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

Table of handwritten notes

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        <div xml:id="echoid-div12" type="section" level="1" n="11">
          <pb o="18" file="0032" n="32" rhead="HYDRODYNAMICÆ."/>
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        <div xml:id="echoid-div13" type="section" level="1" n="12">
          <head xml:id="echoid-head18" xml:space="preserve">Theorema 2.</head>
          <p>
            <s xml:id="echoid-s464" xml:space="preserve">§. </s>
            <s xml:id="echoid-s465" xml:space="preserve">3. </s>
            <s xml:id="echoid-s466" xml:space="preserve">Fluidum homogeneum, duobus tubis @ communicantibus
              <lb/>
            utcunque formatis incluſum, ad æquilibrium eſt compoſitum, quando
              <lb/>
            ambæ ſuperficies ad libellam poſitæ ſunt, id eſt, æqualem à puncto vaſis
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            infimo diſtantiam verticalem ſervant.</s>
            <s xml:id="echoid-s467" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div14" type="section" level="1" n="13">
          <head xml:id="echoid-head19" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s468" xml:space="preserve">Sit fluidum vaſi ABC, (Fig. </s>
            <s xml:id="echoid-s469" xml:space="preserve">2.) </s>
            <s xml:id="echoid-s470" xml:space="preserve">ex duobus cruribus ſeu tubis
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              <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">Fig. 2.</note>
            communicantibus compoſito incluſum, ponaturque in utroque crure
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            ad eandem altitudinem poſitum: </s>
            <s xml:id="echoid-s471" xml:space="preserve">dico non poſſe ſitum hunc mutari, quin
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            corpus aliquod grave ex ſitu inferiori in altiorem ſe recipiat, quod eſſet
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            contra naturam gravium; </s>
            <s xml:id="echoid-s472" xml:space="preserve">Nam ſi ſuperficies E deſcendat in e, & </s>
            <s xml:id="echoid-s473" xml:space="preserve">ab al-
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            tera parte D ex D elevetur in d, quoniam pars vaſis reliqua eodem fluido
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            ante & </s>
            <s xml:id="echoid-s474" xml:space="preserve">poſt ſitum mutatum plenum eſt, omnis mutationis effectus in hoc
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            ſitus eſt, quod particula E e aſcenderit in D d.</s>
            <s xml:id="echoid-s475" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s476" xml:space="preserve">Cæterum idem quoque liquet ex Theoremate primo, quandoquidem
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            in aqua ſtagnante tubus utcunque formatus fingi poteſt, in quo utique aqua
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            ſitum ſervabit, quem antea habuit, cum perinde ſit, ſive aqua tubo incluſa,
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            coërceatur lateribus tubi, ſive circumſtagnante aqua.</s>
            <s xml:id="echoid-s477" xml:space="preserve"/>
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        <div xml:id="echoid-div16" type="section" level="1" n="14">
          <head xml:id="echoid-head20" xml:space="preserve">Scholium 1.</head>
          <p>
            <s xml:id="echoid-s478" xml:space="preserve">§. </s>
            <s xml:id="echoid-s479" xml:space="preserve">4. </s>
            <s xml:id="echoid-s480" xml:space="preserve">Si in demonſtratione prima præcedentis paragraphi tota
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            maſſa D B E ſitum ſuum commutaſſe concipiatur cum ſitu d B e, facile de-
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            monſtratur centrum gravitatis totius maſſæ in ſitum altiorem aſcendiſſe,
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            quod non minus abſurdum eſt: </s>
            <s xml:id="echoid-s481" xml:space="preserve">Quoniam autem in noſtra demonſtratio-
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            ne nulla eſt particula in E e, quæ non aſcenderit poſt mutatum ſitum, exi-
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            ſtimavi ſtrictiorem & </s>
            <s xml:id="echoid-s482" xml:space="preserve">clariorem fore demonſtrationem, ſi centri gravitatis
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            nulla conſideratio habeatur.</s>
            <s xml:id="echoid-s483" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div17" type="section" level="1" n="15">
          <head xml:id="echoid-head21" xml:space="preserve">Scholium 2.</head>
          <p>
            <s xml:id="echoid-s484" xml:space="preserve">§. </s>
            <s xml:id="echoid-s485" xml:space="preserve">5. </s>
            <s xml:id="echoid-s486" xml:space="preserve">De tubis capillaribus phænomena habemus ſingularia;</s>
            <s xml:id="echoid-s487" xml:space="preserve"/>
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