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

Page concordance

< >
Scan Original
31 17
32 18
33 19
34 20
35 21
36 22
37 23
38 24
39 25
40 26
41 27
42 28
43 29
44 30
45 31
46 32
47 33
48 34
49 35
50 36
51 37
52 38
53 39
54 40
55 41
56 42
57 43
58 44
59 45
60 46
< >
page |< < (70) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div77" type="section" level="1" n="54">
          <p>
            <s xml:id="echoid-s1906" xml:space="preserve">
              <pb o="70" file="0084" n="84" rhead="HYDRODYNAMICÆ."/>
            catum fuit, in æquatione paragraphi decimi ponendum x = o, ſint
              <unsure/>
            ulque
              <lb/>
            ſolus primus ſeriei terminus adhibendus rurſusque ponendum m α pro
              <lb/>
            √(mmαα - 2nn); </s>
            <s xml:id="echoid-s1907" xml:space="preserve">atque ſic fit
              <lb/>
            t = {2mα/n}√a.</s>
            <s xml:id="echoid-s1908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1909" xml:space="preserve">Tum denique tempus, quod impenditur in deſcenſum ſuperficiei per
              <lb/>
            altitudinem a - c exprimetur in ſimili hypotheſi hac æquatione
              <lb/>
            t = {2ma/n} (√a - √c).</s>
            <s xml:id="echoid-s1910" xml:space="preserve">}</s>
          </p>
          <p>
            <s xml:id="echoid-s1911" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1912" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1913" xml:space="preserve">Præmiſſæ æquationes non accurate quidem, proxime tamen
              <lb/>
            ſatisfacient, cum vas non infinitæ, permagnæ tamen amplitudinis eſt: </s>
            <s xml:id="echoid-s1914" xml:space="preserve">imo
              <lb/>
            non multum admodum defie
              <unsure/>
            ient, cum numerus m vel mediocriter ſuperat
              <lb/>
            numerum n. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">Liceat quædam hic verba adjicere circa experimentum quod in
              <lb/>
            fine paragraphi undecimi indicavi, deturque hæc venia inſtituto noſtro,
              <lb/>
            quod in phænomenis motuum experientia cognitis potiſſimum verſatur il-
              <lb/>
            luſtrandis examinandisque. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">Dixi autem in citato paragrapho cum aqua ho-
              <lb/>
            rizontaliter effluit, primam guttulam totam ſtatim obtinere amplitudinem
              <lb/>
            jactus; </s>
            <s xml:id="echoid-s1917" xml:space="preserve">atque idem hoc quidem indicat theoria pro vaſis ampliſſimis; </s>
            <s xml:id="echoid-s1918" xml:space="preserve">at ve-
              <lb/>
            ro in vaſis mediocriter amplis, quædam guttulæ minori impetu effluere de-
              <lb/>
            berent, priusquam punctum maximæ velocitatis adſit, hæque guttulæ in-
              <lb/>
            cidere deberent in locum aliquem medium inter maximum jactum & </s>
            <s xml:id="echoid-s1919" xml:space="preserve">pun-
              <lb/>
            ctum, quod foramini verticaliter reſpondet; </s>
            <s xml:id="echoid-s1920" xml:space="preserve">atque hoc etiam ita fieri ob-
              <lb/>
            ſervavi, ex vaſis amplitudinis veluti decies foramine majoris. </s>
            <s xml:id="echoid-s1921" xml:space="preserve">Verum cum
              <lb/>
            experimentum aliquando ſumerem de vaſe pedem dimidium alto, quod am-
              <lb/>
            plitudinem præter propter centuplam haberet foraminis, ne minima quidem
              <lb/>
            particula aquæ, quantum videre potui, notabiliter à jactu aquæ pleno de-
              <lb/>
            fecit. </s>
            <s xml:id="echoid-s1922" xml:space="preserve">Videamus itaque quænam aquæ quantitas in hoc caſu effluere deberet
              <lb/>
            ante punctum maximæ velocitatis; </s>
            <s xml:id="echoid-s1923" xml:space="preserve">erit autem tanta, quantam continet cy-
              <lb/>
            lindrus ejusdem amplitudinis in altitudine
              <lb/>
            a - a: </s>
            <s xml:id="echoid-s1924" xml:space="preserve">({mmαα - nn/nn})
              <emph style="super">nn: (mmαα - 2nn)</emph>
              <lb/>
            (vid. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1926" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">ſub. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">fin.)</s>
            <s xml:id="echoid-s1929" xml:space="preserve">; </s>
            <s xml:id="echoid-s1930" xml:space="preserve">nec differt fere hæc minima altitudo ab hac multo com-
              <lb/>
            pendioſiori, nempe {2nna/mmαα} log. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">{mα/n} (vid. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">§. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">11.) </s>
            <s xml:id="echoid-s1934" xml:space="preserve">ubi nunc per {n/m} </s>
          </p>
        </div>
      </text>
    </echo>
Impressum