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

Table of Notes

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          <pb o="44" file="0058" n="58" rhead="HYDRODYNAMICÆ"/>
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        <div xml:id="echoid-div57" type="section" level="1" n="41">
          <head xml:id="echoid-head51" style="it" xml:space="preserve">De Effluxu Aquarum ex Cylindris verticaliter po-
            <lb/>
          ſitis, qui in alios tubos ſtrictiores pariter
            <lb/>
          verticales deſinunt.</head>
          <head xml:id="echoid-head52" xml:space="preserve">§. 21.</head>
          <p>
            <s xml:id="echoid-s1143" xml:space="preserve">COnſtat experientia, inter duos Cylindros omnino æquales ſimiliterque
              <lb/>
            poſitos, quorum alterius foramini tubus ſtrictior reſpondeat, hunc
              <lb/>
            citius depleri, qui tubum appenſum habet, & </s>
            <s xml:id="echoid-s1144" xml:space="preserve">quidem eo citius, quo
              <lb/>
            magis tubus à loco inſertionis verſus extremitatem amplitudine creſcit, quæ
              <lb/>
            pluribus expoſuit D. </s>
            <s xml:id="echoid-s1145" xml:space="preserve">s’Graveſande in Phyſ. </s>
            <s xml:id="echoid-s1146" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s1147" xml:space="preserve">Math. </s>
            <s xml:id="echoid-s1148" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1149" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1150" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s1151" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1152" xml:space="preserve">Totam rem
              <lb/>
            ſequenti Problemate comprehendemus.</s>
            <s xml:id="echoid-s1153" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div58" type="section" level="1" n="42">
          <head xml:id="echoid-head53" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s1154" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">22. </s>
            <s xml:id="echoid-s1156" xml:space="preserve">Fuerit vas cylindricum A E H B (Fig. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">18.) </s>
            <s xml:id="echoid-s1158" xml:space="preserve">verticaliter poſi-
              <lb/>
              <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">Fig 18.</note>
            tum perforatum in F G, quo lumine communicet cum tubo conico F M N G,
              <lb/>
            per cujus demum orificium M N aquæ effiuant. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">Quæritur velocitas ſuperfi-
              <lb/>
            ciei aqueæ C D, poſtquam à quiete deſcendit per A C vel B D.</s>
            <s xml:id="echoid-s1160" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div60" type="section" level="1" n="43">
          <head xml:id="echoid-head54" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s1161" xml:space="preserve">Sit altitudo aquæ ſupra M N initialis, nempe N G + H B = a, altitu-
              <lb/>
            do ſuperficiei aqueæ in ſitu C D ſupra M N, id eſt, N G + H D = x; </s>
            <s xml:id="echoid-s1162" xml:space="preserve">lon-
              <lb/>
            gitudo tubi annexi ſeu N G = b; </s>
            <s xml:id="echoid-s1163" xml:space="preserve">amplitudo orificii M N = n; </s>
            <s xml:id="echoid-s1164" xml:space="preserve">amplitudo
              <lb/>
            orificii F G = g, amplitudo Cylindri ſuperioris = m; </s>
            <s xml:id="echoid-s1165" xml:space="preserve">ſit velocitas ſuperficiei
              <lb/>
            aqueæ in C D talis quæ debeatur altitudini v, erit in æquatione generali §. </s>
            <s xml:id="echoid-s1166" xml:space="preserve">8.
              <lb/>
            </s>
            <s xml:id="echoid-s1167" xml:space="preserve">y = m & </s>
            <s xml:id="echoid-s1168" xml:space="preserve">N = m (x - b) + {bmm/√gn}, quæ ſubſtitutiones inſtituto calculo con-
              <lb/>
            formes eſſe patebunt cum §. </s>
            <s xml:id="echoid-s1169" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1170" xml:space="preserve">reliquæ autem poſitiones eædem ſunt quæ an-
              <lb/>
            te. </s>
            <s xml:id="echoid-s1171" xml:space="preserve">Abit igitur æquatio paragraphi 8 in hanc
              <lb/>
            m(x - b)dv + {bmm/√gn}dv - {m
              <emph style="super">3</emph>
            vdx/nn} + mvdx = - mxdx
              <lb/>
            quæ porro diviſa per m factoque x - b + {mb/√gn} = z, </s>
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