space
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">Prius vero quam dif-
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ferentiatio inſtituatur oportet pro M ſubſtituere valorem ejus §. </
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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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">tunc
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fit preſſio navem promovens = {N/4√A} - {N√B/4A}, in qua littera N eſt con-
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ſtans, litteræ vero B & </
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>
<
s
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xml:space
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">A variabiles. </
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<
s
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xml:space
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">Sumatur nunc ejus differentiale, facien-
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do d B = o, idque fiat = o; </
s
>
<
s
xml:id
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xml:space
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">atque ſic reperietur A = 4B.</
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>
<
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</
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<
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<
s
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">Eſt igitur vis navem promovens maxima cum altitudo, ad quam aquæ
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elevantur, eſt quadrupla altitudinis velocitati navis debitæ.</
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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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">Ponatur in æquatione B = 2 M C X (A - √AB) ſuperius inventa
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A = 4B & </
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>
<
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M = {1/4C},
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& </
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<
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xml:space
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">quia (per §. </
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<
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">25.) </
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<
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xml:space
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">eſt M = {N/8A√A}, fit tunc
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A = ({1/2} NC)
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, atque
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B = {1/4}({1/2} NC)
<
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>
.</
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<
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<
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">Si ad præceptum præcedentis paragraphi orificio, per quod
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aquæ inferius ex canali verſus puppim effluunt, concilietur amplitudo {1/4C},
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id eſt, talis, quæ ſe habeat ad amplitudinem unius pedis quadrati, ſicuti men-
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ſura unius pedis, ad altitudinem quadruplam velocitati navis, vi 72. </
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<
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rum animatæ, debitam, fiet tunc ut navis dimidia velocitate feratur ejus qua
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aquæ effluunt & </
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<
s
xml:id
="
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xml:space
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">erit vis repellens aquarum effluentium
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2MA = {1/2C} X ({1/2} NC)
<
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">{2/3}</
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</
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