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

List of thumbnails

< >
31
31 (17) 		32
32 (18)
33
33 (19) 		34
34 (20)
35
35 (21) 		36
36 (22)
37
37 (23) 		38
38 (24)
39
39 (25) 		40
40 (26)
< >
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