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

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        <div xml:id="echoid-div176" type="section" level="1" n="137">
          <pb o="164" file="0178" n="178" rhead="HYDRODYNAMICÆ"/>
        </div>
        <div xml:id="echoid-div178" type="section" level="1" n="138">
          <head xml:id="echoid-head184" xml:space="preserve">Definitiones.</head>
          <p>
            <s xml:id="echoid-s4761" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4762" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4763" xml:space="preserve">Per potentiam moventem deinceps intelligam principium illud agens,
              <lb/>
            quod conſiſtit in pondere, preſſione animata aliisve hujuscemodi viribus,
              <lb/>
            uti dicuntur, mortuis.</s>
            <s xml:id="echoid-s4764" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4765" xml:space="preserve">Productum autem quod oritur à multiplicatione potentiæ iſtius moventis
              <lb/>
            per ejusdem velocitatem æque ac tempus durante quo preſſionem ſuam exe-
              <lb/>
            rit, deſignabo per potentiam abſolutam. </s>
            <s xml:id="echoid-s4766" xml:space="preserve">Vel quia productum ex velocitate & </s>
            <s xml:id="echoid-s4767" xml:space="preserve">
              <lb/>
            tempore proportionale eſt ſimpliciter ſpatio percurſo, licebit etiam potentiam
              <lb/>
            abſolutam colligere ex potentia mouente multiplicata per ſpatium, quod eadem
              <lb/>
            percurrit. </s>
            <s xml:id="echoid-s4768" xml:space="preserve">Id vero productum ideo voco potentiam abſolutam, quia ex illo de-
              <lb/>
            mum æſtimandi ſunt labores hominum operariorum in elevandis aquis exant-
              <lb/>
            lati, quod mox demonſtratum dabo in regulis, quæ mihi in hanc rem ob-
              <lb/>
            ſervatæ fuerunt. </s>
            <s xml:id="echoid-s4769" xml:space="preserve">Interim viſæ mihi fuerunt machinæ hydraulicæ commode ſe
              <lb/>
            reduci pati ad duo genera, quorum alterum aquas cum impetu ejicit, alte-
              <lb/>
            rum de loco in locum placide veluti transportat. </s>
            <s xml:id="echoid-s4770" xml:space="preserve">Utrumque ordine ſuo
              <lb/>
            pertractabo genus & </s>
            <s xml:id="echoid-s4771" xml:space="preserve">denique ſub finem quædam addam de diverſis poten-
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            tiis moventibus.</s>
            <s xml:id="echoid-s4772" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div179" type="section" level="1" n="139">
          <head xml:id="echoid-head185" style="it" xml:space="preserve">(A) De machinis aquas cum impetu in altum projicientibus.</head>
          <head xml:id="echoid-head186" xml:space="preserve">Regula 1.</head>
          <p>
            <s xml:id="echoid-s4773" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4774" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4775" xml:space="preserve">Labores hominum operariorum, qui machinis hydraulicis pro
              <lb/>
            aquis elevandis apponuntur, æſtimandi ſunt ex potentia abſoluta, id eſt, ex
              <lb/>
            potentia movente ſeu preſſione quam exerunt, ex tempore & </s>
            <s xml:id="echoid-s4776" xml:space="preserve">ex velocitate
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            puncti, cui potentia movens applicatur.</s>
            <s xml:id="echoid-s4777" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div180" type="section" level="1" n="140">
          <head xml:id="echoid-head187" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s4778" xml:space="preserve">(α) De potentia movente res eſt perſpicua: </s>
            <s xml:id="echoid-s4779" xml:space="preserve">labores enim cæteris omni-
              <lb/>
            bus paribus ſunt utique proportionales numero operariorum ſeu potentiæ mo-
              <lb/>
            venti. </s>
            <s xml:id="echoid-s4780" xml:space="preserve">(β) Ratione temporis res eſt non minus manifeſta ex omnium cir-
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            cumſtantiarum replicatione, quæ ex duplicatione temporis oritur. </s>
            <s xml:id="echoid-s4781" xml:space="preserve">(γ) De-
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            nique quod ad velocitatem attinet res ex eo eſt deducenda, quod ſive poten-
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            tiam moventem duplices, ſive ejus velocitatem non diverſus oriatur </s>
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