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

Page concordance

< >
Scan Original
91 77
92 78
93 79
94 80
95 81
96 82
97 83
98 84
99 85
100 86
101 87
102 88
103 89
104
105 91
106 92
107 93
108 94
109 95
110 96
111 97
112 98
113 99
114 100
115 101
116 102
117 103
118 104
119 105
120 106
< >
page |< < (93) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div96" type="section" level="1" n="71">
          <pb o="93" file="0107" n="107" rhead="SECTIO QUINTA."/>
          <p>
            <s xml:id="echoid-s2629" xml:space="preserve">Debet vero iſtud incrementum æquari deſcenſui actuali centri gravitatis;
              <lb/>
            </s>
            <s xml:id="echoid-s2630" xml:space="preserve">Atqui iſte deſcenſus, poſita D L = a, eſt per paragraphum ſeptimum ſect. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">
              <lb/>
            = {nadx/M}; </s>
            <s xml:id="echoid-s2633" xml:space="preserve">habetur igitur talis æquatio
              <lb/>
            {N/M}dv - {n
              <emph style="super">3</emph>
            /mmM}vdx + {n/M}vdx = {nadx/M}, ſeu
              <lb/>
            dx = Ndv: </s>
            <s xml:id="echoid-s2634" xml:space="preserve">(na - nv + {n
              <emph style="super">3</emph>
            /mm} v);</s>
            <s xml:id="echoid-s2635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2636" xml:space="preserve">Hæc vero ſi ita integretur, ut v & </s>
            <s xml:id="echoid-s2637" xml:space="preserve">x ſimul evaneſcant, dat
              <lb/>
            x = {mmN/n
              <emph style="super">3</emph>
            - nmm} log. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">{mma - mmv + nnv/mma}
              <lb/>
            quæ æquatio, poſito c pro numero cujus logarithmus eſt unitas, æquivalet
              <lb/>
            huic @alteri
              <lb/>
            v = {mma/mm - nn} X (1 - c{n
              <emph style="super">3</emph>
            - nmm/mmN} x)</s>
          </p>
          <p>
            <s xml:id="echoid-s2639" xml:space="preserve">Hæc vero ſolutio quadrat pro caſu primo, ubi aqua ſuperne motu af-
              <lb/>
            ſunditur communi cum deſcenſu ſuperficiei proximæ.</s>
            <s xml:id="echoid-s2640" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div97" type="section" level="1" n="72">
          <head xml:id="echoid-head97" xml:space="preserve">Caſus II.</head>
          <p>
            <s xml:id="echoid-s2641" xml:space="preserve">Quod ſi jam particula c d f e lateraliter continue affundi ponatur, tunc
              <lb/>
            propter inertiam ſuam motui aquæ inferioris reſiſtit atque proinde aſcenſus
              <lb/>
            potentialis ipſius aliter in computum venit. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Tunc autem prius conſideran-
              <lb/>
            dus eſt aſcenſus potentialis maſſæ aqueæ c d m l p i c auctæ guttula mox affunden-
              <lb/>
            da; </s>
            <s xml:id="echoid-s2643" xml:space="preserve">deinde indagandus aſcenſus potent. </s>
            <s xml:id="echoid-s2644" xml:space="preserve">ejusdem aquæ in ſitu c d m l o n p i c,
              <lb/>
            poſtquam nempe guttula jam effluxit, eorumque differentia eſt æquanda cum
              <lb/>
            deſcenſu actuali. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">{nadx/M}. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">Verum aſcenſus potentialis omnis prædictæ aquæ ante
              <lb/>
            affuſionem particulæ ejusdemque poſt affuſionem ita invenitur: </s>
            <s xml:id="echoid-s2647" xml:space="preserve">nempe aſcen-
              <lb/>
            ſus potentialis aquæ c d m l p i c eſt = {Nv/M}, & </s>
            <s xml:id="echoid-s2648" xml:space="preserve">aſcenſus potent. </s>
            <s xml:id="echoid-s2649" xml:space="preserve">particulæ affundi
              <lb/>
            paratæ nullus eſt, quia lateraliter affuſa motum communem nondum habet
              <lb/>
            cum maſſa inferiore; </s>
            <s xml:id="echoid-s2650" xml:space="preserve">Igitur aſcenſus potentialis utriusque aquæ (qui ſcilicet
              <lb/>
            habetur multiplicando maſſam reſpective per ſuum aſcenſum potentialem, di-
              <lb/>
            videndoque productorum aggregatum per aggregatum maſſarum) eſt </s>
          </p>
        </div>
      </text>
    </echo>
Impressum