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

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        <div xml:id="echoid-div462" type="section" level="1" n="153">
          <pb o="71" file="0121" n="131" rhead="MATHEMATICA. LIB. I. CAP. XIX."/>
          <p>
            <s xml:id="echoid-s2953" xml:space="preserve">Dentur duo pendula, CP, cp, quorum longitudines ſint in-
              <lb/>
              <note position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">300.</note>
            terſe, ut vires gravitatis quibus agitantur; </s>
            <s xml:id="echoid-s2954" xml:space="preserve">ſi arcus ſimiles
              <lb/>
              <note position="right" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">TAB. XII.
                <lb/>
              fig. 2.</note>
            excurrant, in punctis reſpondentibus gravitates eandem ſem-
              <lb/>
            per habebunt rationem inter ſe, propter inclinationes æ-
              <lb/>
            quales, & </s>
            <s xml:id="echoid-s2955" xml:space="preserve">quidem rationem arcuum percurrendorum, (quia
              <lb/>
            arcus ſimiles ſunt ut pendulorum longitudines) qui ergo æ-
              <lb/>
            qualibus temporibus percurrentur , id eſt, vibr ationes
              <note symbol="*" position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">94</note>
            runt æ æquè diuturnæ.</s>
            <s xml:id="echoid-s2956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2957" xml:space="preserve">Si ad eandem longitudinem reducantur mutato pendulo
              <lb/>
            c p cujus longitudo fiat cq, æqualis CP; </s>
            <s xml:id="echoid-s2958" xml:space="preserve">quadratum dura-
              <lb/>
            tionis vibrationis penduli cq eſt ad quadratum durationisvi-
              <lb/>
            brationis penduli cp, aut CP, ut longitudo cq, aut CP,
              <lb/>
            ad cp ; </s>
            <s xml:id="echoid-s2959" xml:space="preserve">id eſt ut gravitas quæ in pendulum CP agit
              <note symbol="*" position="right" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">290.</note>
            gravitatem quæ pendulum cq agitat. </s>
            <s xml:id="echoid-s2960" xml:space="preserve">Id circo ſunt qua-
              <lb/>
              <note position="right" xlink:label="note-0121-05" xlink:href="note-0121-05a" xml:space="preserve">301.</note>
            drata durationum vibrationum pendulorum æqualium, inver-
              <lb/>
            sè ut gravitates in pendula agentes. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">Et in genere quadrata
              <lb/>
              <note position="right" xlink:label="note-0121-06" xlink:href="note-0121-06a" xml:space="preserve">302.</note>
            durationum vibrationum ſunt directè ut pendulorum longi-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0121-07" xlink:href="note-0121-07a" xml:space="preserve">290.</note>
            tudines , & </s>
            <s xml:id="echoid-s2962" xml:space="preserve">inversè ut gravitates quibus moventur ,
              <note position="right" xlink:label="note-0121-08" xlink:href="note-0121-08a" xml:space="preserve">303.</note>
            iam gravitates hæ ſunt directè ut longitudines , & </s>
            <s xml:id="echoid-s2963" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0121-09" xlink:href="note-0121-09a" xml:space="preserve">301.
                <lb/>
              * 300.</note>
            ut quadrata durationum vibrationum .</s>
            <s xml:id="echoid-s2964" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">302.</note>
        </div>
        <div xml:id="echoid-div468" type="section" level="1" n="154">
          <head xml:id="echoid-head220" xml:space="preserve">SCHOLIUM I.</head>
          <head xml:id="echoid-head221" style="it" xml:space="preserve">De motu in Cycloide.</head>
          <p>
            <s xml:id="echoid-s2965" xml:space="preserve">Concipiamus portionem cycloïdis aut integram cycloïdem, in linea recta
              <lb/>
            extendi ABD, & </s>
            <s xml:id="echoid-s2966" xml:space="preserve">corpus in hac linea recta moveri juxta legem penduli o-
              <lb/>
              <note position="right" xlink:label="note-0121-11" xlink:href="note-0121-11a" xml:space="preserve">304.</note>
              <note position="right" xlink:label="note-0121-12" xlink:href="note-0121-12a" xml:space="preserve">TAB. XI.
                <lb/>
              fig. 7.</note>
            ſcillati in cycloïde, id eſt dari preſſionem in corpusagentem, quæ ſequatur ratio-
              <lb/>
            nem diſtantiæ corporis a puncto medioB, & </s>
            <s xml:id="echoid-s2967" xml:space="preserve">quæ in corpus motum agat ut in cor-
              <lb/>
            pus quieſcens; </s>
            <s xml:id="echoid-s2968" xml:space="preserve">centro B, radio BA, deſcribatur Semicirculus ALD, quitempus
              <lb/>
            repræſentat, in quo corpus movetur ab A ad D; </s>
            <s xml:id="echoid-s2969" xml:space="preserve">tempora in quibus portiones
              <lb/>
            quæcunque lineæ AD deſcribuntur, erectis ad hanc perpendicularibus, de-
              <lb/>
            terminantur, arcus HI tempus in quo FG, & </s>
            <s xml:id="echoid-s2970" xml:space="preserve">arcus AH tempus in quo AF
              <lb/>
            percurruntur, deſignant: </s>
            <s xml:id="echoid-s2971" xml:space="preserve">celeritates autem in punctis F & </s>
            <s xml:id="echoid-s2972" xml:space="preserve">G proportionales
              <lb/>
            ſunt ipſis perpendicularibus FH, GI.</s>
            <s xml:id="echoid-s2973" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2974" xml:space="preserve">Quæ ut demonſtrentur, concipiendum eſt corpus, quod in linea AD mo-
              <lb/>
              <note position="right" xlink:label="note-0121-13" xlink:href="note-0121-13a" xml:space="preserve">305.</note>
            vetur ita, ut temporibus, quæ ſunt ut arcus AH, HI, percurrat portiones
              <lb/>
            AF, FG, & </s>
            <s xml:id="echoid-s2975" xml:space="preserve">ſic de cæteris: </s>
            <s xml:id="echoid-s2976" xml:space="preserve">ita ut totum tempus repræſentetur per ſemicircu-
              <lb/>
            lum ALD. </s>
            <s xml:id="echoid-s2977" xml:space="preserve">Concipiamus ulterius ſemicirculum in partes minimas æqua-
              <lb/>
            les diviſum, momenta minima æqualia temporis deſignantes, quales ſunt
              <lb/>
            H b & </s>
            <s xml:id="echoid-s2978" xml:space="preserve">I i. </s>
            <s xml:id="echoid-s2979" xml:space="preserve">Id circo poſitis fh & </s>
            <s xml:id="echoid-s2980" xml:space="preserve">g i etiam perpendicularibus lineæ AD, tem-
              <lb/>
            poribus æqualibus lineæ F f & </s>
            <s xml:id="echoid-s2981" xml:space="preserve">G g percurruntur, quæ cum exiguæ ſunt </s>
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