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

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          <pb o="163" file="0235" n="256" rhead="MATHEMATICA. LIB. I. CAP. XXIV."/>
        </div>
        <div xml:id="echoid-div920" type="section" level="1" n="234">
          <head xml:id="echoid-head328" xml:space="preserve">SCHOLIUM 3.</head>
          <head xml:id="echoid-head329" style="it" xml:space="preserve">Paradoxi explicatio.</head>
          <p>
            <s xml:id="echoid-s6476" xml:space="preserve">Ex corporum elafticorum proprietate in n. </s>
            <s xml:id="echoid-s6477" xml:space="preserve">584. </s>
            <s xml:id="echoid-s6478" xml:space="preserve">memorata deducitur para-
              <lb/>
              <note position="right" xlink:label="note-0235-01" xlink:href="note-0235-01a" xml:space="preserve">597.</note>
            doxi, quod non minus notabile eſt quàm vulgare, explicatio.</s>
            <s xml:id="echoid-s6479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6480" xml:space="preserve">Fabri argentarii, qui domus cujuſcunque partem ſuperiorem occupant,
              <lb/>
            incudem pulvino ſuperimponunt, quo magis ictibus mallei incus reſiſtit, & </s>
            <s xml:id="echoid-s6481" xml:space="preserve">
              <lb/>
            minus tremit domus.</s>
            <s xml:id="echoid-s6482" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6483" xml:space="preserve">Ponamus, ſublato pulvino, trabi incudem imponi, incus corpus eſt elaſti-
              <lb/>
            cum, & </s>
            <s xml:id="echoid-s6484" xml:space="preserve">trabs, quæ in extremitatibus fixa eſt, etiam corpus eſt elaſticum.
              <lb/>
            </s>
            <s xml:id="echoid-s6485" xml:space="preserve">Ponamus malleo incudem percuti.</s>
            <s xml:id="echoid-s6486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6487" xml:space="preserve">Dicatur mallei maſſa M; </s>
            <s xml:id="echoid-s6488" xml:space="preserve">incudis maſſa I; </s>
            <s xml:id="echoid-s6489" xml:space="preserve">& </s>
            <s xml:id="echoid-s6490" xml:space="preserve">maſſa trabis cum corporibus
              <lb/>
            cohærentibus & </s>
            <s xml:id="echoid-s6491" xml:space="preserve">quæ cum ipſa agitantur T; </s>
            <s xml:id="echoid-s6492" xml:space="preserve">ſit etiam velocitas mallei v.
              <lb/>
            </s>
            <s xml:id="echoid-s6493" xml:space="preserve">Multiplicando M per v, & </s>
            <s xml:id="echoid-s6494" xml:space="preserve">dividendo productum per ſummam Maſſarum
              <lb/>
            mallei & </s>
            <s xml:id="echoid-s6495" xml:space="preserve">incudis & </s>
            <s xml:id="echoid-s6496" xml:space="preserve">habemus dimidium velocitatis incudi communicatæ
              <note symbol="*" position="right" xlink:label="note-0235-02" xlink:href="note-0235-02a" xml:space="preserve">519 567.</note>
            nam licet trabi impoſita ſit incus agitatur quaſi ſola eſſet , & </s>
            <s xml:id="echoid-s6497" xml:space="preserve">ipſius
              <note symbol="*" position="right" xlink:label="note-0235-03" xlink:href="note-0235-03a" xml:space="preserve">585.</note>
            eſt {2Mxv/M + I}, qua velocitate incus percutit trabem & </s>
            <s xml:id="echoid-s6498" xml:space="preserve">corpora cum hac conjun-
              <lb/>
            cta; </s>
            <s xml:id="echoid-s6499" xml:space="preserve">multiplicando velocitatem incudis per maſſam habemus {2MxIxv/M + I} divi-
              <lb/>
            dendo duplum hujus producti per ſummam maſſarum habemus {4MxIxv/M + Ix1 + T}
              <lb/>
            trabis velocitatem . </s>
            <s xml:id="echoid-s6500" xml:space="preserve">Denominator hujus fractionis MxI + IxI +
              <note symbol="*" position="right" xlink:label="note-0235-04" xlink:href="note-0235-04a" xml:space="preserve">519. 585.</note>
            + TxI, propter M exiguum reſpectu 1 & </s>
            <s xml:id="echoid-s6501" xml:space="preserve">T, vix ab hoc alio differt M x I
              <lb/>
            + IxI + TxI, quo poſito, velocitas detecta mutatur in hanc {4Mxv/M + I + T}.</s>
            <s xml:id="echoid-s6502" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6503" xml:space="preserve">Interpoſito corpore molli, pulvino nempe, inter trabem & </s>
            <s xml:id="echoid-s6504" xml:space="preserve">incudem, cor-
              <lb/>
            pora hæc unicam quaſi formant maſſam, ideoque cum nunc malleus majus
              <lb/>
            percutiat corpus majorem patitur refiſtentiam, & </s>
            <s xml:id="echoid-s6505" xml:space="preserve">velocitas trabi communicata
              <lb/>
            habetur dividendo 2 Mxv per ſummam maſſarum M + I + T , & </s>
            <s xml:id="echoid-s6506" xml:space="preserve">velocitas
              <note symbol="*" position="right" xlink:label="note-0235-05" xlink:href="note-0235-05a" xml:space="preserve">519. 567.</note>
            {2Mxv/M + I + T} dimidium velocitatis ſublato pulvino; </s>
            <s xml:id="echoid-s6507" xml:space="preserve">& </s>
            <s xml:id="echoid-s6508" xml:space="preserve">agitatio, ſublato hoc i-
              <lb/>
            pſo, quadruplum poteſt edere effectum .</s>
            <s xml:id="echoid-s6509" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">447. 459.</note>
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