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

Table of figures

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        <div xml:id="echoid-div446" type="section" level="1" n="150">
          <p>
            <s xml:id="echoid-s2883" xml:space="preserve">
              <pb o="69" file="0119" n="129" rhead="MATHEMATICA. LIB. I. CAP. XIX."/>
            quam per chordas vibratur corpus.</s>
            <s xml:id="echoid-s2884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2885" xml:space="preserve">Durationes vibrationum pendulorum inæqualium poſſunt
              <lb/>
              <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">290.</note>
            inter ſe comparari. </s>
            <s xml:id="echoid-s2886" xml:space="preserve">Quando arcus ſunt ſimiles, deviationes re-
              <lb/>
            ſpectu chordarum ſunt etiam ſimiles & </s>
            <s xml:id="echoid-s2887" xml:space="preserve">tempora vibrationum
              <lb/>
            per arcus ſunt ut tempora vibrationum per chordas; </s>
            <s xml:id="echoid-s2888" xml:space="preserve">hæc vero
              <lb/>
            ut tempora deſcenſus per longitudines octuplas longitudinum
              <lb/>
            pendulorum ; </s>
            <s xml:id="echoid-s2889" xml:space="preserve">& </s>
            <s xml:id="echoid-s2890" xml:space="preserve">ſic quadrata durationum ſunt ut iſtæ
              <note symbol="*" position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">279.</note>
            gitudines octuplæ ; </s>
            <s xml:id="echoid-s2891" xml:space="preserve">ſive ut ipſæ longitudines pendulorum.</s>
            <s xml:id="echoid-s2892" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">225.</note>
        </div>
        <div xml:id="echoid-div454" type="section" level="1" n="151">
          <head xml:id="echoid-head217" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          2.</head>
          <p>
            <s xml:id="echoid-s2893" xml:space="preserve">Duo pendula CP, cp, quorum longitudines ſunt ut 4.
              <lb/>
            </s>
            <s xml:id="echoid-s2894" xml:space="preserve">
              <note position="right" xlink:label="note-0119-04" xlink:href="note-0119-04a" xml:space="preserve">291.</note>
            ad 1.</s>
            <s xml:id="echoid-s2895" xml:space="preserve">, eodem tempore dimittuntur a punctis P & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">p, ita ut
              <lb/>
              <note position="right" xlink:label="note-0119-05" xlink:href="note-0119-05a" xml:space="preserve">TAB XI.
                <lb/>
              fig. 5.</note>
            vibrationbius arcus ſimiles deſcribant; </s>
            <s xml:id="echoid-s2897" xml:space="preserve">pendulum majus ſe-
              <lb/>
            mel vibratur, dum minus duas peragit vibrationes; </s>
            <s xml:id="echoid-s2898" xml:space="preserve">& </s>
            <s xml:id="echoid-s2899" xml:space="preserve">ita
              <lb/>
            quadrata durationum vibrationum ſunt ut 4. </s>
            <s xml:id="echoid-s2900" xml:space="preserve">ad 1.</s>
            <s xml:id="echoid-s2901" xml:space="preserve">, nem-
              <lb/>
            pe ut longitudines pendulorum.</s>
            <s xml:id="echoid-s2902" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2903" xml:space="preserve">Quando vibrationes ſunt exiguæ, hæc ratio etiam locum
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            habet, licèt pendula non vibrentur per arcus ſimiles .</s>
            <s xml:id="echoid-s2904" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">280.</note>
          <p>
            <s xml:id="echoid-s2905" xml:space="preserve">Velocitates pendulorum in puncto infimo, in vibrationibus
              <lb/>
              <note position="right" xlink:label="note-0119-07" xlink:href="note-0119-07a" xml:space="preserve">292.</note>
            inæqualibus, ſunt inter ſe, ut ſubtenſæ arcuum, quos corpus
              <lb/>
            deſcendendo deſcribit. </s>
            <s xml:id="echoid-s2906" xml:space="preserve">Sic velocitas corporis P, cadentis per
              <lb/>
              <note position="right" xlink:label="note-0119-08" xlink:href="note-0119-08a" xml:space="preserve">TAB. XI.
                <lb/>
              fig. 2.</note>
            arcum PB, eſt ad ejus velocitatem quando cadit per DB,
              <lb/>
            ut chorda PB ad chordam DB. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">Nam ductis lineis hori-
              <lb/>
              <note position="right" xlink:label="note-0119-09" xlink:href="note-0119-09a" xml:space="preserve">293.</note>
            zonti parallelis P f, D d & </s>
            <s xml:id="echoid-s2908" xml:space="preserve">junctis P & </s>
            <s xml:id="echoid-s2909" xml:space="preserve">A, triangula P f B,
              <lb/>
            BPA ſunt ſimilia : </s>
            <s xml:id="echoid-s2910" xml:space="preserve">idèo B f, BP, BA ſunt in
              <note symbol="*" position="right" xlink:label="note-0119-10" xlink:href="note-0119-10a" xml:space="preserve">31-El. III.
                <lb/>
              8: El. VI.</note>
            tinuâ proportione, & </s>
            <s xml:id="echoid-s2911" xml:space="preserve">quadratum chordæ BP valet produ-
              <lb/>
            ctum diametri per B f: </s>
            <s xml:id="echoid-s2912" xml:space="preserve">eodem modo quadratum chordæ
              <lb/>
            B d æquale eſt producto diametri per BD: </s>
            <s xml:id="echoid-s2913" xml:space="preserve">ergo quadrata
              <lb/>
            chordarum ſunt inter ſe ut producta hæc, quæ ſunt ut li-
              <lb/>
            neæ f B, dB. </s>
            <s xml:id="echoid-s2914" xml:space="preserve">Quadrata prædictarum velocitatum ſunt et-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0119-11" xlink:href="note-0119-11a" xml:space="preserve">271. 255.
                <lb/>
              253.</note>
            iâm ut iſtæ lineæ f B, d B ; </s>
            <s xml:id="echoid-s2915" xml:space="preserve">ergo velocitates ut chordæ.</s>
            <s xml:id="echoid-s2916" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2917" xml:space="preserve">Circa omnia, quæ hucuſque dependulis dicta ſunt, non in-
              <lb/>
            tereſt quantum ponderet corpus quod agitatur, aut an corpora
              <lb/>
              <note position="right" xlink:label="note-0119-12" xlink:href="note-0119-12a" xml:space="preserve">294.</note>
            diver ſorum pendulorum inæqualiter ponderent, aut ex diverſa
              <lb/>
            dentur materiæ. </s>
            <s xml:id="echoid-s2918" xml:space="preserve">Cùm vis gravitatis proportionalis ſit quan-
              <lb/>
            titati materiæ in omnibus corporibus , omnia corpora,
              <note symbol="*" position="right" xlink:label="note-0119-13" xlink:href="note-0119-13a" xml:space="preserve">121.</note>
            iiſdem circumſtantiis, gravitate æque celeriter moventur.</s>
            <s xml:id="echoid-s2919" xml:space="preserve"/>
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