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

Table of Notes

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              <pb o="189" file="0203" n="203" rhead="SECTIO NONA."/>
            angulum quam Vitruvius, & </s>
            <s xml:id="echoid-s5447" xml:space="preserve">cum eo pauciores ſuper eodem nucleo circum-
              <lb/>
            flecti poſſint canales, quo obliquius ſunt inſerti, Vitruvius octo, Cardanus
              <lb/>
            tres tantum ponendos ſtatuit: </s>
            <s xml:id="echoid-s5448" xml:space="preserve">ſunt autem canales longiores in cochlea Car-
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            dani, ita ut longitudinibus accedat, quod numero canalium decedit. </s>
            <s xml:id="echoid-s5449" xml:space="preserve">Ra-
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            tione alterius anguli N M G obſervari meretur, aquam altius elevari poſſe,
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            quo major iſte fiat angulus, ſed e contrario minorem aquæ quantitatem
              <lb/>
            ſingulis ejici revolutionibus. </s>
            <s xml:id="echoid-s5450" xml:space="preserve">Juſtum fortaſſe tenebunt medium, qui angu-
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            lum iſtum 60. </s>
            <s xml:id="echoid-s5451" xml:space="preserve">facient gradum.</s>
            <s xml:id="echoid-s5452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5453" xml:space="preserve">(XI.) </s>
            <s xml:id="echoid-s5454" xml:space="preserve">Subducemus nunc hujus noſtræ quoque ad normam præceden-
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            tis articuli conſtructæ cochleæ calculum, prouti fecimus de cochlea ad Vi-
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            truvii præceptum conſtructa, art. </s>
            <s xml:id="echoid-s5455" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s5456" xml:space="preserve">Quia vero per hypotheſin angulus
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            s a o eſt 5
              <emph style="super">0</emph>
            & </s>
            <s xml:id="echoid-s5457" xml:space="preserve">angulus N M G = 60
              <emph style="super">0</emph>
            ; </s>
            <s xml:id="echoid-s5458" xml:space="preserve">reperietur per art. </s>
            <s xml:id="echoid-s5459" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s5460" xml:space="preserve">arcus a g 8
              <emph style="super">0</emph>
            , 43
              <emph style="super">1</emph>
            ,
              <lb/>
            & </s>
            <s xml:id="echoid-s5461" xml:space="preserve">linea verticalis o r = 1, 00574, cui æqualis erit altera verticalis q x, ſi
              <lb/>
            dentur arcui a g h M s 284
              <emph style="super">0</emph>
            , 57
              <emph style="super">1</emph>
            , a quo ſi ſubtrahatur arcus a g, remanet ar-
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            cus g h M s 276
              <emph style="super">0</emph>
            , 14
              <emph style="super">1</emph>
            : </s>
            <s xml:id="echoid-s5462" xml:space="preserve">qui reſpondet arcui helicis aquam retinere valenti: </s>
            <s xml:id="echoid-s5463" xml:space="preserve">eſt
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            igitur hæc pars ad totam helicem ut 16574 ad 21600 vel ut 8287 ad 10800,
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            ſic ut ſingulis revolutioniqus ejici poſſint plus quam quatuor quintæ partes
              <lb/>
            integræ helicis capacitatis, duplumque cum triente præterpropter hac ma-
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            china efficiatur, quam obtinetur ſimili machinatione ad mentem Vitruvii fa-
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            bricata: </s>
            <s xml:id="echoid-s5464" xml:space="preserve">altius quoque eodem nucleo elevantur aquæ in ratione ut √3 ad √2.
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            </s>
            <s xml:id="echoid-s5465" xml:space="preserve">Venio jam ad potentiam tum moventem tum abſolutam, quæ in elevandis aquis
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            impenditur.</s>
            <s xml:id="echoid-s5466" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div226" type="section" level="1" n="179">
          <head xml:id="echoid-head227" xml:space="preserve">Problema.</head>
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            <s xml:id="echoid-s5467" xml:space="preserve">(XII.) </s>
            <s xml:id="echoid-s5468" xml:space="preserve">Dato pondere aquæ in helice quieſcentis, invenire potentiam
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            tangentialem in f in æquilibrio cum illo pondere poſitam.</s>
            <s xml:id="echoid-s5469" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div227" type="section" level="1" n="180">
          <head xml:id="echoid-head228" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s5470" xml:space="preserve">Vidimus quomodo problema hoc geometrice ſolvendum ſit ratione
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            globi in puncto infimo p quieſcentis. </s>
            <s xml:id="echoid-s5471" xml:space="preserve">In præſenti vero caſu paullo aliter ſe
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            res habet, quod pondus aquæ per magnum helicis arcum eſt diſtributum,
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            neque in puncto aliquo dato concentratum. </s>
            <s xml:id="echoid-s5472" xml:space="preserve">Facile quidem eſt in anteceſ-
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            ſum prævidere, in utroque caſu easdem fore potentias ex regulis </s>
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