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

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              <pb o="166" file="0180" n="180" rhead="HYDRODYNAMICÆ"/>
            doquidem nemo nec ſuper plano verticali incedere nec dato tempore viam in-
              <lb/>
            finitam abſolvere poteſt; </s>
            <s xml:id="echoid-s4818" xml:space="preserve">Statuamus viam hanc minimæ defatigationis cum
              <lb/>
            horizontali angulum facere A C B 30. </s>
            <s xml:id="echoid-s4819" xml:space="preserve">graduum.</s>
            <s xml:id="echoid-s4820" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4821" xml:space="preserve">Quod ſi ita ſit, erit tympanum calcatorium ita fabricandum, ut pon-
              <lb/>
            dus deſiderata velocitate ſuperetur, cum calcator perpetuo triginta gradib{us} à
              <lb/>
            puncto tympani infimo diſtat.</s>
            <s xml:id="echoid-s4822" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4823" xml:space="preserve">Ex eodem principio etiam inter machinas diverſi generis ſelectus eſt
              <lb/>
            faciendus: </s>
            <s xml:id="echoid-s4824" xml:space="preserve">ita v. </s>
            <s xml:id="echoid-s4825" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4826" xml:space="preserve">ſi in ergatis vectiarius potentiam exerat, ſeu preſſionem
              <lb/>
            horizontalem, quæ efficiat quartam ſui proprii ponderis partem, hocque niſu
              <lb/>
            ſingulis minutis primis ſpatium 200. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">ped. </s>
            <s xml:id="echoid-s4828" xml:space="preserve">abſolvat, is fere ut puto eodem de-
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            fatigabitur modo, ac ſi eadem velocitate tympanum rotatorium ad angulum
              <lb/>
            30. </s>
            <s xml:id="echoid-s4829" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s4830" xml:space="preserve">calcet; </s>
            <s xml:id="echoid-s4831" xml:space="preserve">interim tamen pondus duplum eodem tempore ad eandem al-
              <lb/>
            titudinem hoc modo feret calcator, quia cæteris paribus preſſionem duplam
              <lb/>
            exerit.</s>
            <s xml:id="echoid-s4832" xml:space="preserve"/>
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        <div xml:id="echoid-div183" type="section" level="1" n="142">
          <head xml:id="echoid-head189" xml:space="preserve">Regula 2.</head>
          <p>
            <s xml:id="echoid-s4833" xml:space="preserve">§. </s>
            <s xml:id="echoid-s4834" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4835" xml:space="preserve">Exiſtente eadem potentia abſoluta dico omnes machinas, quæ
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            nullas patiuntur frictiones & </s>
            <s xml:id="echoid-s4836" xml:space="preserve">quæ nullos motus ad propoſitum finem inutiles
              <lb/>
            generant, eundem effectum præſtare neque adeo unam alteri præferendam
              <lb/>
            eſſe.</s>
            <s xml:id="echoid-s4837" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div184" type="section" level="1" n="143">
          <head xml:id="echoid-head190" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s4838" xml:space="preserve">Ex mechanicis conſtat machinam utcunque compoſitam reduci poſſe
              <lb/>
            ad vectem ſimplicem: </s>
            <s xml:id="echoid-s4839" xml:space="preserve">igitur omnem machinationem hydraulicam repræſen-
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            tare licebit ſimplici antlia vecte inſtructa Fig. </s>
            <s xml:id="echoid-s4840" xml:space="preserve">47. </s>
            <s xml:id="echoid-s4841" xml:space="preserve">ubi nempe embolus ope ve-
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              <note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">Fig. 47.</note>
            ctis M N mobilis circa punctum M detruditur, atque ſic aqua per orificium F
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            expellitur. </s>
            <s xml:id="echoid-s4842" xml:space="preserve">At vero ſi potentia movens P vecti applicata intelligatur in N, vi-
              <lb/>
            demus ex præcedente propoſitione nihil lucri accedere potentiæ abſolutæ ab aucta
              <lb/>
            vel diminuta longitudine vectis M N: </s>
            <s xml:id="echoid-s4843" xml:space="preserve">& </s>
            <s xml:id="echoid-s4844" xml:space="preserve">certe quæcunque ſit iſta longitudo
              <lb/>
            fieri poteſt, ut potentia movens eadem atque invariata velocitate mota eandem
              <lb/>
            aquæ quantitatem eodem impetu expellat, ſi modo amplitudo antliæ A B ra-
              <lb/>
            tionem habeat conſtantem ad longitudinem vectis M N. </s>
            <s xml:id="echoid-s4845" xml:space="preserve">Ex quibus perſpi-
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            cuum eſt, omnes machinas eadem potentia abſoluta eundem effectum præſtare,
              <lb/>
            ſi modo à frictionibus motibuſque ad deſtinatum finem inutilibus animus ab-
              <lb/>
            ſtrahatur.</s>
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