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

Page concordance

< >
Scan Original
241 227
242 228
243 229
244 230
245 231
246 232
247 233
248 234
249 235
250 236
251 237
252 238
253 239
254 240
255 241
256 242
257 243
258 244
259 245
260 246
261 247
262 248
263 249
264 250
265 251
266 252
267 253
268 254
269 255
270 256
< >
page |< < (233) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div249" type="section" level="1" n="193">
          <p>
            <s xml:id="echoid-s6857" xml:space="preserve">
              <pb o="233" file="0247" n="247" rhead="SECTIO DECIMA."/>
            poteſt ejus ope pondus 865 librarum ad altitudinem unius pedis elevari, ſi
              <lb/>
            modo machina adhibeatur perfectiſſima.</s>
            <s xml:id="echoid-s6858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6859" xml:space="preserve">Ab auctis autem aëris tum denſitate tum calore pendent omnium re-
              <lb/>
            rum hic expoſitarum effectus.</s>
            <s xml:id="echoid-s6860" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6861" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6862" xml:space="preserve">44. </s>
            <s xml:id="echoid-s6863" xml:space="preserve">Interim non ſolum ab aëre condenſato calefactove vis viva pro
              <lb/>
            machinis movendis impendenda obtineri poteſt, ſed & </s>
            <s xml:id="echoid-s6864" xml:space="preserve">ab aëre rariore aut
              <lb/>
            frigidiore. </s>
            <s xml:id="echoid-s6865" xml:space="preserve">Ubicunque enim æquilibrium ſublatum eſt, vis viva adeſt, quæ
              <lb/>
            impendi poteſt, ſi debita machina excogitetur, ad onera elevanda machina-
              <lb/>
            mentaque circumagenda. </s>
            <s xml:id="echoid-s6866" xml:space="preserve">Methodus autem determinans vim vivam, quæ ab
              <lb/>
            aëre datæ denſitatis datique caloris ſpatium datum occupante elici poteſt,
              <lb/>
            mutatis mutandis eadem eſt cum illa quam §. </s>
            <s xml:id="echoid-s6867" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6868" xml:space="preserve">adhibuimus.</s>
            <s xml:id="echoid-s6869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6870" xml:space="preserve">45. </s>
            <s xml:id="echoid-s6871" xml:space="preserve">Fuerit nempe rurſus cylindrus verticalis A B C D (Fig. </s>
            <s xml:id="echoid-s6872" xml:space="preserve">63.) </s>
            <s xml:id="echoid-s6873" xml:space="preserve">cum dia-
              <lb/>
              <note position="right" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">Fig. 63.</note>
            phragmate mobili E F: </s>
            <s xml:id="echoid-s6874" xml:space="preserve">puta aërem E B C F, ut §. </s>
            <s xml:id="echoid-s6875" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6876" xml:space="preserve">naturalem & </s>
            <s xml:id="echoid-s6877" xml:space="preserve">in æquili-
              <lb/>
            brio cum aëre externo: </s>
            <s xml:id="echoid-s6878" xml:space="preserve">preſſio autem aëris cujusvis in E F dicatur p
              <emph style="super">0</emph>
            : </s>
            <s xml:id="echoid-s6879" xml:space="preserve">Finge
              <lb/>
            dein pondus P, quod mediante fune trans duas trochleas M & </s>
            <s xml:id="echoid-s6880" xml:space="preserve">N ducto cum
              <lb/>
            diaphragmate cohæreat, idemque verſus A D trahat, perveneritque ſic dia-
              <lb/>
            phragma ex ſitu E F in G H: </s>
            <s xml:id="echoid-s6881" xml:space="preserve">Denique ponatur rurſus F C = a, F H = x:
              <lb/>
            </s>
            <s xml:id="echoid-s6882" xml:space="preserve">velocitas diaphragmatis in ſitu G H ſeu ponderis in ſitu P = v; </s>
            <s xml:id="echoid-s6883" xml:space="preserve">His poſitis
              <lb/>
            ſi conferantur §. </s>
            <s xml:id="echoid-s6884" xml:space="preserve">§. </s>
            <s xml:id="echoid-s6885" xml:space="preserve">40. </s>
            <s xml:id="echoid-s6886" xml:space="preserve">& </s>
            <s xml:id="echoid-s6887" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6888" xml:space="preserve">patebit fore nunc
              <lb/>
            dv = (P + {ap/a + x} - p) X {dx/v}: </s>
            <s xml:id="echoid-s6889" xml:space="preserve">P vel
              <lb/>
            Pvdv = (P - {px/a + x}) dx, quæ integrata dat
              <lb/>
            {1/2}Pvv = Px - px + ap log.</s>
            <s xml:id="echoid-s6890" xml:space="preserve">{a + x/a}.</s>
            <s xml:id="echoid-s6891" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6892" xml:space="preserve">At rurſus deſcenſus ponderis P per altitudinem x producta fuit vis viva
              <lb/>
            P x, dum ipſi interim ponderi velocitate v moto ineſt tantum vis viva {1/2} P v v
              <lb/>
            ſeu Px - px + ap log.</s>
            <s xml:id="echoid-s6893" xml:space="preserve">{a + x/a}, Igitur vis viva, quæ reſidua eſt, nempe p x -
              <lb/>
            a p log.</s>
            <s xml:id="echoid-s6894" xml:space="preserve">{a + x/a}, ad aërem tranſiit rurſusque reſtitutione æquilibrii inter aërem
              <lb/>
            internum & </s>
            <s xml:id="echoid-s6895" xml:space="preserve">externum, illa vis viva ad alia corpora pro lubitu transfundi po-
              <lb/>
            terit: </s>
            <s xml:id="echoid-s6896" xml:space="preserve">Igitur ſi habeas ſpatium G B C H aëre plenum cujus denſitas ſit ad
              <lb/>
            denſitatem aëris externi ut C F ad C H, in poteſtate erit vis viva p x -
              <lb/>
            a p log.</s>
            <s xml:id="echoid-s6897" xml:space="preserve">{a + x/a}.</s>
            <s xml:id="echoid-s6898" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum