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

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          <pb o="17" file="0031" n="31" rhead="(o)"/>
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        <div xml:id="echoid-div9" type="section" level="1" n="9">
          <head xml:id="echoid-head12" xml:space="preserve">HYDRODYNAMICÆ
            <lb/>
          SECTIO SECUNDA,</head>
          <head xml:id="echoid-head13" style="it" xml:space="preserve">Quæ agit de fluidis ſtagnantibus eorundemque
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          æquilibrio tum inter ſe, tum ad alias po-
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          tentias relato.</head>
          <head xml:id="echoid-head14" xml:space="preserve">Theorema 1.</head>
          <head xml:id="echoid-head15" xml:space="preserve">§. 1.</head>
          <p>
            <s xml:id="echoid-s447" xml:space="preserve">SUperficies fluidi ſtagnantis horizonti eſt parallela.</s>
            <s xml:id="echoid-s448" xml:space="preserve"/>
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        <div xml:id="echoid-div10" type="section" level="1" n="10">
          <head xml:id="echoid-head16" xml:space="preserve">Demonſtratio.</head>
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            <s xml:id="echoid-s449" xml:space="preserve">Contineat vas A B C D (Fig. </s>
            <s xml:id="echoid-s450" xml:space="preserve">1.) </s>
            <s xml:id="echoid-s451" xml:space="preserve">fluidum E B C F, cu-
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              <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">Fig. 1.</note>
            jus ſuperficies E G F, ſi fieri poſſit, horizonti non ſit parallela: </s>
            <s xml:id="echoid-s452" xml:space="preserve">conſi-
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            deretur guttula in loco eminentiori a, quæ gravitate ſua verticaliter
              <lb/>
            deorſum ſollicitatur vi repræſentata per a c, reſolvatur hæc vis in duas
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            collaterales a d & </s>
            <s xml:id="echoid-s453" xml:space="preserve">a b alteram perpendicularem ad ſuperficiem, alte-
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            ram quæ tangat illam: </s>
            <s xml:id="echoid-s454" xml:space="preserve">Cum autem nihil adſit, quod huic vi poſteriori
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            reſiſtat, hæc non poteſt non effectum ſuum exerere, ipſamque adeo
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            guttulam verſus E trahere, quod eſſet contra hypotheſin ſtagnationis, ſeu
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            ſtatus permanentis: </s>
            <s xml:id="echoid-s455" xml:space="preserve">Igitur neceſſe eſt, ut vis tangentialis a b ubique nulla
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            ſit, quod non aliter contingit, quam cum ſuperficies tota horizonti eſt
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            parallela. </s>
            <s xml:id="echoid-s456" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s457" xml:space="preserve">E. </s>
            <s xml:id="echoid-s458" xml:space="preserve">D.</s>
            <s xml:id="echoid-s459" xml:space="preserve"/>
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          <head xml:id="echoid-head17" xml:space="preserve">Corollarium.</head>
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            <s xml:id="echoid-s460" xml:space="preserve">§. </s>
            <s xml:id="echoid-s461" xml:space="preserve">2. </s>
            <s xml:id="echoid-s462" xml:space="preserve">Hinc intelligitur veritas propoſitionis generalis, quod nempe
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            ſuperficies fluidi, cujus partes viribus quibuscunque ſollicitantur, ſe
              <lb/>
            ita ſemper componat, ut quælibet guttula, in ſuperficie poſita, trahatur
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            ſub directione, ad ſuperficiem perpendiculari.</s>
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