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

Page concordance

< >
Scan Original
301 287
302 288
303 289
304 290
305 291
306 292
307 293
308 294
309 295
310 296
311 297
312 298
313 299
314 300
315 301
316 302
317 303
318 304
319
320
321
322
323
324
325
326
327
328
329
330
< >
page |< < (296) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div302" type="section" level="1" n="226">
          <p>
            <s xml:id="echoid-s8812" xml:space="preserve">
              <pb o="296" file="0310" n="310" rhead="HYDRODYNAMICÆ"/>
            vis vel liberrime moveretur ſuper mari, non acquireret tamen ab actione
              <lb/>
            aquarum, quæ continue hauriuntur inferiusque effluunt, majorem velocita-
              <lb/>
            tem quam eam, qua aquæ effluunt, non quod aquæ ex vaſe uniformiter mo-
              <lb/>
            to effluentes vas minori vi quam ex vaſe immoto repellant, ſed quod tunc in-
              <lb/>
            ertia aquarum reſiſtentiam producat vi repellenti æqualem.</s>
            <s xml:id="echoid-s8813" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div303" type="section" level="1" n="227">
          <head xml:id="echoid-head289" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s8814" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8815" xml:space="preserve">25. </s>
            <s xml:id="echoid-s8816" xml:space="preserve">Data potentia operariorum, qui aquas elevant, & </s>
            <s xml:id="echoid-s8817" xml:space="preserve">data altitudi-
              <lb/>
            ne ad quam aquæ elevantur, invenire amplitudinem foraminis effluxus & </s>
            <s xml:id="echoid-s8818" xml:space="preserve">vim
              <lb/>
            repellentem.</s>
            <s xml:id="echoid-s8819" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div304" type="section" level="1" n="228">
          <head xml:id="echoid-head290" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s8820" xml:space="preserve">Sit potentia talis, qua ſingulis minutis ſecundis numerus pedum cu-
              <lb/>
            bicorum aquæ N poſſit ad altitudinem unius pedis elevari, quam potentiam
              <lb/>
            vi experimenti ſecundi ſectioni nonæſubjuncti exerere poteſt operariorum nu-
              <lb/>
            merus deſignandus per {5/4} N. </s>
            <s xml:id="echoid-s8821" xml:space="preserve">Sit altitudo ad quam aquæ continue elevantur
              <lb/>
            = A in pedilus expreſſa: </s>
            <s xml:id="echoid-s8822" xml:space="preserve">amplitudo orificii in pedibus quadratis = M; </s>
            <s xml:id="echoid-s8823" xml:space="preserve">erit
              <lb/>
            numerus pedum cubicorum aquæ, quem operarii data potentia ad altitudi-
              <lb/>
            nem A ſingulis minutis ſecundis elevare poſſunt, = {N/A} (per §. </s>
            <s xml:id="echoid-s8824" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8825" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s8826" xml:space="preserve">9.)
              <lb/>
            </s>
            <s xml:id="echoid-s8827" xml:space="preserve">erit igitur orificium ejus amplitudinis conſtruendum, ut ſingulis minutis
              <lb/>
            ſecundis numerus iſte pedum cubicorum aquæ per id effluere poſſit, ſi liber-
              <lb/>
            rime effluant. </s>
            <s xml:id="echoid-s8828" xml:space="preserve">Sumamus autem loco minutorum ſecundorum tempus, quod
              <lb/>
            corpus inſumit, dum libere cadit per altitudinem A: </s>
            <s xml:id="echoid-s8829" xml:space="preserve">tempus id eſt hic expri-
              <lb/>
            mendum {1/4} √ A, (poſito concinnioris calculi gratia corpus à quiete libere
              <lb/>
            cadens intra minutum ſec. </s>
            <s xml:id="echoid-s8830" xml:space="preserve">abſolvere 16. </s>
            <s xml:id="echoid-s8831" xml:space="preserve">ped.) </s>
            <s xml:id="echoid-s8832" xml:space="preserve">& </s>
            <s xml:id="echoid-s8833" xml:space="preserve">hoc tempore debet effluere
              <lb/>
            numerus pedum cubicorum aquæ deſignandus per {N/A} X {1/4} √ A ſeu {N/4 √ A}: </s>
            <s xml:id="echoid-s8834" xml:space="preserve">
              <lb/>
            effluit autem revera 2 M A, nempe cylindrus aqueus cujus baſis eſt M & </s>
            <s xml:id="echoid-s8835" xml:space="preserve">cu-
              <lb/>
            jus longitudo facit duplicem altitudinem A: </s>
            <s xml:id="echoid-s8836" xml:space="preserve">eſt igitur {N/4 √ A} = 2MA; </s>
            <s xml:id="echoid-s8837" xml:space="preserve">unde
              <lb/>
            amplitudo orificii ſeu</s>
          </p>
          <p>
            <s xml:id="echoid-s8838" xml:space="preserve">M = {N/8A √ A}.</s>
            <s xml:id="echoid-s8839" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8840" xml:space="preserve">Vis autem repellens fit æqualis 2 M A ſeu = {N/4 √ A}.</s>
            <s xml:id="echoid-s8841" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum