Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

Table of Notes

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          <p>
            <s xml:id="echoid-s3796" xml:space="preserve">
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            ei annexum, & </s>
            <s xml:id="echoid-s3797" xml:space="preserve">pro una libra, ſemi - libra adhibeatur, Ex-
              <lb/>
            perimentum procedet, & </s>
            <s xml:id="echoid-s3798" xml:space="preserve">pondera eodem tempore adſcen-
              <lb/>
            dere incipient. </s>
            <s xml:id="echoid-s3799" xml:space="preserve">Multiplicando globum ſemi-libræ per di-
              <lb/>
            ſtantiam a centro ſedecim, productum eſt octo; </s>
            <s xml:id="echoid-s3800" xml:space="preserve">& </s>
            <s xml:id="echoid-s3801" xml:space="preserve">mul-
              <lb/>
            tiplicando globum unius libræ per diſtantiam viginti quatuor
              <lb/>
            a centro, productum eſt viginti quatuor, quæ producta
              <lb/>
            ſunt inter ſe ut unum ad tria, id eſt, ut pondera ſemi-libræ,
              <lb/>
            & </s>
            <s xml:id="echoid-s3802" xml:space="preserve">unius libræ cum ſemiſſe, quæ in hoc Experimento ſimul
              <lb/>
            elevantur.</s>
            <s xml:id="echoid-s3803" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3804" xml:space="preserve">Differentiæ virium centralium, ex differentiis diſtantia-
              <lb/>
            rum a centro & </s>
            <s xml:id="echoid-s3805" xml:space="preserve">quantitatum materiæ oriundæ, ſeſe mu-
              <lb/>
            tuo poſſunt compenſare; </s>
            <s xml:id="echoid-s3806" xml:space="preserve">nam poſitis quantit atibus materiæ
              <lb/>
              <note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">367.</note>
            in corporibus circumactis in ratione inverſa diſtantiarum a
              <lb/>
            centro, vires centrales erunt æquales; </s>
            <s xml:id="echoid-s3807" xml:space="preserve">quantum vis una al-
              <lb/>
            teri major eſt reſpectu quantitatis materiæ, tantum hæc il-
              <lb/>
            lam ſuperat propter majorem diſtantiam.</s>
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        <div xml:id="echoid-div567" type="section" level="1" n="174">
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            <emph style="sc">Experimentum</emph>
          7.</head>
          <p>
            <s xml:id="echoid-s3809" xml:space="preserve">Sit globus ſemi libræ ad diſtantiam a centro viginti qua-
              <lb/>
              <note position="left" xlink:label="note-0148-02" xlink:href="note-0148-02a" xml:space="preserve">368.</note>
            tuor partium; </s>
            <s xml:id="echoid-s3810" xml:space="preserve">globus unius libræ ad diſtantiam duodecim
              <lb/>
            partium; </s>
            <s xml:id="echoid-s3811" xml:space="preserve">cæteris manentibus ut in Experimento præceden-
              <lb/>
            ti, ſi pondera in ſuſten aculis Orbium fuerint æqualia, eo-
              <lb/>
            dem momento adſcendent.</s>
            <s xml:id="echoid-s3812" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3813" xml:space="preserve">Caſus hujus propoſitionis exſtat, quando duo corpora fi-
              <lb/>
              <note position="left" xlink:label="note-0148-03" xlink:href="note-0148-03a" xml:space="preserve">369.</note>
            lo juncta circa commune centrum gravitatis revolvuntur. </s>
            <s xml:id="echoid-s3814" xml:space="preserve">Di-
              <lb/>
            ſtantiæ enim ab illo centro ſu nt in ratione inverſa ponde-
              <lb/>
            rum corporum , & </s>
            <s xml:id="echoid-s3815" xml:space="preserve">ergo vires centrales æquales. </s>
            <s xml:id="echoid-s3816" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0148-04" xlink:href="note-0148-04a" xml:space="preserve">143. 134.</note>
            corpus unum a centro conatur recedere, alterum ad cen-
              <lb/>
            trum trahitur; </s>
            <s xml:id="echoid-s3817" xml:space="preserve">& </s>
            <s xml:id="echoid-s3818" xml:space="preserve">propter virium æqualitatem ſeſe mutuo
              <lb/>
            netinent & </s>
            <s xml:id="echoid-s3819" xml:space="preserve">motum continuant; </s>
            <s xml:id="echoid-s3820" xml:space="preserve">ſi circa aliud punctum revol-
              <lb/>
            vantur, motum non continuant, & </s>
            <s xml:id="echoid-s3821" xml:space="preserve">corpus, cujus vis
              <lb/>
            centrifuga præpollet, a centro recedit, & </s>
            <s xml:id="echoid-s3822" xml:space="preserve">corpus aliud ſe-
              <lb/>
            cum fert.</s>
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        <div xml:id="echoid-div570" type="section" level="1" n="175">
          <head xml:id="echoid-head247" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          8.</head>
          <p>
            <s xml:id="echoid-s3824" xml:space="preserve">Corpora duo inæqualia P & </s>
            <s xml:id="echoid-s3825" xml:space="preserve">Q, filo junguntur, & </s>
            <s xml:id="echoid-s3826" xml:space="preserve">in
              <lb/>
              <note position="left" xlink:label="note-0148-05" xlink:href="note-0148-05a" xml:space="preserve">370.</note>
            hoc notatur punctum C, centrum commune gravitatis il-
              <lb/>
              <note position="left" xlink:label="note-0148-06" xlink:href="note-0148-06a" xml:space="preserve">TAB. XIV.
                <lb/>
              fig. 10.</note>
            lorum corporum quando filum diſtenditur.</s>
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