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

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        <div xml:id="echoid-div573" type="section" level="1" n="176">
          <pb o="94" file="0150" n="163" rhead="PHYSCES ELEMENTA"/>
          <p>
            <s xml:id="echoid-s3861" xml:space="preserve">Quomodocunque inter ſe vires centrales differant, ex
              <lb/>
              <note position="left" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">373.</note>
            jam dictis inter ſe poſſunt comparari; </s>
            <s xml:id="echoid-s3862" xml:space="preserve">nam ſunt ſemper in
              <lb/>
            ratione compoſita, ex ratione quantitatum materiæ in cor-
              <lb/>
            poribus revolutis , & </s>
            <s xml:id="echoid-s3863" xml:space="preserve">ratione diſtantiarum a centro ,
              <note symbol="*" position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">361.
                <lb/>
              363.</note>
            & </s>
            <s xml:id="echoid-s3864" xml:space="preserve">ratione inverſa quadratorum temporum periodicorum .</s>
            <s xml:id="echoid-s3865" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0150-03" xlink:href="note-0150-03a" xml:space="preserve">371.</note>
            Multiplicando quantitatem materiæ in unoquoque corpore
              <lb/>
            per ſuam diſtantiam a centro, & </s>
            <s xml:id="echoid-s3866" xml:space="preserve">dividendo productum per
              <lb/>
            quadratum temporis periodici, quotientes diviſionum erunt
              <lb/>
            in dicta ratione compoſita, id eſt, ut vires centrales.</s>
            <s xml:id="echoid-s3867" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div576" type="section" level="1" n="177">
          <head xml:id="echoid-head249" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          . 10.</head>
          <p>
            <s xml:id="echoid-s3868" xml:space="preserve">Obſervatis iiſdem quæ in Experimento præcedenti, de-
              <lb/>
              <note position="left" xlink:label="note-0150-04" xlink:href="note-0150-04a" xml:space="preserve">374.</note>
            tur globus ſemi-libræ, ad diſtantiam ſedecim a centro Or-
              <lb/>
            bis B, & </s>
            <s xml:id="echoid-s3869" xml:space="preserve">cum pondere {3/4} unius libræ in ſuſtentaculo con-
              <lb/>
            jungatur; </s>
            <s xml:id="echoid-s3870" xml:space="preserve">globus alter ſit unius libræ, ad diſtantiam vigin-
              <lb/>
            ti quatuor a centro Orbis A, & </s>
            <s xml:id="echoid-s3871" xml:space="preserve">conjungatur cum pondere
              <lb/>
            unius libræ; </s>
            <s xml:id="echoid-s3872" xml:space="preserve">circumagantur Orbes, eodem momento pon-
              <lb/>
            dera elevantur.</s>
            <s xml:id="echoid-s3873" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3874" xml:space="preserve">Corpora hic ſunt ut {1/2} ad 1.</s>
            <s xml:id="echoid-s3875" xml:space="preserve">; diſtantiæ ut 16. </s>
            <s xml:id="echoid-s3876" xml:space="preserve">ad 24.</s>
            <s xml:id="echoid-s3877" xml:space="preserve">; qua-
              <lb/>
            drata temporum periodicorum ut 4. </s>
            <s xml:id="echoid-s3878" xml:space="preserve">ad 9.</s>
            <s xml:id="echoid-s3879" xml:space="preserve">; multiplicando
              <lb/>
            {1/2} per 16.</s>
            <s xml:id="echoid-s3880" xml:space="preserve">, & </s>
            <s xml:id="echoid-s3881" xml:space="preserve">dividendo productum per 4.</s>
            <s xml:id="echoid-s3882" xml:space="preserve">, quotiens eſt 2.
              <lb/>
            </s>
            <s xml:id="echoid-s3883" xml:space="preserve">multiplicando 1. </s>
            <s xml:id="echoid-s3884" xml:space="preserve">per 24.</s>
            <s xml:id="echoid-s3885" xml:space="preserve">, & </s>
            <s xml:id="echoid-s3886" xml:space="preserve">dividendo productum per 9.</s>
            <s xml:id="echoid-s3887" xml:space="preserve">,
              <lb/>
            quotiens diviſionis eſt 2 {2/3}. </s>
            <s xml:id="echoid-s3888" xml:space="preserve">Vires ergo centrales ſunt inter
              <lb/>
            ſe ut 2. </s>
            <s xml:id="echoid-s3889" xml:space="preserve">ad 2 {2/3}, aut ut 3. </s>
            <s xml:id="echoid-s3890" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s3891" xml:space="preserve">quam rationem pondera in
              <lb/>
            ſuſtentaculis etiam inter ſe habent.</s>
            <s xml:id="echoid-s3892" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3893" xml:space="preserve">Quando quantitates materiæ ſunt æquales, diſtantiæ ipſæ
              <lb/>
              <note position="left" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">375.</note>
            per quadrata temporum periodicorum dividuntur ad deter-
              <lb/>
            minandam proportionem inter vires centrales.</s>
            <s xml:id="echoid-s3894" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3895" xml:space="preserve">In hoc caſu ſi quadratatemporum periodicorum fuerint in-
              <lb/>
              <note position="left" xlink:label="note-0150-06" xlink:href="note-0150-06a" xml:space="preserve">376.</note>
            ter ſe ut cubi diſtantiarum, quotientes diviſionum erunt in
              <lb/>
            ratione inverſa quadratorum diſtantiarum; </s>
            <s xml:id="echoid-s3896" xml:space="preserve">& </s>
            <s xml:id="echoid-s3897" xml:space="preserve">in hac ratio-
              <lb/>
            ne etiam vires centrales.</s>
            <s xml:id="echoid-s3898" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div580" type="section" level="1" n="178">
          <head xml:id="echoid-head250" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          II.</head>
          <p>
            <s xml:id="echoid-s3899" xml:space="preserve">Sint tempora periodica Orbis B & </s>
            <s xml:id="echoid-s3900" xml:space="preserve">A, ut 1. </s>
            <s xml:id="echoid-s3901" xml:space="preserve">ad 2.</s>
            <s xml:id="echoid-s3902" xml:space="preserve">; den-
              <lb/>
              <note position="left" xlink:label="note-0150-07" xlink:href="note-0150-07a" xml:space="preserve">377.</note>
            tur globi æquales, & </s>
            <s xml:id="echoid-s3903" xml:space="preserve">diſtantia a centro in orbe B ſit decem
              <lb/>
            alterius globi diſtantia a centro ſit ſedecim, pondus primo
              <lb/>
            annexum ſit unius libræ cum quadrante, & </s>
            <s xml:id="echoid-s3904" xml:space="preserve">pondus in </s>
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