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

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        <div xml:id="echoid-div993" type="section" level="1" n="245">
          <pb o="184" file="0262" n="286" rhead="PHYSICES ELEMENTA"/>
        </div>
        <div xml:id="echoid-div1002" type="section" level="1" n="246">
          <head xml:id="echoid-head348" xml:space="preserve">SCHOLIUM 3.</head>
          <head xml:id="echoid-head349" xml:space="preserve">Demonſtratio n. 637.</head>
          <p>
            <s xml:id="echoid-s7241" xml:space="preserve">Diximus ſummam virium poſt ictum æqualem eſſe ſummæ virium ante i-
              <lb/>
            ctum in colliſione in n. </s>
            <s xml:id="echoid-s7242" xml:space="preserve">636. </s>
            <s xml:id="echoid-s7243" xml:space="preserve">explicata; </s>
            <s xml:id="echoid-s7244" xml:space="preserve">Poſitâ igitur velocitatum determi-
              <lb/>
              <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">
                <emph style="sc">TAB. XXV.</emph>
                <lb/>
              fig. 6.</note>
            natione ibi traditâ demonſtrandum Corpus C tantum virium acquirere quan-
              <lb/>
            tum amittunt A & </s>
            <s xml:id="echoid-s7245" xml:space="preserve">B.</s>
            <s xml:id="echoid-s7246" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7247" xml:space="preserve">Quadratum lineæ KN æquale eſt quadratis linearum KO & </s>
            <s xml:id="echoid-s7248" xml:space="preserve">ON, aut
              <lb/>
              <note position="left" xlink:label="note-0262-02" xlink:href="note-0262-02a" xml:space="preserve">649.</note>
            KP, & </s>
            <s xml:id="echoid-s7249" xml:space="preserve">bis rectangulo IOK ; </s>
            <s xml:id="echoid-s7250" xml:space="preserve">etiam æquale eſt idem quadratum
              <note symbol="*" position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">12. El. 11.</note>
            KO & </s>
            <s xml:id="echoid-s7251" xml:space="preserve">KP & </s>
            <s xml:id="echoid-s7252" xml:space="preserve">bis rectangulo MPK ; </s>
            <s xml:id="echoid-s7253" xml:space="preserve">unde ſequitur æqualia eſſe rectangula
              <note symbol="*" position="left" xlink:label="note-0262-04" xlink:href="note-0262-04a" xml:space="preserve">12. El. 11.</note>
            & </s>
            <s xml:id="echoid-s7254" xml:space="preserve">quadratum KN valere quadratum KO, & </s>
            <s xml:id="echoid-s7255" xml:space="preserve">rectangulum IOK, ut & </s>
            <s xml:id="echoid-s7256" xml:space="preserve">
              <lb/>
            quadratum KP cum rectangulo MPK; </s>
            <s xml:id="echoid-s7257" xml:space="preserve">ergo quadratum KN æquale eſt
              <lb/>
            rectangulis IKO & </s>
            <s xml:id="echoid-s7258" xml:space="preserve">MKP; </s>
            <s xml:id="echoid-s7259" xml:space="preserve">& </s>
            <s xml:id="echoid-s7260" xml:space="preserve">quadratum K n, duplæ ipſius KN, quod
              <lb/>
            quadruplum eſt quadrati KN, valebit quater ſummam rectangulorum IKO
              <lb/>
            & </s>
            <s xml:id="echoid-s7261" xml:space="preserve">MKP. </s>
            <s xml:id="echoid-s7262" xml:space="preserve">Multiplicatis his per C, habemus vim corporis C, ictu acquiſi-
              <lb/>
            tam, æqualem 4CxKOxKl + 4CxKPxKM .</s>
            <s xml:id="echoid-s7263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7264" xml:space="preserve">Vis, quam ictu amiſit corpus A, habetur multiplicando A per difterenti-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0262-05" xlink:href="note-0262-05a" xml:space="preserve">470.</note>
            am quadratorum KD, K i, velocitatum ante & </s>
            <s xml:id="echoid-s7265" xml:space="preserve">poſt ictum ,
              <note symbol="*" position="left" xlink:label="note-0262-06" xlink:href="note-0262-06a" xml:space="preserve">598.</note>
            autem hæc propter æquales DI, I i, valet quater rectangulum KID ; </s>
            <s xml:id="echoid-s7266" xml:space="preserve">& </s>
            <s xml:id="echoid-s7267" xml:space="preserve">vis
              <note symbol="*" position="left" xlink:label="note-0262-07" xlink:href="note-0262-07a" xml:space="preserve">8. El. 11.</note>
            miſſa eſt 4AxIDxKI: </s>
            <s xml:id="echoid-s7268" xml:space="preserve">Sed in n, 635 vidimus A, C:</s>
            <s xml:id="echoid-s7269" xml:space="preserve">:KO, ID; </s>
            <s xml:id="echoid-s7270" xml:space="preserve">ergo
              <lb/>
            AxID = CxKO, & </s>
            <s xml:id="echoid-s7271" xml:space="preserve">vis quam amittit A eſt 4CxKOxKI.</s>
            <s xml:id="echoid-s7272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7273" xml:space="preserve">Eodem modo demonſtramus vim quam amittit B æqualem eſſe 4CxKP
              <lb/>
            xKM, ideoque ſummam virium amiſſarum valere vim quam C acquiſivit
              <lb/>
            Q. </s>
            <s xml:id="echoid-s7274" xml:space="preserve">D. </s>
            <s xml:id="echoid-s7275" xml:space="preserve">E.</s>
            <s xml:id="echoid-s7276" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7277" xml:space="preserve">Vix differt demonſtratio quando agitur de caſu fig. </s>
            <s xml:id="echoid-s7278" xml:space="preserve">7.</s>
            <s xml:id="echoid-s7279" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1006" type="section" level="1" n="247">
          <head xml:id="echoid-head350" xml:space="preserve">CAPUT XXVIII.</head>
          <head xml:id="echoid-head351" xml:space="preserve">De Motu Centri gravitatis.</head>
          <p>
            <s xml:id="echoid-s7280" xml:space="preserve">IN colliſione corporum, motus reſpectivos, a motibus ab-
              <lb/>
            ſolutis diſtingui, in variis occaſionibus jam notavimus;
              <lb/>
            </s>
            <s xml:id="echoid-s7281" xml:space="preserve">his nunc ulterius addendum, corporum ipſorum motus ab-
              <lb/>
            ſolutos, cum motu abſoluto omnium corporum ſimul conſi-
              <lb/>
            deratorum non debere confundi.</s>
            <s xml:id="echoid-s7282" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1007" type="section" level="1" n="248">
          <head xml:id="echoid-head352" xml:space="preserve">
            <emph style="sc">Definitio.</emph>
          </head>
          <p style="it">
            <s xml:id="echoid-s7283" xml:space="preserve">Motum abſolutum corporum quorumcumque ſimul conſider a-
              <lb/>
              <note position="left" xlink:label="note-0262-08" xlink:href="note-0262-08a" xml:space="preserve">650.</note>
            torum vocamus motum centri gravitatis communis.</s>
            <s xml:id="echoid-s7284" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7285" xml:space="preserve">Ut in ſingulis corporibus de motu dijudicamus ex motu
              <lb/>
            centri gravitatis, & </s>
            <s xml:id="echoid-s7286" xml:space="preserve">hoc ad plura ſimul conſiderata applica-
              <lb/>
            ri poſſe clarum eſt.</s>
            <s xml:id="echoid-s7287" xml:space="preserve"/>
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