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

Table of Notes

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          <pb o="281" file="0295" n="295" rhead="SECTIO DECIMA TERTIA."/>
          <p>
            <s xml:id="echoid-s8320" xml:space="preserve">At ut rem plane in apricum ponamus, eam generalius nunc proſe-
              <lb/>
            quemur, idque tentabimus, ut vim repellentem à fluxus initio, dum veloci-
              <lb/>
            tates continue mutantur, determinemus: </s>
            <s xml:id="echoid-s8321" xml:space="preserve">neque enim primum noſtrum theo-
              <lb/>
            rema aliter quam cum velocitas invariata manet locum habet. </s>
            <s xml:id="echoid-s8322" xml:space="preserve">Ut in quæſtio-
              <lb/>
            ne hâc paullo intricatiore pertractanda eo intelligibiliores ſimus, hîc quædam
              <lb/>
            generaliora præmonuiſſe juvabit.</s>
            <s xml:id="echoid-s8323" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8324" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8325" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8326" xml:space="preserve">Quantit{as} mot{us} eſt factum ex velocitate in maſſam: </s>
            <s xml:id="echoid-s8327" xml:space="preserve">ſi velocitates
              <lb/>
            ſint inæquales, habebitur quantitas mot{us} abſoluta, ſi ſingulæ particulæ per ſuam
              <lb/>
            reſpective velocitatem multiplicentur productorumque fumma accipiatur.
              <lb/>
            </s>
            <s xml:id="echoid-s8328" xml:space="preserve">Quantitas mot{us} generatur à preſſionibus motricibus dato tempore urgentibus & </s>
            <s xml:id="echoid-s8329" xml:space="preserve">
              <lb/>
            effectus cauſæ eſt æqualis cenſendus: </s>
            <s xml:id="echoid-s8330" xml:space="preserve">Igitur ſumma preſſionum motricium per
              <lb/>
            ſua tempuſcula multiplicatorum æſtimanda eſt ex genita quantitate motus. </s>
            <s xml:id="echoid-s8331" xml:space="preserve">Et
              <lb/>
            quia quælibet preſſio motrix reagit in vas, ex quo aquæ effluunt, erit tota vis re-
              <lb/>
            pellens pro quovis momento æqualis novæ quantitati motus diviſæ per tempuſ-
              <lb/>
            culum, quo generatur. </s>
            <s xml:id="echoid-s8332" xml:space="preserve">His præmonitis ad quæſtionem ipſam progredior.</s>
            <s xml:id="echoid-s8333" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8334" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8335" xml:space="preserve">8. </s>
            <s xml:id="echoid-s8336" xml:space="preserve">Sit igitur vas infinitæ amplitudinis A C D B (Fig. </s>
            <s xml:id="echoid-s8337" xml:space="preserve">82.) </s>
            <s xml:id="echoid-s8338" xml:space="preserve">eique ho-
              <lb/>
              <note position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">Fig. 82.</note>
            rizontaliter infixa fiſtula E H I D, cujus amplitudines utcunque inæquales po-
              <lb/>
            nuntur: </s>
            <s xml:id="echoid-s8339" xml:space="preserve">amplitudo orificii H I fuerit = 1, longitudo fiftulæ = m; </s>
            <s xml:id="echoid-s8340" xml:space="preserve">velocitas
              <lb/>
            utcunque variabilis in H I = √ 2 v, ſeu talis, quæ debeatur altitudini v: </s>
            <s xml:id="echoid-s8341" xml:space="preserve">dico
              <lb/>
            primo, fore quantitatem motus abſolutam aquæ in fiſtula contentæ æqualem
              <lb/>
            m√2v, id eſt, talem ac ſi fiſtula eſſet cylindrica ſuaque amplitudine orificium
              <lb/>
            H I exæquaret, quia nempe cujuslibet ſtrati F G gf velocitas eſt maſſæ reci-
              <lb/>
            proce proportionalis.</s>
            <s xml:id="echoid-s8342" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8343" xml:space="preserve">Jam vero fingamus dato tempuſculo infinite parvo exilire per orificium
              <lb/>
            H I columellam H L M I, cujus longitudinem H L vel I M ponemus = a:
              <lb/>
            </s>
            <s xml:id="echoid-s8344" xml:space="preserve">erit maſſa hujus columellæ = a, habebitque quantitatem motus = a√2v: </s>
            <s xml:id="echoid-s8345" xml:space="preserve">
              <lb/>
            fed eodem tempore maſſa aquæ in fiſtula contentæ acquiſivit quantitatem mo-
              <lb/>
            tus {mdv/√2v} (habuit enim m√2v); </s>
            <s xml:id="echoid-s8346" xml:space="preserve">eſt igitur quantitas motus abſoluta dato tem-
              <lb/>
            puſculo genita = a√2v + {mdv/√2v}; </s>
            <s xml:id="echoid-s8347" xml:space="preserve">hæc vero ſi dividatur per idem tempuſ-
              <lb/>
            culum (quod exprimendum eſt per {a/√2v}) habebitur, ut vidimus §. </s>
            <s xml:id="echoid-s8348" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8349" xml:space="preserve">preſſio
              <lb/>
            quæſita vas repellens, quæ proinde ſi vocetur p, </s>
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