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

Page concordance

< >
Scan Original
121 107
122 108
123 109
124 110
125 111
126 112
127 113
128 114
129 115
130 116
131 117
132 118
133 119
134 120
135 121
136 122
137 123
138
139 125
140 126
141 127
142 128
143 129
144 130
145 131
146 132
147 133
148 134
149 135
150 136
< >
page |< < (189) of 361 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div225" type="section" level="1" n="178">
          <p>
            <s xml:id="echoid-s5446" xml:space="preserve">
              <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-
              <lb/>
            dani, ita ut longitudinibus accedat, quod numero canalium decedit. </s>
            <s xml:id="echoid-s5449" xml:space="preserve">Ra-
              <lb/>
            tione alterius anguli N M G obſervari meretur, aquam altius elevari poſſe,
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            tis articuli conſtructæ cochleæ calculum, prouti fecimus de cochlea ad Vi-
              <lb/>
            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
              <lb/>
            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-
              <lb/>
            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
              <lb/>
            igitur hæc pars ad totam helicem ut 16574 ad 21600 vel ut 8287 ad 10800,
              <lb/>
            ſic ut ſingulis revolutioniqus ejici poſſint plus quam quatuor quintæ partes
              <lb/>
            integræ helicis capacitatis, duplumque cum triente præterpropter hac ma-
              <lb/>
            china efficiatur, quam obtinetur ſimili machinatione ad mentem Vitruvii fa-
              <lb/>
            bricata: </s>
            <s xml:id="echoid-s5464" xml:space="preserve">altius quoque eodem nucleo elevantur aquæ in ratione ut √3 ad √2.
              <lb/>
            </s>
            <s xml:id="echoid-s5465" xml:space="preserve">Venio jam ad potentiam tum moventem tum abſolutam, quæ in elevandis aquis
              <lb/>
            impenditur.</s>
            <s xml:id="echoid-s5466" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div226" type="section" level="1" n="179">
          <head xml:id="echoid-head227" xml:space="preserve">Problema.</head>
          <p>
            <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
              <lb/>
            tangentialem in f in æquilibrio cum illo pondere poſitam.</s>
            <s xml:id="echoid-s5469" xml:space="preserve"/>
          </p>
        </div>
        <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
              <lb/>
            globi in puncto infimo p quieſcentis. </s>
            <s xml:id="echoid-s5471" xml:space="preserve">In præſenti vero caſu paullo aliter ſe
              <lb/>
            res habet, quod pondus aquæ per magnum helicis arcum eſt diſtributum,
              <lb/>
            neque in puncto aliquo dato concentratum. </s>
            <s xml:id="echoid-s5472" xml:space="preserve">Facile quidem eſt in anteceſ-
              <lb/>
            ſum prævidere, in utroque caſu easdem fore potentias ex regulis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum