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

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        <div xml:id="echoid-div135" type="section" level="1" n="105">
          <pb o="119" file="0133" n="133" rhead="SECTIO SEXTA."/>
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        <div xml:id="echoid-div136" type="section" level="1" n="106">
          <head xml:id="echoid-head136" xml:space="preserve">Corollarium. 1.</head>
          <p>
            <s xml:id="echoid-s3415" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3416" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3417" xml:space="preserve">Si ponatur canalis c A d ejuſdem amplitudinis cum tubis con-
              <lb/>
            junctis, ejuſque longitudo vocetur l, erit maſſa aquæ in eo contentæ, quam
              <lb/>
            vocavimus M = gl; </s>
            <s xml:id="echoid-s3418" xml:space="preserve">& </s>
            <s xml:id="echoid-s3419" xml:space="preserve">aſcenſuspotent. </s>
            <s xml:id="echoid-s3420" xml:space="preserve">aquæ in illo contentæ, quem poſuimus =
              <lb/>
            N v, erit = v, ita ut habeatur N = 1. </s>
            <s xml:id="echoid-s3421" xml:space="preserve">Subſtitutis autem, iſtis valoribus pro
              <lb/>
            litteris M & </s>
            <s xml:id="echoid-s3422" xml:space="preserve">N, prodit longitudo penduli tautochroni pro iſto caſu particulari =
              <lb/>
            {aaα + aαα + aαl/αb + aβ} = {aα/αb + aβ} X (a + α + l) = {a + α + l/{b/a} + {β/α}</s>
          </p>
          <p>
            <s xml:id="echoid-s3423" xml:space="preserve">Quia vero a + α + l eſt longitudo totius tractus aqua pleni & </s>
            <s xml:id="echoid-s3424" xml:space="preserve">{b/a} ſigni-
              <lb/>
            ficat rationem ſinus anguli bac ad ſinum totum pariter atque {β/α} denotat ra-
              <lb/>
            tionem ſinus anguli efd ad ſinum totum, videmus non differre noſtram ſo-
              <lb/>
            lutionem ab illa, quam Pater meus pro iſto caſu dedit, quamque ſupra
              <lb/>
            recenſui §. </s>
            <s xml:id="echoid-s3425" xml:space="preserve">4.</s>
            <s xml:id="echoid-s3426" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div137" type="section" level="1" n="107">
          <head xml:id="echoid-head137" xml:space="preserve">Corollarium 2.</head>
          <p>
            <s xml:id="echoid-s3427" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3428" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3429" xml:space="preserve">Si ponatur canalis c A d infinitæ ubique amplitudinis, erit
              <lb/>
            MN = o (per §. </s>
            <s xml:id="echoid-s3430" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3431" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s3432" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s3433" xml:space="preserve">& </s>
            <s xml:id="echoid-s3434" xml:space="preserve">longitudo penduli tantochroni = {a + α/{b/a} + {β/α}}, qua-
              <lb/>
            ſi nempe totus canalis intermedius c A d abeſſet, tubique cylindrici inter ſe
              <lb/>
            immediate eſſent conjuncti.</s>
            <s xml:id="echoid-s3435" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3436" xml:space="preserve">Eſt tamen hîc ſpeciale aliquid conſiderandum, quod infra monebo.</s>
            <s xml:id="echoid-s3437" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div138" type="section" level="1" n="108">
          <head xml:id="echoid-head138" xml:space="preserve">Scholion.</head>
          <p>
            <s xml:id="echoid-s3438" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3439" xml:space="preserve">16. </s>
            <s xml:id="echoid-s3440" xml:space="preserve">Complectitur hoc theorema omnes caſus, qui oſcillationes tan-
              <lb/>
            tochronas faciunt, ubi tubi a c & </s>
            <s xml:id="echoid-s3441" xml:space="preserve">p d ſunt recti: </s>
            <s xml:id="echoid-s3442" xml:space="preserve">cum vero hi tubi, in qui-
              <lb/>
            bus fluidi ſuperficies excurrunt, incurvati ſunt, dantur alii inſuper tanto-
              <lb/>
            chronismi caſus, quos facile foret determinare, ſi hiſce diutius immorari
              <lb/>
            vellemus. </s>
            <s xml:id="echoid-s3443" xml:space="preserve">Cæterum cum tubi hi inæqualis amplitudinis ſunt, fiunt quoque
              <lb/>
            tempora oſcillationbus diverſarum magnitudinum reſpondentia inæqualia,
              <lb/>
            & </s>
            <s xml:id="echoid-s3444" xml:space="preserve">quomodo tempus tale definiri debeat unicuique apparet ex §. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3446" xml:space="preserve">ubi velo-
              <lb/>
            citatem fiuidi in quolibet puncto dedimus.</s>
            <s xml:id="echoid-s3447" xml:space="preserve"/>
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