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

Table of figures

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            <s xml:id="echoid-s7256" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7257" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7258" xml:space="preserve">Exiſtimo autem non poſſe vorticem in ſtatu ſuo per tempus aliquod
              <lb/>
            notabile permanere, ſi vires centrifugæ partium æqualium in fluido homoge-
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            neo creſcant ab axe verſus peripheriam: </s>
            <s xml:id="echoid-s7259" xml:space="preserve">hoc enim ſi eſſet, cum nihil ſit, quod
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            partium axi viciniorum vim centrifugam ſufficienter coërceat, fieret utique, ut
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            partes illæ viciniores perpetuo ab ax@ recederent, remotioresque ad illum
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            propellerent, neque unquam in hoc ſtatu æquilibrium aut ſtatus durationis
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            obtineri poſſet. </s>
            <s xml:id="echoid-s7260" xml:space="preserve">Apparet inde quantitatem hanc {2gV/y} (quæ nempe in fluidis
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            homogeneis vim centrifugam partium æqualium exprimit) aut una creſcere
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            cum γ aut ſaltem non decreſcere, atque ſic ſi rurſus ad ſpecialem hypotheſin
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            antea factam (2V = fy
              <emph style="super">e</emph>
            ) deſcendamus, non poterit e eſſe minor unitate. </s>
            <s xml:id="echoid-s7261" xml:space="preserve">Igi-
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            tur in omnibus vorticibus, de quibus hic ſermo eſt, ad ſtatum durationis re-
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            ductis, ſuperficies nunquam convexa erit, ut in figura 66, ſed ſemper aut con-
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            cava, ut in figura 65. </s>
            <s xml:id="echoid-s7262" xml:space="preserve">aut conica: </s>
            <s xml:id="echoid-s7263" xml:space="preserve">& </s>
            <s xml:id="echoid-s7264" xml:space="preserve">quia e vel major eſt unitate vel eidem æqua-
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            lis, aliter fieri non poteſt, quin velocitates aut æquali aut majori ratione cre-
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            ſcant cum radicibus diſtantiarum ab axe. </s>
            <s xml:id="echoid-s7265" xml:space="preserve">Hæc cum ita mecum perpendo, non
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            intelligo quemadmodum Newtonus fingere ſibi potuerit duos vortices fluidi
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            ubique homogenei ad ſtatum perpetuæ durationis reductos, in quorum altero
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            tempora periodica partium ſint ut earum diſtantiæ ab axe cylindri, in altero au-
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            tem ut quadrata diſtantiarum à centro ſphæræ: </s>
            <s xml:id="echoid-s7266" xml:space="preserve">Nam in horum vorticum altero
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            velocitates ubique eſſent æquales, & </s>
            <s xml:id="echoid-s7267" xml:space="preserve">in altero plane decreſcerent ab axe ver-
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            ſus peripheriam.</s>
            <s xml:id="echoid-s7268" xml:space="preserve"/>
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            <s xml:id="echoid-s7269" xml:space="preserve">Magis veroſimile eſt, in pleriſque vorticibus, qui ſtatum perduratio-
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            nis jam attigerint, fluidi ſive homogenei ſive heterogenei partium ſingularum
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            tempora periodica eadem fore, quaſi totus cylindrus ſolidus fuerit, partes au-
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            tem quæ ſint ſpecifice graviores circumferentiæ, viciniores futuras eſſe. </s>
            <s xml:id="echoid-s7270" xml:space="preserve">In hoc
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            caſu fit v proportionale ipſi y & </s>
            <s xml:id="echoid-s7271" xml:space="preserve">V proportionale ejusdem quadrato, curvaque
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            E O F erit parabola Apolloniana, cujus vertex in O & </s>
            <s xml:id="echoid-s7272" xml:space="preserve">cujus axis ſit O G.</s>
            <s xml:id="echoid-s7273" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s7274" xml:space="preserve">Præſertim hæc ita proxime fore præſumo, ſi vortex generetur à rota-
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            tione vaſis cylindrici circa axem H G, vel etiam ab agitatione uniformi baculi
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            juxta latera vaſis, cujuſmodi vorticum phænomena expoſuit D. </s>
            <s xml:id="echoid-s7275" xml:space="preserve">Saulmon i@
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            Comm. </s>
            <s xml:id="echoid-s7276" xml:space="preserve">Acad. </s>
            <s xml:id="echoid-s7277" xml:space="preserve">Reg. </s>
            <s xml:id="echoid-s7278" xml:space="preserve">ſc. </s>
            <s xml:id="echoid-s7279" xml:space="preserve">Pariſ. </s>
            <s xml:id="echoid-s7280" xml:space="preserve">a. </s>
            <s xml:id="echoid-s7281" xml:space="preserve">1716.</s>
            <s xml:id="echoid-s7282" xml:space="preserve"/>
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            <s xml:id="echoid-s7283" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7284" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7285" xml:space="preserve">Preſſiones quas diverſæ cylindri A B C D partes à fluido </s>
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