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

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          <p>
            <s xml:id="echoid-s5408" xml:space="preserve">
              <pb o="136" file="0202" n="220" rhead="PHYSICES ELEMENTA"/>
            poteſt, ita ut corporis vis minuenda ſit, ſi hujus inertia, id
              <lb/>
            eſt, materiæ quantitas augeatur, ut in utroque
              <note symbol="*" position="left" xlink:label="note-0202-01" xlink:href="note-0202-01a" xml:space="preserve">13.</note>
            æqualiter alii corpori reſiſtat, unde paradoxi explicationem
              <lb/>
            deducimus. </s>
            <s xml:id="echoid-s5409" xml:space="preserve">Nam, ut ex hac obſervatione ſequitur, Quando
              <lb/>
              <note position="left" xlink:label="note-0202-02" xlink:href="note-0202-02a" xml:space="preserve">509.</note>
            duo corpora in ſe mutuo incurrunt, duæ dantur actiones, & </s>
            <s xml:id="echoid-s5410" xml:space="preserve">
              <lb/>
            duæ reactiones, utraque actio ſuæ reactioni æqualis eſt; </s>
            <s xml:id="echoid-s5411" xml:space="preserve">ut
              <lb/>
            corpora quieſcant poſt ictum, non requiritur ut ante ictum
              <lb/>
            vires contrariæ ſint æquales, ſed ut utrumque corpus
              <lb/>
            patiatur reſiſtentiam talem, ut agendo poſſit vim ſuam con-
              <lb/>
            ſumere.</s>
            <s xml:id="echoid-s5412" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5413" xml:space="preserve">Ex demonſtratis facile deducimus quomodo datis corpo-
              <lb/>
              <note position="left" xlink:label="note-0202-03" xlink:href="note-0202-03a" xml:space="preserve">510.</note>
            ribus, & </s>
            <s xml:id="echoid-s5414" xml:space="preserve">horum velocitate reſpectiva, vis ictu deſtructa de-
              <lb/>
            terminetur: </s>
            <s xml:id="echoid-s5415" xml:space="preserve">determinatâ, nempe ſummâ virium, poſitis, eâ-
              <lb/>
            dem velocitate reſpectivâ, motibus contrariis, & </s>
            <s xml:id="echoid-s5416" xml:space="preserve">velocita-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0202-04" xlink:href="note-0202-04a" xml:space="preserve">497. 500.</note>
            tibus in ratione inverſa maſſarum . </s>
            <s xml:id="echoid-s5417" xml:space="preserve">Hanc autem ſummam dari in ſcholio 1. </s>
            <s xml:id="echoid-s5418" xml:space="preserve">ſequenti demonſtramus, Si produ-
              <lb/>
            ctum maſſarum per quadratum velocitatis reſpectivæ multi-
              <lb/>
            plicetur, & </s>
            <s xml:id="echoid-s5419" xml:space="preserve">per ſummam maſſarum dividatur.</s>
            <s xml:id="echoid-s5420" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div775" type="section" level="1" n="203">
          <head xml:id="echoid-head289" xml:space="preserve">
            <emph style="sc">Experimentum</emph>
          7.</head>
          <note position="left" xml:space="preserve">511.</note>
          <p>
            <s xml:id="echoid-s5421" xml:space="preserve">Suſpenſis cylindris E (fig. </s>
            <s xml:id="echoid-s5422" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5423" xml:space="preserve">Tab 18.) </s>
            <s xml:id="echoid-s5424" xml:space="preserve">& </s>
            <s xml:id="echoid-s5425" xml:space="preserve">G, ſæpius memo-
              <lb/>
              <note position="left" xlink:label="note-0202-06" xlink:href="note-0202-06a" xml:space="preserve">
                <emph style="sc">TAB. XXII.</emph>
                <lb/>
              fig. 1.</note>
            rato, redacto hoc ad pondus cylindri D, id eſt ſint maſſæ ut
              <lb/>
            tria ad duo; </s>
            <s xml:id="echoid-s5426" xml:space="preserve">incurrant corpora hæc in ſe mutuo dum am-
              <lb/>
            bo in contrarias partes feruntur, majus velocitate ſeptemde-
              <lb/>
            cim, minus velocitate tria, in quo caſu velocitas reſpe-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0202-07" xlink:href="note-0202-07a" xml:space="preserve">475.</note>
            ctiva eſt viginti . </s>
            <s xml:id="echoid-s5427" xml:space="preserve">Poſt ictum moventur ſimul velocitate novem, id eſt ad nonam uſque diviſionem adſcendunt.</s>
            <s xml:id="echoid-s5428" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5429" xml:space="preserve">Multiplicando maſſas habemus 6. </s>
            <s xml:id="echoid-s5430" xml:space="preserve">Quadratum velocitatis
              <lb/>
            reſpectivæ eſt 400. </s>
            <s xml:id="echoid-s5431" xml:space="preserve">cujus productum per productum maſſa-
              <lb/>
            rum eſt 2400; </s>
            <s xml:id="echoid-s5432" xml:space="preserve">dividendo numerum hunc per 5. </s>
            <s xml:id="echoid-s5433" xml:space="preserve">ſummam
              <lb/>
            maſſarum habemus, vim amiſſam 480. </s>
            <s xml:id="echoid-s5434" xml:space="preserve">Hanc autem bene
              <lb/>
            determinari demonſtramus.</s>
            <s xml:id="echoid-s5435" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5436" xml:space="preserve">Vis corporis majoris ante ictum habetur multiplicando
              <lb/>
            289. </s>
            <s xml:id="echoid-s5437" xml:space="preserve">per 3 , eſt ergo 867. </s>
            <s xml:id="echoid-s5438" xml:space="preserve">Minoris vis habetur
              <note symbol="*" position="left" xlink:label="note-0202-08" xlink:href="note-0202-08a" xml:space="preserve">470.</note>
            cando 9. </s>
            <s xml:id="echoid-s5439" xml:space="preserve">per 2 . </s>
            <s xml:id="echoid-s5440" xml:space="preserve">eſt ideo 18; </s>
            <s xml:id="echoid-s5441" xml:space="preserve">& </s>
            <s xml:id="echoid-s5442" xml:space="preserve">ſumma virium eſt 885.</s>
            <s xml:id="echoid-s5443" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0202-09" xlink:href="note-0202-09a" xml:space="preserve">470.</note>
            Poſt ictum maſſa eſt 5 & </s>
            <s xml:id="echoid-s5444" xml:space="preserve">quadratum velocitatis 81, id circo
              <lb/>
            ſupereſt vis 405, quæ ſi ſubducatur ex 885. </s>
            <s xml:id="echoid-s5445" xml:space="preserve">habemus ut an-
              <lb/>
            te vim amiſſam 480.</s>
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