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

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            obturato orificio gutta eidem imminens vi ſimplicis altitudinis urgeri manife-
              <lb/>
            ſte appareat, reſpondit, diſtinguendum eſſe ſtatum quietis à ſtatu motus.</s>
            <s xml:id="echoid-s8411" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8412" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8413" xml:space="preserve">10. </s>
            <s xml:id="echoid-s8414" xml:space="preserve">Si fiſtula vaſi implantata non ſit cylindrica, calculus ita erit po-
              <lb/>
            nendus.</s>
            <s xml:id="echoid-s8415" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8416" xml:space="preserve">Sit amplitudo canalis in F G vel fg = y; </s>
            <s xml:id="echoid-s8417" xml:space="preserve">diſtantia ſtrati F G gf ab ori-
              <lb/>
            ficio E D = x, retineanturque cæteræ denominationes: </s>
            <s xml:id="echoid-s8418" xml:space="preserve">erit vis viva aquæ in
              <lb/>
            fiſtula contentæ = vſ {dx/y}, ejusque incrementum = dvſ {dx/y}, cui ut in §.
              <lb/>
            </s>
            <s xml:id="echoid-s8419" xml:space="preserve">præcedente factum eſt, addatur vis viva columellæ H L M I ſeu a v, eritque
              <lb/>
            d vſ {dx/y} + αv = αa; </s>
            <s xml:id="echoid-s8420" xml:space="preserve">unde ſic oritur
              <lb/>
            {d v/α} = (a - v): </s>
            <s xml:id="echoid-s8421" xml:space="preserve">ſ {dx/y},
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            quo valore ſubſtituto in æquatione §. </s>
            <s xml:id="echoid-s8422" xml:space="preserve">8. </s>
            <s xml:id="echoid-s8423" xml:space="preserve">fit
              <lb/>
            p = 2v + m (a - v): </s>
            <s xml:id="echoid-s8424" xml:space="preserve">ſ{dx/y}.</s>
            <s xml:id="echoid-s8425" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8426" xml:space="preserve">Igitur cum in fluxu aquarum uniformi ſit v = a, erit tunc rurſus
              <lb/>
            p = 2a. </s>
            <s xml:id="echoid-s8427" xml:space="preserve">Cæterum quamdiu aquarum fluxus acceleratur, motus aquæ in
              <lb/>
            vaſe A C D B orificio D E proximæ, à quo in toto hoc opere animum ab-
              <lb/>
            ſtraximus, hic non eſt negligendus: </s>
            <s xml:id="echoid-s8428" xml:space="preserve">determinari autem recte motus iſte non
              <lb/>
            poteſt, nec igitur accurate quadrat expreſſio quam dedi pro vi repellente ſi
              <lb/>
            aquæ nondum uniformiter fluere ceperint, ſed cum æquabiliter fluunt aquæ
              <lb/>
            valet expreſſio accuratiſſime.</s>
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            <s xml:id="echoid-s8430" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8431" xml:space="preserve">11. </s>
            <s xml:id="echoid-s8432" xml:space="preserve">Poſtquam ſic demonſtravimus pro effluxu aquarum uniformi,
              <lb/>
            vim repellentem ſemper eſſe æqualem ponderi cylindri aquei foramini ſuper-
              <lb/>
            inſtructi & </s>
            <s xml:id="echoid-s8433" xml:space="preserve">ad duplam aquæ altitudinem exſurgentis, lubet id etiam indire-
              <lb/>
            cte demonſtrare per deductionem ad abſurdum, ut & </s>
            <s xml:id="echoid-s8434" xml:space="preserve">regularum mechanicarum
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            ignari propoſitionis hujus ſatis paradoxæ veritatem perſpiciant.</s>
            <s xml:id="echoid-s8435" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8436" xml:space="preserve">Hunc in finem conſiderabimus aquas verticaliter defluentes ex cylindro,
              <lb/>
            abſtrahendo animum ab impedimentis velocitati aquarum aliquid deroganti-
              <lb/>
            bus & </s>
            <s xml:id="echoid-s8437" xml:space="preserve">ab illa contractione venæ, quæ vitari poteſt. </s>
            <s xml:id="echoid-s8438" xml:space="preserve">Foramini reſpondeat tu-
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            bus verticalis, qualis conſpicitur Fig. </s>
            <s xml:id="echoid-s8439" xml:space="preserve">76. </s>
            <s xml:id="echoid-s8440" xml:space="preserve">habeant ſe omnia, ut in Sect. </s>
            <s xml:id="echoid-s8441" xml:space="preserve">XII.
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            <s xml:id="echoid-s8442" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8443" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8444" xml:space="preserve">dictum fuit: </s>
            <s xml:id="echoid-s8445" xml:space="preserve">aquæ habeant fluxum æquabilem: </s>
            <s xml:id="echoid-s8446" xml:space="preserve">latera vaſis & </s>
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