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

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              <pb o="279" file="0293" n="293" rhead="SECTIO DECIMA TERTIA."/>
            ſit infinitæ amplitudinis, vis repulſionis una cum velocitate aquarum effluen-
              <lb/>
            tium ſenſim ſenſimque creſcat, aut etiam decreſcat pro circumſtantiarum na-
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              <note position="right" xlink:label="note-0293-01" xlink:href="note-0293-01a" xml:space="preserve">Fig. 74.</note>
            tura: </s>
            <s xml:id="echoid-s8246" xml:space="preserve">Ab his autem mutationibus momentaneis animum primo abſtrahemus,
              <lb/>
            fluxum ex vaſe infinito fieri æquabilem ponendo. </s>
            <s xml:id="echoid-s8247" xml:space="preserve">Atque ſic optime definietur
              <lb/>
            vis repulſionis, ſi inquiratur, quænam ſit vis ad motum producendum re-
              <lb/>
            quiſita: </s>
            <s xml:id="echoid-s8248" xml:space="preserve">Hunc vero in finem non ſolum ad velocitatem aquæ effluentis, ſed & </s>
            <s xml:id="echoid-s8249" xml:space="preserve">
              <lb/>
            ad illius quantitatem erit reſpiciendum; </s>
            <s xml:id="echoid-s8250" xml:space="preserve">quantitas autem pendet partim à ma-
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            gnitudine orificii, partim à contractione venæ, quæ poſterior variabilis eſt:
              <lb/>
            </s>
            <s xml:id="echoid-s8251" xml:space="preserve">Vidimus quidem in Sect. </s>
            <s xml:id="echoid-s8252" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s8253" xml:space="preserve">poſſe totam evitari; </s>
            <s xml:id="echoid-s8254" xml:space="preserve">ſi tamen quædam ſit, erit
              <lb/>
            Sectio venæ maxime contractæ ſive attenuatæ ceu orificium conſiderandum & </s>
            <s xml:id="echoid-s8255" xml:space="preserve">
              <lb/>
            tunc dico fore vim repulſionis æqualem ponderi cylindri aquei, cujus baſis ſit
              <lb/>
            orificium aquas tranſmittens (id eſt, Sectio venæ horizontalis maxime con-
              <lb/>
            tractæ) & </s>
            <s xml:id="echoid-s8256" xml:space="preserve">cujus altitudo ſit æqualis duplæ altitudini ſuperficiei aqueæ ſuprafo-
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            ramen vel accuratius, duplæ altitudini, velocitati aquæ effluentis debitæ. </s>
            <s xml:id="echoid-s8257" xml:space="preserve">
              <lb/>
            Igitur ſi nulla ſit venæ contractio, prouti nulla eſt, cum per tubulum brevem
              <lb/>
            aquæ effluant, repulſio duplo aut fere duplo major erit, quam à Newtono de-
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            finita fuit.</s>
            <s xml:id="echoid-s8258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8259" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8260" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8261" xml:space="preserve">Ut hanc propoſitionem demonſtremus, conſiderandum hic erit
              <lb/>
            principium aliquod Mechanicum cujus uſum in aliis etiam quæſtionibus ſol-
              <lb/>
            vendis ſæpe expertus ſum: </s>
            <s xml:id="echoid-s8262" xml:space="preserve">principium hoc eſt:</s>
            <s xml:id="echoid-s8263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8264" xml:space="preserve">Si corpus à quiete velocitatem eandem per preßiones motrices directas
              <lb/>
            utcunque variabiles acquiſiverit, at que ſingulæ preßiones in tempuſcula ſua mul-
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            tiplicentur, erit ſumma omnium productorum ſemper eadem, id eſt, ſi preßio
              <lb/>
            fit = p, tempuſculum = dt, erit ſ p d t conſtans. </s>
            <s xml:id="echoid-s8265" xml:space="preserve">Hanc rem clarius expoſui
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            in Comment. </s>
            <s xml:id="echoid-s8266" xml:space="preserve">Acad. </s>
            <s xml:id="echoid-s8267" xml:space="preserve">Imp. </s>
            <s xml:id="echoid-s8268" xml:space="preserve">Petrop. </s>
            <s xml:id="echoid-s8269" xml:space="preserve">tom. </s>
            <s xml:id="echoid-s8270" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8271" xml:space="preserve">pag. </s>
            <s xml:id="echoid-s8272" xml:space="preserve">132.</s>
            <s xml:id="echoid-s8273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8274" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8275" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8276" xml:space="preserve">Ponamus jam cylindrum infinitæ veluti amplitudinis, ex quo
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            aquæ horizontaliter effluant velocitate uniformi, abſtrahendo ab actione, quam
              <lb/>
            gravitas exerit in particulas, poſtquam jam effluxerunt, ita ut ſingulæ hori-
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            zontaliter & </s>
            <s xml:id="echoid-s8277" xml:space="preserve">uniformiter moveri pergant; </s>
            <s xml:id="echoid-s8278" xml:space="preserve">particulæ autem accelerantur preſ-
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            ſionemque patiuntur, quamdiu maximus velocitatis gradus nondum adeſt,
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            huncque obtinent cum ad locum venæ maxime contractæ pervenerunt; </s>
            <s xml:id="echoid-s8279" xml:space="preserve">hæc
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            eſt ratio, quod ſectionem venæ ibidem conceptam ceu orificium effluxus </s>
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