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

Page concordance

< >
Scan Original
111 97
112 98
113 99
114 100
115 101
116 102
117 103
118 104
119 105
120 106
121 107
122 108
123 109
124 110
125 111
126 112
127 113
128 114
129 115
130 116
131 117
132 118
133 119
134 120
135 121
136 122
137 123
138
139 125
140 126
< >
page |< < (116) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div125" type="section" level="1" n="95">
          <p>
            <s xml:id="echoid-s3339" xml:space="preserve">
              <pb o="116" file="0130" n="130" rhead="HYDRODYNAMICÆ"/>
            aquæ in c A d per C A, aggregatumque horum productorum dividendo per
              <lb/>
            ſummam harum maſſarum. </s>
            <s xml:id="echoid-s3340" xml:space="preserve">Unde invenitur.</s>
            <s xml:id="echoid-s3341" xml:space="preserve"> A F = {ga X (f + {1/2}
              <emph style="super">b</emph>
            ) + γα X (φ + {1/2}
              <emph style="super">β</emph>
            ) + Mm/ga + γα + M}</s>
          </p>
        </div>
        <div xml:id="echoid-div126" type="section" level="1" n="96">
          <head xml:id="echoid-head126" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s3342" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">Determinare ubique velocitates aquæ oſcillantis, poſito oſcilla-
              <lb/>
            tiones ultra terminos tuborum cylindricorum non divagari.</s>
            <s xml:id="echoid-s3345" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div127" type="section" level="1" n="97">
          <head xml:id="echoid-head127" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s3346" xml:space="preserve">Sit aqua oſcillationem inchoans in ſitu a c A d f perveneritque poſtmo-
              <lb/>
            dum in ſitum o c A d p, retentiſque denominationibus |in præcedente paragra-
              <lb/>
            pho factis, ponatur a o = x; </s>
            <s xml:id="echoid-s3347" xml:space="preserve">erit f p = {gx/γ}: </s>
            <s xml:id="echoid-s3348" xml:space="preserve">unde (ſi nempe centrum gravita-
              <lb/>
            tis omnis aquæ deſcendiſſe putetur ex F in O) erit vi præcedentis paragraphi
              <lb/>
            A O = {g X (a - x) X (f + {1/2}
              <emph style="super">b</emph>
            - {bx/2a}) + γ X (a + {gx/γ}) X (φ + {1/2}
              <emph style="super">β</emph>
            + {βgx/2αγ}) + Mm/ga + γα + M}</s>
          </p>
          <p>
            <s xml:id="echoid-s3349" xml:space="preserve">Inde deducitur deſcenſus centri gravitatis ſeu deſcenſus actualis
              <lb/>
            F O = {(b - β + f - φ)gx - ({bg/2a} + {bgg/2αγ}) xx/ga + γα + M}</s>
          </p>
          <p>
            <s xml:id="echoid-s3350" xml:space="preserve">Sit nunc velocitas aquæ in tubo a c (cum nempe ſuperficies eſt in o) ta-
              <lb/>
            lis quæ reſpondeat altitudini v, & </s>
            <s xml:id="echoid-s3351" xml:space="preserve">erit tunc aſcenſus potent. </s>
            <s xml:id="echoid-s3352" xml:space="preserve">aquæ in altero tubo
              <lb/>
            = {gg/γγ} v: </s>
            <s xml:id="echoid-s3353" xml:space="preserve">pariterque aſcenſus potent. </s>
            <s xml:id="echoid-s3354" xml:space="preserve">aquæ c A d, erit proportionalis altitudini v,
              <lb/>
            eamque proinde ponemus = N v (ubi N pendet à figura utris c A d & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">deter-
              <lb/>
            minari poteſt per §. </s>
            <s xml:id="echoid-s3356" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s3358" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s3359" xml:space="preserve">Jam vero ſi multiplicatis ubique aſcenſibus po-
              <lb/>
            tentialibus per ſuas maſſas producta dividantur per ſummam maſſarum, habebi-
              <lb/>
            tur aſcenſ{us} potent. </s>
            <s xml:id="echoid-s3360" xml:space="preserve">omnis aquæ o c A d p =
              <lb/>
            {(ga - gx + {αgg/γ} + {g
              <emph style="super">3</emph>
            x/γγ} + MN)v/ga + γα + M}</s>
          </p>
          <p>
            <s xml:id="echoid-s3361" xml:space="preserve">Et quia hic aſcenſus potentialis eſt æqualis deſcenſui actuali F O paullo ante
              <lb/>
            invento, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum