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

Table of Notes

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            <emph style="bf">HYDRODYNAMICÆ</emph>
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          <head xml:id="echoid-head247" xml:space="preserve">SECTIO UNDECIMA.</head>
          <head xml:id="echoid-head248" style="it" xml:space="preserve">De fluidis in vorticem actis, tum etiam de iis, quæ
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          in vaſis motis continentur.</head>
          <head xml:id="echoid-head249" xml:space="preserve">§. 1.</head>
          <p>
            <s xml:id="echoid-s7193" xml:space="preserve">EX eo tempore quo Keplerus & </s>
            <s xml:id="echoid-s7194" xml:space="preserve">Carteſius vortices adhibuere pro
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            variis naturæ phænomenis explicandis, multi operam ſuam haud
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            male ſe collocaturos rati ſollicite iſtud argumentum ruminati ſunt:
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            </s>
            <s xml:id="echoid-s7195" xml:space="preserve">primus autem, ni fallor, naturam ejus recte penetravit Huge-
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            nius in tract. </s>
            <s xml:id="echoid-s7196" xml:space="preserve">ſur la peſanteur; </s>
            <s xml:id="echoid-s7197" xml:space="preserve">ſuperaddam quædam, quæ ad in-
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            ſtitutum meum pertinent, ab aliis fortaſſe non ſatis examinata.</s>
            <s xml:id="echoid-s7198" xml:space="preserve"/>
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            <s xml:id="echoid-s7199" xml:space="preserve">Poni autem ſolent vortices ad ſtatum permanentiæ ſeu durationis redu-
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            cti, ita ut nulli mutationi ſubjectum lege conſtanter eadem moveatur flui-
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            dum.</s>
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            <s xml:id="echoid-s7201" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7202" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7203" xml:space="preserve">Sit cylindrus A B C D (Fig. </s>
            <s xml:id="echoid-s7204" xml:space="preserve">65. </s>
            <s xml:id="echoid-s7205" xml:space="preserve">& </s>
            <s xml:id="echoid-s7206" xml:space="preserve">66.) </s>
            <s xml:id="echoid-s7207" xml:space="preserve">verticaliter poſitus, cujus
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              <note position="left" xlink:label="note-0258-01" xlink:href="note-0258-01a" xml:space="preserve">Fig. 65.</note>
            axis G H, iſque ad certam altitudinem plenus ſit, concipiatur aqua in vorti-
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              <note position="left" xlink:label="note-0258-02" xlink:href="note-0258-02a" xml:space="preserve">& 66.</note>
            cem acta ſintque omnia jam ad ſtatum durationis reducta: </s>
            <s xml:id="echoid-s7208" xml:space="preserve">Ita ſuperficies aquæ
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            deprimetur verſus axem & </s>
            <s xml:id="echoid-s7209" xml:space="preserve">elevabitur verſus latera: </s>
            <s xml:id="echoid-s7210" xml:space="preserve">Sectionem per axem termi-
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            natam à ſuperficie aquæ repræſentabimus curva E O F, hujuſque curvæ nunc
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            indolem dabimus ex data relatione, quam inter ſe habent velocitates ſub certis
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            ab axe diſtantiis.</s>
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            <s xml:id="echoid-s7212" xml:space="preserve">Ducantur g a & </s>
            <s xml:id="echoid-s7213" xml:space="preserve">f n infinite propinquæ & </s>
            <s xml:id="echoid-s7214" xml:space="preserve">horizontales, agaturque a m
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            verticalis: </s>
            <s xml:id="echoid-s7215" xml:space="preserve">Sit O g = x, gf ſeu am = dx, ga = y, mn = dy: </s>
            <s xml:id="echoid-s7216" xml:space="preserve">Patet autem
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            quamlibet guttulam in ſuperficie poſitam niſu ſuo, ex vi centriſuga horizontali
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            & </s>
            <s xml:id="echoid-s7217" xml:space="preserve">vi gravitatis verticali, compoſito perpendiculariter ſuperficiei inſiſtere, quia
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            ſi oblique contranitatur nihil ſit, quod guttulam in loco ſuo conſervet.</s>
            <s xml:id="echoid-s7218" xml:space="preserve"/>
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            <s xml:id="echoid-s7219" xml:space="preserve">Igitur ſi vis centrifuga guttulæ in a poſitæ exprimatur per </s>
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