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

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          <pb o="159" file="0173" n="173" rhead="SECTIO OCTAVA."/>
          <p>
            <s xml:id="echoid-s4624" xml:space="preserve">III. </s>
            <s xml:id="echoid-s4625" xml:space="preserve">Si vero nunc alterum foramen N admodum exiguum præ ambo-
              <lb/>
            bus reliquis ponatur, erit facto γ = o
              <lb/>
            x = {ααa/αα + ββ}; </s>
            <s xml:id="echoid-s4626" xml:space="preserve">deinde
              <lb/>
            x + b = {ααa + ααb + ββb/αα + ββ}, & </s>
            <s xml:id="echoid-s4627" xml:space="preserve">
              <lb/>
            a - x = {ββa/αα + ββ}.</s>
            <s xml:id="echoid-s4628" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4629" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s4630" xml:space="preserve">Si γγb = ααa, fit x = o. </s>
            <s xml:id="echoid-s4631" xml:space="preserve">Nullam igitur in hoc caſu preſſionem
              <lb/>
            ſuſtinent partes laminæ L Q: </s>
            <s xml:id="echoid-s4632" xml:space="preserve">imo inferiora verſus premitur, ſi γ ſit majus
              <lb/>
            quam {ααa/b}, & </s>
            <s xml:id="echoid-s4633" xml:space="preserve">lamina nullibi ſit perforata.</s>
            <s xml:id="echoid-s4634" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4635" xml:space="preserve">Iſta vero omnia ſimiliter ex §. </s>
            <s xml:id="echoid-s4636" xml:space="preserve">19. </s>
            <s xml:id="echoid-s4637" xml:space="preserve">facile colliguntur.</s>
            <s xml:id="echoid-s4638" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4639" xml:space="preserve">V. </s>
            <s xml:id="echoid-s4640" xml:space="preserve">Ita quoque ope ejusdem paragraphi ſine calculo novo prævideri po-
              <lb/>
            tuiſſet, quid fieri debeat, cum poſitis foraminibus H & </s>
            <s xml:id="echoid-s4641" xml:space="preserve">N in eadem altitudi-
              <lb/>
            ne ſumma foraminum eorum, ceu unicum amplitudinis β + γ conſiderari
              <lb/>
            poteſt: </s>
            <s xml:id="echoid-s4642" xml:space="preserve">Indicant nempe tam §. </s>
            <s xml:id="echoid-s4643" xml:space="preserve">19. </s>
            <s xml:id="echoid-s4644" xml:space="preserve">quam §. </s>
            <s xml:id="echoid-s4645" xml:space="preserve">26. </s>
            <s xml:id="echoid-s4646" xml:space="preserve">eſſe
              <lb/>
            x = {ααa/αα + (β + γ)
              <emph style="super">2</emph>
            },</s>
          </p>
          <p>
            <s xml:id="echoid-s4647" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s4648" xml:space="preserve">Notari etiam poteſt, cum valor ipſius x fit imaginarius, id pro-
              <lb/>
            venire ex eo, quod aquæ non ſolum non effluant, in aliquibus caſibus per
              <lb/>
            H, ſed quod ſuperficies L Q etiam deſcendat; </s>
            <s xml:id="echoid-s4649" xml:space="preserve">unde fieri poteſt, ut infra
              <lb/>
            orificium M deſcendat, quo ipſo ceſſat aqua@um contiguitas contra hypothe-
              <lb/>
            ſin propoſitionis. </s>
            <s xml:id="echoid-s4650" xml:space="preserve">Si autem valor x eſt realis, tum dupliciter exprimitur,
              <lb/>
            ſed alter valor inutilis eſt reputandus; </s>
            <s xml:id="echoid-s4651" xml:space="preserve">ſic igitur cavendum ne præpoſtera
              <lb/>
            radix ceu utilis aſſumatur.</s>
            <s xml:id="echoid-s4652" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4653" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s4654" xml:space="preserve">Denique ut caſum ſpecialiſſimum attingamus, ponemus om-
              <lb/>
            nia foramina inter ſe æqualia, & </s>
            <s xml:id="echoid-s4655" xml:space="preserve">prodibit 5xx + (2b - 6a) x = - aa +
              <lb/>
            2ab - bb, ſeu x = {3a - b - 2√ (aa + ab - bb)/5}; </s>
            <s xml:id="echoid-s4656" xml:space="preserve">atque ſi fuerit præterea
              <lb/>
            a = 3b, erit x = (proxime) {4/15} b, deinde altitudo velocitatis in forami-
              <lb/>
            ne N ſeu x + b = {19/15}b atque altitudo velocitati in M debita ſeu a - x = {41/15}b.
              <lb/>
            </s>
            <s xml:id="echoid-s4657" xml:space="preserve">Sunt itaque velocitates ſeu etiam, quia foramina æqualia ſunt, </s>
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