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

Page concordance

< >
Scan Original
131 117
132 118
133 119
134 120
135 121
136 122
137 123
138
139 125
140 126
141 127
142 128
143 129
144 130
145 131
146 132
147 133
148 134
149 135
150 136
151 137
152 138
153 139
154 140
155 141
156 142
157
158 144
159 145
160 146
< >
page |< < (118) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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"/>
          </p>
        </div>
        <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"/>
          </p>
        </div>
      </text>
    </echo>
Impressum