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

Table of handwritten notes

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              <pb o="33" file="0047" n="47" rhead="SECTIO TERTIA."/>
            vel poſt effluxum guttulæ, G H amplitudinem illam aſſumtam, I L mag-
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            nitudinem fundi, P L magnitudinem foraminis, dum adhærens parallelo-
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            grammum minimum P N O L reſpondet guttulæ cylindricæ pnol: </s>
            <s xml:id="echoid-s914" xml:space="preserve">dein con-
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            ſtruatur alia curva T R U, cujus applicatæ ſint rurſus æquales quadrato lineæ
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            G H, diviſo per applicatam reſpondentem curvæ C G I, cui curvæ eadem
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            conditione annexum eſt parallelogrammulum L O Y X, cujus nempe latus
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            L X eſt æquale quadrato lineæ G H diviſo per lineam PL.</s>
            <s xml:id="echoid-s915" xml:space="preserve"/>
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            <s xml:id="echoid-s916" xml:space="preserve">Jam igitur apparet aſcenſum potent. </s>
            <s xml:id="echoid-s917" xml:space="preserve">aquæ ante effluxum guttulæ eſſe =
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            quartæ proportionali ad ſpatium D C I P L, ſpatium D T U L & </s>
            <s xml:id="echoid-s918" xml:space="preserve">altitudi-
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            nem qs, eundemque poſt effluxum guttulæ eſſe = quartæ proportionali
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            ad ſpat. </s>
            <s xml:id="echoid-s919" xml:space="preserve">FEIPNOL, ſpat. </s>
            <s xml:id="echoid-s920" xml:space="preserve">FWUXYOL & </s>
            <s xml:id="echoid-s921" xml:space="preserve">altit. </s>
            <s xml:id="echoid-s922" xml:space="preserve">qz: </s>
            <s xml:id="echoid-s923" xml:space="preserve">ſunt autem in utra-
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            que analogia termini primi (nempe ſpat. </s>
            <s xml:id="echoid-s924" xml:space="preserve">DCIPL & </s>
            <s xml:id="echoid-s925" xml:space="preserve">ſpat. </s>
            <s xml:id="echoid-s926" xml:space="preserve">FEIPNOL) in-
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            ter ſe æquales, igitur ſi quodvis horum ſpatiorum indicetur per M, ſpa-
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            tium D T U L per N, ſpat FWUXYOL per N + dN, altitudo qs per
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            v&</s>
            <s xml:id="echoid-s927" xml:space="preserve">qz per v + dv, erit incrementum aſcenſus potentialis durante guttulæ efflu-
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            xu = {Ndv + vdN/M}. </s>
            <s xml:id="echoid-s928" xml:space="preserve">Quod ſi nunc ponatur L D = x, F D = - dx, D C
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            = y, H G = m, P L = n, erit D T = {mm/y}, L X = {mm/n}, L O = {-ydx/n}
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            (quia ſpatium D F E C = ſpatio L O N P), hincque dN = L O Y X -
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            D F W T = - {mmydx/nn} + {mmdx/y}, unde nunc incrementum quæſitum
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            aſcenſus petentialis eſt = (Ndv - {mmvydx/nn} + {mmvdx/y}): </s>
            <s xml:id="echoid-s929" xml:space="preserve">M. </s>
            <s xml:id="echoid-s930" xml:space="preserve">Q.</s>
            <s xml:id="echoid-s931" xml:space="preserve">E.</s>
            <s xml:id="echoid-s932" xml:space="preserve">I.</s>
            <s xml:id="echoid-s933" xml:space="preserve"/>
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        <div xml:id="echoid-div47" type="section" level="1" n="32">
          <head xml:id="echoid-head41" xml:space="preserve">Problema.</head>
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            <s xml:id="echoid-s934" xml:space="preserve">§. </s>
            <s xml:id="echoid-s935" xml:space="preserve">7. </s>
            <s xml:id="echoid-s936" xml:space="preserve">Retentis iisdem poſitionibus inven@re deſcenſum actualem infi-
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            nitè parvum aquæ, dum guttula effluit.</s>
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        <div xml:id="echoid-div48" type="section" level="1" n="33">
          <head xml:id="echoid-head42" xml:space="preserve">Solutio.</head>
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            <s xml:id="echoid-s938" xml:space="preserve">Cum in Figura decima quinta aqua ſitum cdmi mutat cum ſitu efml
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            onpi, patet in utroque ſitu centrum gravitatis partis aquæ efmi in eodem
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            loco eſſe, poſſeque proin concipi ſolam particulam cdfe, (quæ eſt = - ydx
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            dum tota aquæ maſſa eſt = M) deſcendiſſe in lonp. </s>
            <s xml:id="echoid-s939" xml:space="preserve">Sit jam altitudo </s>
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