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

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        <div xml:id="echoid-div37" type="section" level="1" n="25">
          <pb o="31" file="0045" n="45" rhead="SECTIO TERTIA."/>
        </div>
        <div xml:id="echoid-div38" type="section" level="1" n="26">
          <head xml:id="echoid-head35" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s849" xml:space="preserve">Sit canalis utcunque formatus S T (Fig. </s>
            <s xml:id="echoid-s850" xml:space="preserve">13. </s>
            <s xml:id="echoid-s851" xml:space="preserve">& </s>
            <s xml:id="echoid-s852" xml:space="preserve">14.) </s>
            <s xml:id="echoid-s853" xml:space="preserve">per quem aqua fluit
              <lb/>
            b c f g; </s>
            <s xml:id="echoid-s854" xml:space="preserve">aſſumitur, ſi in axe a e accipiatur punctum quodcunque n, per
              <lb/>
              <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">Fig. 13.
                <lb/>
              & 14.</note>
            quod planum ad axem perpendiculare p m tranſeat, fore, ut omnes parti-
              <lb/>
            culæ aqueæ in illo plano exiſtentes æquali velocitate fluant, & </s>
            <s xml:id="echoid-s855" xml:space="preserve">quidem ta-
              <lb/>
            li, quæ ſit ubique reciproce proportionalis magnitudini ſectionis p m. </s>
            <s xml:id="echoid-s856" xml:space="preserve">Sit
              <lb/>
            autem velocitas aquæ in g f talis, quæ debetur altitudini verticali q s, id eſt,
              <lb/>
            ſit aſcenſus potentialis ſtrati aquei in g f æqualis lineæ q s, & </s>
            <s xml:id="echoid-s857" xml:space="preserve">quoniam hujus-
              <lb/>
            modi altitudines ſunt in ratione quadrata velocitatum, ſequitur eſſe aſcen-
              <lb/>
            ſum potentialem aquæ in p m æqualem quartæ proportionali ad quadratum
              <lb/>
            amplitudinis p m, quadratum amplitudinis g f & </s>
            <s xml:id="echoid-s858" xml:space="preserve">altitudinem q s, nempe
              <lb/>
            = {gf
              <emph style="super">2</emph>
            /pm
              <emph style="super">2</emph>
            } X qs. </s>
            <s xml:id="echoid-s859" xml:space="preserve">His ita præmonitis ponemus in figura decima quarta eſſe
              <lb/>
            curvam B P G, ſcalam amplitudinum canalis, ita ut poſita A N = a n, denotet
              <lb/>
            N P amplitudinem in p m: </s>
            <s xml:id="echoid-s860" xml:space="preserve">dein curvam H I K eſſe ſcalam aſcenſuum poten-
              <lb/>
            tialium, ita ut ſit N I = {EG
              <emph style="super">2</emph>
            /NP
              <emph style="super">2</emph>
            } X qs. </s>
            <s xml:id="echoid-s861" xml:space="preserve">fingatur nunc elementa ſingula curvæ
              <lb/>
            H I K habere pondus æquale ponderi ſtrati aquei reſpondentis, & </s>
            <s xml:id="echoid-s862" xml:space="preserve">cadere
              <lb/>
            centrum gravitatis iſtius curvæ in punctum L, & </s>
            <s xml:id="echoid-s863" xml:space="preserve">ducatur L O perpendicu-
              <lb/>
            laris ad axem A E; </s>
            <s xml:id="echoid-s864" xml:space="preserve">ſic erit L O aſcenſus potentialis totius aquæ quæſitus. </s>
            <s xml:id="echoid-s865" xml:space="preserve">Ex
              <lb/>
            mechanicis autem conſtat, fi fiat tertia curva U X Z, cujus applicata N X
              <lb/>
            ſit ubique æqualis {EG
              <emph style="super">2</emph>
            /NP}, fore L O æqualem quartæ proportionali ad ſpa-
              <lb/>
            tium A E G B & </s>
            <s xml:id="echoid-s866" xml:space="preserve">A E Z U atque lineam q s vel E K. </s>
            <s xml:id="echoid-s867" xml:space="preserve">Patet igitur quæſitum.
              <lb/>
            </s>
            <s xml:id="echoid-s868" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s869" xml:space="preserve">E. </s>
            <s xml:id="echoid-s870" xml:space="preserve">I.</s>
            <s xml:id="echoid-s871" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s872" xml:space="preserve">§. </s>
            <s xml:id="echoid-s873" xml:space="preserve">3. </s>
            <s xml:id="echoid-s874" xml:space="preserve">Fuerit v. </s>
            <s xml:id="echoid-s875" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s876" xml:space="preserve">canalis conicus, in quo ſuperficies anterior g f
              <lb/>
            & </s>
            <s xml:id="echoid-s877" xml:space="preserve">poſterior b c diametros habeant ut m ad n, erit aſcenſus potentialis aquæ
              <lb/>
            = {3m3/n(mm + mn + nn)} X qs.</s>
            <s xml:id="echoid-s878" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div40" type="section" level="1" n="27">
          <head xml:id="echoid-head36" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s879" xml:space="preserve">§. </s>
            <s xml:id="echoid-s880" xml:space="preserve">4. </s>
            <s xml:id="echoid-s881" xml:space="preserve">Datis variationibus infinite parvis tam ratione ſitus quam ve-
              <lb/>
            locitatis, quæ ſuperficiei aquæ anteriori reſpondent, invenire variationes
              <lb/>
            ad aſcenſus potentiales totius aquæ pertinentes.</s>
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          </p>
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