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 |< < (25) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div28" type="section" level="1" n="22">
          <p>
            <s xml:id="echoid-s666" xml:space="preserve">
              <pb o="25" file="0039" n="39" rhead="SECTIO SECUNDA."/>
            ſus ſimpliciſſimus hujus rei eſt, cum ſupponitur f = m = o, tunc enim fit
              <lb/>
            - dx = {-gydy/√(4nnhh - ggyy)} ſeu facta integratione cum additione debitæ conſtan-
              <lb/>
            tis, x = - √({4nnhh/gg} - yy) + {2nh/g}, quæ eſt æquatio ad ſemicirculum, ad
              <lb/>
            quem nempe ſe linteum accommodabit in ſequenti hypotheſi: </s>
            <s xml:id="echoid-s667" xml:space="preserve">Sit filum lin-
              <lb/>
            tei gravis AEG (Fig. </s>
            <s xml:id="echoid-s668" xml:space="preserve">8.) </s>
            <s xml:id="echoid-s669" xml:space="preserve">in ſemicirculum incurvatum. </s>
            <s xml:id="echoid-s670" xml:space="preserve">cujus diameter AG
              <lb/>
              <note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve">Fig. 8.</note>
            ad libellam poſita ſit; </s>
            <s xml:id="echoid-s671" xml:space="preserve">ſuperincumbat ſilo fluidum usque ad AG, dico ſi
              <lb/>
            fluidi pondus ſit æquale ponderi fili, fore ut filum perfecte flexile & </s>
            <s xml:id="echoid-s672" xml:space="preserve">uni-
              <lb/>
            formis craſſitiei figuram ſemicircularem conſervet. </s>
            <s xml:id="echoid-s673" xml:space="preserve">Quomodo autem pon-
              <lb/>
            dera fili & </s>
            <s xml:id="echoid-s674" xml:space="preserve">fluidi, ut æqualia fiant, efficiendum ſit ex elementis Geometriæ
              <lb/>
            conſtat. </s>
            <s xml:id="echoid-s675" xml:space="preserve">Denique ſi ſtatuatur tam potentias A quam C eſſe ubique applica-
              <lb/>
            tæ reſpondenti y proportionales (quæ hypotheſis ſane maxime convenire vi-
              <lb/>
            detur cum vera figura veſicæ in figura ſexta) poterit rurſus æquatio canoni-
              <lb/>
            ca, quæ continet differentialia tertii Ordinis, reduci ad æquationem ſimpli-
              <lb/>
            citer differentialem eamque per quadraturas facile conſtruendam. </s>
            <s xml:id="echoid-s676" xml:space="preserve">Sit nem-
              <lb/>
            pe A = my & </s>
            <s xml:id="echoid-s677" xml:space="preserve">C = ny, dico naturam curvæ A D G in fig. </s>
            <s xml:id="echoid-s678" xml:space="preserve">7. </s>
            <s xml:id="echoid-s679" xml:space="preserve">exprimi hâc æquatione
              <lb/>
            dx = (g
              <emph style="super">3</emph>
            + {1/2} myy) dy: </s>
            <s xml:id="echoid-s680" xml:space="preserve">√[(f
              <emph style="super">3</emph>
            + {1/2} nyy)
              <emph style="super">2</emph>
            - (g
              <emph style="super">3</emph>
            + {1/2} myy)
              <emph style="super">2</emph>
            ]
              <lb/>
            in qua literæ conſtantis magnitudinis f & </s>
            <s xml:id="echoid-s681" xml:space="preserve">g rurſus ab integrationibus pro-
              <lb/>
            dierunt: </s>
            <s xml:id="echoid-s682" xml:space="preserve">fit autem valor literæ n negativus, cum æquatio ad veſicæ inflatæ
              <lb/>
            figuram determinandam adhibetur.</s>
            <s xml:id="echoid-s683" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s684" xml:space="preserve">§. </s>
            <s xml:id="echoid-s685" xml:space="preserve">16. </s>
            <s xml:id="echoid-s686" xml:space="preserve">Nolui his nimis inſiſtere, quod non proxime pertinent ad Hy-
              <lb/>
            drodynamicam: </s>
            <s xml:id="echoid-s687" xml:space="preserve">Nihil etiam addo de fluidis elaſticis, quia horum theoriam
              <lb/>
            ſeorſim tradere conſtitui; </s>
            <s xml:id="echoid-s688" xml:space="preserve">attamen quod ad preſſiones fluidorum elaſtico-
              <lb/>
            rum attinet, poterunt illæ ex natura fluidorum ſimpliciter gravium ſupra ex-
              <lb/>
            poſita facile deduci & </s>
            <s xml:id="echoid-s689" xml:space="preserve">demonſtrari, fingendo fluidum elaſticitate eſſe deſti-
              <lb/>
            tutum, cylindrumque fluidi ſimilis altitudinis infinitæ vel quaſi infinitæ ſu-
              <lb/>
            perimcumbere; </s>
            <s xml:id="echoid-s690" xml:space="preserve">hæc autem quomodo intelligenda ſint ſuo loco dicemus:
              <lb/>
            </s>
            <s xml:id="echoid-s691" xml:space="preserve">Nunc quidem pergo ad id, quod in rebus aquariis potiſſimum quæri ſolet,
              <lb/>
            quanta nempe debeat eſſe firmitas canalium, ut preſſioni aquæ reſiſtere poſ-
              <lb/>
            ſint, ubi præſertim conſiderantur canales, qui aquas ad fontes vehunt, de
              <lb/>
            quibus ego quoque pauca monebo.</s>
            <s xml:id="echoid-s692" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s693" xml:space="preserve">§. </s>
            <s xml:id="echoid-s694" xml:space="preserve">17. </s>
            <s xml:id="echoid-s695" xml:space="preserve">Probe diſtinguendæ ſunt preſſiones aquarum in canalibus </s>
          </p>
        </div>
      </text>
    </echo>
Impressum