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

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        <div xml:id="echoid-div131" type="section" level="1" n="101">
          <pb o="118" file="0132" n="132" rhead="HYDRODYNAMICÆ"/>
          <p>
            <s xml:id="echoid-s3388" xml:space="preserve">Notandum quoque eſt, ſimiles eſſe inter ſe retardationes & </s>
            <s xml:id="echoid-s3389" xml:space="preserve">accelera-
              <lb/>
            tiones in diſtantiis ſimilibus ſuperficierum à punctis mediarum excurſionum,
              <lb/>
            id eſt, à locis maximarum velocitatum.</s>
            <s xml:id="echoid-s3390" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div132" type="section" level="1" n="102">
          <head xml:id="echoid-head132" xml:space="preserve">Theorema.</head>
          <p>
            <s xml:id="echoid-s3391" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3392" xml:space="preserve">12. </s>
            <s xml:id="echoid-s3393" xml:space="preserve">Cum amplitudines tuborum cylindricorum prædicto modo
              <lb/>
            ſunt æquales, erunt oſcillationes tam majores quam minores inter ſe Iſochro-
              <lb/>
            næ, modo ſuperficies nunquam deſcendant infra orificia eorundem tuborum.</s>
            <s xml:id="echoid-s3394" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div133" type="section" level="1" n="103">
          <head xml:id="echoid-head133" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s3395" xml:space="preserve">Ex mechanicis conſtat, quod ſi mobile oſcillans ſpatium perfecerit
              <lb/>
            = x, habeatque in ſingulis locis elementum temporis dt = {mdx/√nx - xx}, intel-
              <lb/>
            ligendo per m & </s>
            <s xml:id="echoid-s3396" xml:space="preserve">n quantitates conſtantes, id faciat oſcillationes ſuas tam majo-
              <lb/>
            res quam minores eodem tempore.</s>
            <s xml:id="echoid-s3397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3398" xml:space="preserve">Quia vero in noſtro caſu eſt
              <lb/>
            v = {2gaαcx - (gαb + gaβ)xx/2gaaα + 2gaαα + 2aαMN},
              <lb/>
            & </s>
            <s xml:id="echoid-s3399" xml:space="preserve">quia velocitas ipſa eſt æqualis √ v, erit
              <lb/>
            dt = dx√({2gaaα + 2gaαα + 2aαMN/gαb + gaβ}):</s>
            <s xml:id="echoid-s3400" xml:space="preserve">√({2aαcx/gαb + gaβ} - xx),
              <lb/>
            ubi pariter omnes litteræ conſtantem habent valorem præter x, quæ ſpatium
              <lb/>
            percurſum denotat; </s>
            <s xml:id="echoid-s3401" xml:space="preserve">patet has quoque fluidi oſcillationes iſochronas fore
              <lb/>
            Q. </s>
            <s xml:id="echoid-s3402" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3404" xml:space="preserve"/>
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        <div xml:id="echoid-div134" type="section" level="1" n="104">
          <head xml:id="echoid-head134" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s3405" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3406" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">Invenire longitudinem penduli ſimplicis, quod ſit tautochro-
              <lb/>
            num cum oſcillationibus fluidi præfatis.</s>
            <s xml:id="echoid-s3408" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div135" type="section" level="1" n="105">
          <head xml:id="echoid-head135" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s3409" xml:space="preserve">In mechanicis demonſtratur, quod, cum dt = {mdx/√nx - xx}, ſit longitu-
              <lb/>
            do penduli ſimplicis tautochroni = {1/2} mm: </s>
            <s xml:id="echoid-s3410" xml:space="preserve">Erit igitur in noſtro caſu de quo
              <lb/>
            ſermo eſt longitudo penduli quæſita = {gaaα + gaαα + aαMN/gαb + gaβ}. </s>
            <s xml:id="echoid-s3411" xml:space="preserve"># Q.</s>
            <s xml:id="echoid-s3412" xml:space="preserve">E.</s>
            <s xml:id="echoid-s3413" xml:space="preserve">I.</s>
            <s xml:id="echoid-s3414" xml:space="preserve"/>
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