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

Table of Notes

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            <s xml:id="echoid-s502" xml:space="preserve">
              <pb o="20" file="0034" n="34" rhead="HYDRODYNAMICÆ."/>
            niat, & </s>
            <s xml:id="echoid-s503" xml:space="preserve">ſi ex noſtra hypotheſi argumentamur, dicendum erit, Mercurium
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            quoque ſupra libellam fuiſſe aſcenſurum, ſi modo particulæ ejus non majo-
              <lb/>
            ri vi ſe invicem attraherent, quam particulæ aquæ; </s>
            <s xml:id="echoid-s504" xml:space="preserve">huic enim attractioni
              <lb/>
            omnia tribuo, quæ Mercurium in diverſa ire faciunt. </s>
            <s xml:id="echoid-s505" xml:space="preserve">Experimenta, quæ
              <lb/>
            ad hanc ſententiam me manuduxerunt, apponam in fine hujus ſectionis.</s>
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          </p>
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        <div xml:id="echoid-div18" type="section" level="1" n="16">
          <head xml:id="echoid-head22" xml:space="preserve">Lemma.</head>
          <p>
            <s xml:id="echoid-s507" xml:space="preserve">§. </s>
            <s xml:id="echoid-s508" xml:space="preserve">6. </s>
            <s xml:id="echoid-s509" xml:space="preserve">Sit tubus cylindricus A B D C (Fig. </s>
            <s xml:id="echoid-s510" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s511" xml:space="preserve">utcunque verſus
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">Fig. 3.</note>
            horizontem inclinatus, cujus fundum CD ad latera tubi ſit perpendiculare,
              <lb/>
            plenusque intelligatur aquâ usque in AB; </s>
            <s xml:id="echoid-s512" xml:space="preserve">dico preſſionem omnis aquæ in
              <lb/>
            fundum CD eſſe æqualem ponderi cylindri aquei, cujus baſis eſt CD, & </s>
            <s xml:id="echoid-s513" xml:space="preserve">
              <lb/>
            cujus altitudo eſt verticalis DE, terminata ab horizontali BE.</s>
            <s xml:id="echoid-s514" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div20" type="section" level="1" n="17">
          <head xml:id="echoid-head23" xml:space="preserve">Demonſtratio.</head>
          <p>
            <s xml:id="echoid-s515" xml:space="preserve">Cum forma tubi ſit cylindrica, & </s>
            <s xml:id="echoid-s516" xml:space="preserve">fundum inſuper ad late-
              <lb/>
            ra tubi perpendiculare, quilibet videt, quod actio fluidi in fundum ea-
              <lb/>
            dem ſit, quam haberet cylindrus ſolidus ejusdem ponderis ſuper plano in-
              <lb/>
            clinato, conſtat autem ex mechanicis, preſſionem cylindri ſolidi in fundum
              <lb/>
            eam eſſe, quæ in propoſitione definitur, ergo & </s>
            <s xml:id="echoid-s517" xml:space="preserve">talis erit actio fluidi, ſi
              <lb/>
            modo non reſpiciatur adhæſio fluidi in lateribus tubi, ejusdemque indoles
              <lb/>
            ratione tubulorum capillarium, à quibus animum abſtrahimus. </s>
            <s xml:id="echoid-s518" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s519" xml:space="preserve">E. </s>
            <s xml:id="echoid-s520" xml:space="preserve">D.</s>
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          <head xml:id="echoid-head24" xml:space="preserve">Theorema 3.</head>
          <p>
            <s xml:id="echoid-s522" xml:space="preserve">§. </s>
            <s xml:id="echoid-s523" xml:space="preserve">7. </s>
            <s xml:id="echoid-s524" xml:space="preserve">Sit jam generaliter vas utcunque formatum A H M B (Fig. </s>
            <s xml:id="echoid-s525" xml:space="preserve">4.)
              <lb/>
            </s>
            <s xml:id="echoid-s526" xml:space="preserve">
              <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">Fig. 4.</note>
            & </s>
            <s xml:id="echoid-s527" xml:space="preserve">aqua repletum usque in D E, erit preſſio aquæ in ſingulas vaſis
              <lb/>
            particulas, veluti in G aut H, ſemper æqualis ponderi cylindri aquei, cu-
              <lb/>
            jus baſis eſt ſuperficies illius particulæ, & </s>
            <s xml:id="echoid-s528" xml:space="preserve">cujus altitudo æqualis eſt diſtan-
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            tiæ verticali ejusdem particulæ à ſuperficie aquea.</s>
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          </p>
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        <div xml:id="echoid-div23" type="section" level="1" n="19">
          <head xml:id="echoid-head25" xml:space="preserve">Demonſtratio.</head>
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            <s xml:id="echoid-s530" xml:space="preserve">Primo concipiatur in G tubulus cylindricus CG perpendicula-
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            riter vaſi inſiſtens, productaque ED, intelligatur hic tubus ſimili </s>
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