Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Table of Notes

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            omni cura perpendere, experimentisque confirmare, quod paſſim in hoc
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            tractatu, præſértim autem in ſectione tertia, feci.</s>
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            <s xml:id="echoid-s7549" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7550" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7551" xml:space="preserve">Si ubique motus definiri poſſet, facile foret ſtaticam in fluidis
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            motis generaliſſimam formare: </s>
            <s xml:id="echoid-s7552" xml:space="preserve">ſi enim foramen, ſed id infinite parvum fin-
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            gas, eo ipſo in loco pro quo preſſio aquarum deſideratur, quæres primo
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            quanta velocitate aquæ per illud foraminulum ſint erupturæ & </s>
            <s xml:id="echoid-s7553" xml:space="preserve">cui altitudini
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            illa velocitas debeatur: </s>
            <s xml:id="echoid-s7554" xml:space="preserve">intelligis autem huic ipſi altitudini proportionalem
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            eſſe preſſionem, quam quæris.</s>
            <s xml:id="echoid-s7555" xml:space="preserve"/>
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            <s xml:id="echoid-s7556" xml:space="preserve">Ex hoc principio petenda eſt preſſio quam ſuſtinet lamina horizonta-
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            lis L Q in figura quadrageſima tertia, ſi perforata non fuerit: </s>
            <s xml:id="echoid-s7557" xml:space="preserve">poſtquam enim
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            demonſtratum à nobis fuit in corollario ſecundo paragraphi trigeſimi primi
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            Sectionis octavæ, ſi foraminulum H infinite parvum fuerit ratione foraminum
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            M & </s>
            <s xml:id="echoid-s7558" xml:space="preserve">N: </s>
            <s xml:id="echoid-s7559" xml:space="preserve">ratioque horum foraminum M & </s>
            <s xml:id="echoid-s7560" xml:space="preserve">N indicetur per α & </s>
            <s xml:id="echoid-s7561" xml:space="preserve">γ, fore altitu-
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            dinem velocitati aquæ per H erumpentis debitam = {αα X LB - γγ X NQ/αα + γγ}, inde
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            judicabimus niſum aquæ in laminam L Q non perforatam huic ipſi altitudini
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            proportionalem eſſe: </s>
            <s xml:id="echoid-s7562" xml:space="preserve">quod idem alio modo demonſtratum dedimus in para-
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            grapho decimo nono citatæ Sectionis: </s>
            <s xml:id="echoid-s7563" xml:space="preserve">Hinc ſequitur fieri poſſe, ut lamina L Q
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            nullam preſſionem patiatur, quantumvis magna ſupra eam fuerit altitudo aquæ,
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            ſcilicet quando γ = α √ (L B: </s>
            <s xml:id="echoid-s7564" xml:space="preserve">N Q), imo preſſionem in ſuctionem mutari
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            poſſe.</s>
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            <s xml:id="echoid-s7566" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7567" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7568" xml:space="preserve">Similiter obtinetur preſſio aquæ in laminam L Q, ſi vel hæc per-
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            forata fuerit foramine finitæ ratione amborum reliquorum magnitudinis. </s>
            <s xml:id="echoid-s7569" xml:space="preserve">Si
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            enim foraminulo infinite parvo lamina præter illud, quod eſt in H, perforata
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            fuerit, non poteſt non velocitate communi aqua per utrumque erumpere: </s>
            <s xml:id="echoid-s7570" xml:space="preserve">Et
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            cum hæc velocitas cognita ſit (per §. </s>
            <s xml:id="echoid-s7571" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7572" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s7573" xml:space="preserve">8.) </s>
            <s xml:id="echoid-s7574" xml:space="preserve">pro foramine H, habetur
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            quoque velocitas, qua aqua per foraminulum, quod nempe concipimus,
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            erumpere debeat, atque ſic preſſionem aquæ cognoſcimus. </s>
            <s xml:id="echoid-s7575" xml:space="preserve">Fuerint v. </s>
            <s xml:id="echoid-s7576" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s7577" xml:space="preserve">fora-
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            mina M, H & </s>
            <s xml:id="echoid-s7578" xml:space="preserve">N inter ſe æqualia, altitudo autem B L habuerit ad altitudi-
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            nem L Q rationem ut 10 ad 3, erit preſſio in laminam L Q ſubdecupla illius,
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            quæ eſt obturatis foraminibus H & </s>
            <s xml:id="echoid-s7579" xml:space="preserve">N.</s>
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            <s xml:id="echoid-s7581" xml:space="preserve">Denique ſi in alio loco preſſionem aquæ deſideres, addes ſaltem alti-
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            tudinem, qua lamina L Q ſupra illum locum eminet, altitudini jactus per </s>
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