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 |< < (264) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div269" type="section" level="1" n="204">
          <p>
            <s xml:id="echoid-s7733" xml:space="preserve">
              <pb o="264" file="0278" n="278" rhead="HYDRODYNAMICÆ"/>
            eſſe, quanta in aqua ſtagnante ad altitudinem a - b. </s>
            <s xml:id="echoid-s7734" xml:space="preserve">Ubi notari poteſt eſſe al-
              <lb/>
            titudinem b ad altitudinem o S, ſi nulla motus impedimenta aliena ſint, vena-
              <lb/>
            que effluens in o non contrahatur, in ratione quadrata foraminis o & </s>
            <s xml:id="echoid-s7735" xml:space="preserve">ſectionis
              <lb/>
            CE (aut c e).</s>
            <s xml:id="echoid-s7736" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div271" type="section" level="1" n="205">
          <head xml:id="echoid-head262" xml:space="preserve">Corollarium.</head>
          <p>
            <s xml:id="echoid-s7737" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7738" xml:space="preserve">11. </s>
            <s xml:id="echoid-s7739" xml:space="preserve">Cùm b major eſt quam a, fit quantitas a - b negativa atque ſic
              <lb/>
            preſſio in ſuctionem mutatur, id eſt, latera canalis introrſum premuntur: </s>
            <s xml:id="echoid-s7740" xml:space="preserve">tunc
              <lb/>
            autem res ita conſideranda eſt, ac ſi loco columnæ aqueæ CT ſuperincumben-
              <lb/>
            tis & </s>
            <s xml:id="echoid-s7741" xml:space="preserve">in æquilibrio poſitæ cum aqua præterfluente, ſit columna aquea appen-
              <lb/>
            ſa e t, cujus niſus deſcendendi impediatur ab attractione aquæ præterfluentis:
              <lb/>
            </s>
            <s xml:id="echoid-s7742" xml:space="preserve">veluti ſi v. </s>
            <s xml:id="echoid-s7743" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s7744" xml:space="preserve">amplitudo canalis c e æqualis ſit orificio o, tunc erit b = o S, nul-
              <lb/>
            la habita ratione motus impedimentorum accidentalium: </s>
            <s xml:id="echoid-s7745" xml:space="preserve">hinc ſi tubulus ex ca-
              <lb/>
            nali deſcendat c r, hicque ſit aqua plenus à ſua origine c uſque in punctum t
              <lb/>
            cum orificio o ad libellam poſitum, manebit aqua c t ſuſpenſa ſine motu: </s>
            <s xml:id="echoid-s7746" xml:space="preserve">ſi verò
              <lb/>
            punctum t infra o poſitum ſit, deſcendet aqua per tubulum cr, & </s>
            <s xml:id="echoid-s7747" xml:space="preserve">effluet perpe-
              <lb/>
            tuo in r, neque tamen ut facile quis exiſtimare potuiſſet nondum hâc viſa theo-
              <lb/>
            ria, velocitas aquæ in r effluentis talis erit, quæ debeatur altitudini N P ſu-
              <lb/>
            pra r, etiamſi omnia impedimen@a auferantur, reſpondebit potius hæc velo-
              <lb/>
            citas, ſi modo tubulus admodum ſtrictus ſit ratione canalis, altitudini t r. </s>
            <s xml:id="echoid-s7748" xml:space="preserve">
              <lb/>
            Si punctum t altius poſitum ſit puncto o, aqua ſua ſponte aſcendet & </s>
            <s xml:id="echoid-s7749" xml:space="preserve">cum
              <lb/>
            omnis canalem ingreſſa erit, aër per tubulum attrahetur, moxque vena aquea
              <lb/>
            in o effluens ab admixto aëre turbabitur pelluciditate atque ſoliditate orbata. </s>
            <s xml:id="echoid-s7750" xml:space="preserve">Ap-
              <lb/>
            paret igitur, quando preſſio futura ſit affirmativa & </s>
            <s xml:id="echoid-s7751" xml:space="preserve">quando negativa: </s>
            <s xml:id="echoid-s7752" xml:space="preserve">nempe
              <lb/>
            eo major eſt in tubo preſſio, quo amplior eſt & </s>
            <s xml:id="echoid-s7753" xml:space="preserve">quo humilius poſitus: </s>
            <s xml:id="echoid-s7754" xml:space="preserve">Al-
              <lb/>
            titudo b eſt quidem in theoria = {1/nn} X oS, ſi {1/n} denotet rationem inter am-
              <lb/>
            plitudinem orificii & </s>
            <s xml:id="echoid-s7755" xml:space="preserve">ejus tubi ſectionis, pro qua preſſio eſt definienda. </s>
            <s xml:id="echoid-s7756" xml:space="preserve">Cum vero
              <lb/>
            obſtacula notabiliter diminuunt motum, conveniet potius in æſtimandis preſ-
              <lb/>
            ſionibus, ut'velocitas aquæ, qualis actu eſt, experimento cognoſcatur & </s>
            <s xml:id="echoid-s7757" xml:space="preserve">alti-
              <lb/>
            tudo illi velocitati debita pro b ſubſtituatur: </s>
            <s xml:id="echoid-s7758" xml:space="preserve">ſimiliter accuratius æſtimabitur
              <lb/>
            preſſio, ſi pro a non tam ponatur altitudo ſuperficiei aqueæ N P ſupra
              <lb/>
            effluxus locum, quam altitudo velocitatis, quacum aquæ actu effluant
              <lb/>
            ex canali eodem in loco abrupto: </s>
            <s xml:id="echoid-s7759" xml:space="preserve">Hæ tamen correctiones non ſemper locum
              <lb/>
            habent: </s>
            <s xml:id="echoid-s7760" xml:space="preserve">Iſtam vero theoriam generalem jam exemplis quibuſdam illuſtrabo.</s>
            <s xml:id="echoid-s7761" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum