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

Table of contents

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[151.] Experimentum 2.
[152.] Experimentum 3.
[153.] Experimentum 4.
[154.] SCHOLIUM I. De motu in Cycloide.
[155.] SCHOLIUM 2. De Centro oſcillationis determinando.
[156.] SCHOLIUM. 3. In quo quædam in boc capite memoratæ Cycloidis proprietates demonſtrantur.
[157.] SHOLIUM 4. De linea celerrimi deſcenſus.
[158.] CAPUT XX. De Projectione Gravium.
[159.] Machina Qua demonſtrata de corporum projectione confirmantur.
[160.] Experimentum.
[161.] Definitio.
[162.] CAPUT XXI. De Viribus Centralibus.
[163.] Definitio 1.
[164.] Definitio 2.
[165.] Definitio 3.
[166.] Machina
[167.] Experimentum 1.
[168.] Experimentum 2.
[169.] Experimentum 3.
[170.] Definitio 4.
[171.] Experimentum 4.
[172.] Experimentum 5.
[173.] Experimentum 6.
[174.] Experimentum 7.
[175.] Experimentum 8.
[176.] Experimentum 9.
[177.] Experimentum. 10.
[178.] Experimentum II.
[179.] Experimentum 12
[180.] Experimentum 13.
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          <pb o="91" file="0147" n="160" rhead="MATHEMATICA. LIB. I. CAP. XXI."/>
          <p>
            <s xml:id="echoid-s3765" xml:space="preserve">Nunc ſit pondus in ſeparatione ſuſtentaculi Orbis A uni-
              <lb/>
            us libræ, in ſeparatione ſuſtentaculi Orbis B ſemi-libræ;
              <lb/>
            </s>
            <s xml:id="echoid-s3766" xml:space="preserve">aut ſit hoc unius libræ, & </s>
            <s xml:id="echoid-s3767" xml:space="preserve">illud duarum librarum.</s>
            <s xml:id="echoid-s3768" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3769" xml:space="preserve">Moveatur rota Q celerius atque celerius, donec globo-
              <lb/>
            rum vi centrifuga pondera ſtatim memorata eleventur; </s>
            <s xml:id="echoid-s3770" xml:space="preserve">am-
              <lb/>
            bo eodem exactè temporis momento in altum ferentur,
              <lb/>
            quod ex ſtrepitu memorato manifeſtum fit. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">Pondera ergo
              <lb/>
            quæ ſunt ut corpora, cæteris paribus, vi centrifuga ſupe-
              <lb/>
            rantur.</s>
            <s xml:id="echoid-s3772" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3773" xml:space="preserve">Quando quantitates materiæ in corporibus circumrotatis
              <lb/>
              <note position="right" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">363.</note>
            ſunt æquales, & </s>
            <s xml:id="echoid-s3774" xml:space="preserve">tempora periodica æqualia, vires centrales
              <lb/>
            ſunt ut diſtantiæ a centro.</s>
            <s xml:id="echoid-s3775" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div561" type="section" level="1" n="172">
          <head xml:id="echoid-head244" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          5.</head>
          <p>
            <s xml:id="echoid-s3776" xml:space="preserve">Hocce Experimentum eodem modo ac præcedens pera
              <lb/>
              <note position="right" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">364.</note>
            gitur; </s>
            <s xml:id="echoid-s3777" xml:space="preserve">pro globo ſemi-libræ, pyxidi Orbis B globus alteri
              <lb/>
              <note position="right" xlink:label="note-0147-03" xlink:href="note-0147-03a" xml:space="preserve">TAB. XIV.
                <lb/>
              fig. 1.</note>
            æqualis, id eſt, unius libræ, imponitur. </s>
            <s xml:id="echoid-s3778" xml:space="preserve">Diſtantiæ globo-
              <lb/>
            rum a centro ſint in quacunque ratione, ſi pondera cum
              <lb/>
            quibus globi conjunguntur eandem inter ſe habeant propor-
              <lb/>
            tionem, & </s>
            <s xml:id="echoid-s3779" xml:space="preserve">rota Q motu continuo accelerato circumagatur,
              <lb/>
            eodem exacte temporis momento pondera elevantur. </s>
            <s xml:id="echoid-s3780" xml:space="preserve">Sit
              <lb/>
            ex. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3782" xml:space="preserve">diſtantia globi Orbis A partium viginti quatuor, & </s>
            <s xml:id="echoid-s3783" xml:space="preserve">
              <lb/>
            pondus ei annexum unius libræ cum ſemiſſe; </s>
            <s xml:id="echoid-s3784" xml:space="preserve">diſtantia al-
              <lb/>
            terius globi ſedecim partium, & </s>
            <s xml:id="echoid-s3785" xml:space="preserve">pondus annexum unius li-
              <lb/>
            bræ; </s>
            <s xml:id="echoid-s3786" xml:space="preserve">Experimentum procedet.</s>
            <s xml:id="echoid-s3787" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3788" xml:space="preserve">Quando tempora periodica ſunt æqualia, ſed diſtantiæ à
              <lb/>
              <note position="right" xlink:label="note-0147-04" xlink:href="note-0147-04a" xml:space="preserve">365.</note>
            centro & </s>
            <s xml:id="echoid-s3789" xml:space="preserve">quantitates materiæ in corporibus revolutis diffe-
              <lb/>
            runt, vires centrales ſunt in ratione compoſita, quantitatum
              <lb/>
            materiæ, & </s>
            <s xml:id="echoid-s3790" xml:space="preserve">diſtantiarum; </s>
            <s xml:id="echoid-s3791" xml:space="preserve">quod ex duabus ultimis propo-
              <lb/>
            ſitionibus ſequitur. </s>
            <s xml:id="echoid-s3792" xml:space="preserve">Ratio hæc compoſita determinatur, ſi
              <lb/>
            quantitas materiæ in unoquoque corpore per ſuam diſtan-
              <lb/>
            tiam a centro multiplicetur, & </s>
            <s xml:id="echoid-s3793" xml:space="preserve">producta quæſitam inter ſe
              <lb/>
            rationem habent.</s>
            <s xml:id="echoid-s3794" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div564" type="section" level="1" n="173">
          <head xml:id="echoid-head245" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          6.</head>
          <p>
            <s xml:id="echoid-s3795" xml:space="preserve">Si in Experimento ultimo globus Orbi B impoſitus mu-
              <lb/>
              <note position="right" xlink:label="note-0147-05" xlink:href="note-0147-05a" xml:space="preserve">366.</note>
            tetur, & </s>
            <s xml:id="echoid-s3796" xml:space="preserve">globus ſemi-libræ ad eandem diſtantiam partium
              <lb/>
              <note position="right" xlink:label="note-0147-06" xlink:href="note-0147-06a" xml:space="preserve">TAB. XIV.
                <lb/>
              fig. 1.</note>
            ſedecim a centro pyxidi imponatur, mutetur etiam </s>
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