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

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        <div xml:id="echoid-div1023" type="section" level="1" n="250">
          <head xml:id="echoid-head355" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head356" style="it" xml:space="preserve">Demonſtrationes n. 658. ut & 648.</head>
          <p>
            <s xml:id="echoid-s7381" xml:space="preserve">DIximus in caſu n. </s>
            <s xml:id="echoid-s7382" xml:space="preserve">633. </s>
            <s xml:id="echoid-s7383" xml:space="preserve">quem in n. </s>
            <s xml:id="echoid-s7384" xml:space="preserve">645. </s>
            <s xml:id="echoid-s7385" xml:space="preserve">peculiarius explicavimus
              <note symbol="*" position="left" xlink:label="note-0266-01" xlink:href="note-0266-01a" xml:space="preserve">658.</note>
            motum centri gravitatis non mutari, quod ut demonſtrctur, probandum
              <lb/>
            corpora ita à ſe invicem ſeparari, ut conſideratis ſolis motibus quibus ſepa-
              <lb/>
            rantur, quieſcat centrum gravitatis; </s>
            <s xml:id="echoid-s7386" xml:space="preserve">tunc enim ſi concipiamus corpora ſe-
              <lb/>
            parari in nave, ea velocitate mota qua corpora conjunctim ante ſeparationem
              <lb/>
            moventur, velocitate qua navis fertur commune gravitatis centrum motum
              <lb/>
            continuabit.</s>
            <s xml:id="echoid-s7387" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7388" xml:space="preserve">Poſitis quæ in n. </s>
            <s xml:id="echoid-s7389" xml:space="preserve">645. </s>
            <s xml:id="echoid-s7390" xml:space="preserve">fuere expllcata demonſtrandum A multiplicatum
              <lb/>
              <note position="left" xlink:label="note-0266-02" xlink:href="note-0266-02a" xml:space="preserve">664.</note>
            per velocitatem ibi determinatam quod productum eſt@ f √AB + 2AC\x{0020},
              <lb/>
            valere ſummam productorum corporum B & </s>
            <s xml:id="echoid-s7391" xml:space="preserve">C, ſingulorum multiplicato-
              <lb/>
            rum per velocitates ibi detectas . </s>
            <s xml:id="echoid-s7392" xml:space="preserve">Producta hæc
              <note symbol="*" position="left" xlink:label="note-0266-03" xlink:href="note-0266-03a" xml:space="preserve">654.</note>
            {fB√AB + 2AC\x{0020} - fB√AC + BC + CC\x{0020}/B + C} & </s>
            <s xml:id="echoid-s7393" xml:space="preserve">
              <lb/>
            {fC√AB + 2AC\x{0020} + fB√AC + BC + CC\x{0020}/B + C} quorum ſumma eſt
              <lb/>
            {fB√AB + 2AC\x{0020} + fC√AB + 2AC\x{0020}/B + C}, id eſt f√AB + 2AC\x{0020}.
              <lb/>
            </s>
            <s xml:id="echoid-s7394" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s7395" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7396" xml:space="preserve">Hiſce demonſtratis facile patent, quæ in n. </s>
            <s xml:id="echoid-s7397" xml:space="preserve">648. </s>
            <s xml:id="echoid-s7398" xml:space="preserve">fuere memorata, ſummam
              <lb/>
            virium ante & </s>
            <s xml:id="echoid-s7399" xml:space="preserve">poſt ictum, in motu in n. </s>
            <s xml:id="echoid-s7400" xml:space="preserve">645. </s>
            <s xml:id="echoid-s7401" xml:space="preserve">& </s>
            <s xml:id="echoid-s7402" xml:space="preserve">ſeq. </s>
            <s xml:id="echoid-s7403" xml:space="preserve">memorato eſſe æqualem.
              <lb/>
            </s>
            <s xml:id="echoid-s7404" xml:space="preserve">
              <note position="left" xlink:label="note-0266-04" xlink:href="note-0266-04a" xml:space="preserve">665.</note>
            Vires quibus partes elaſticas inflexas poſuimus, ſunt vires quibus ad centrum
              <lb/>
            commune gravitatis acceſſere corpora , ſervatâ eâdem virium ſummâ à ſe- invicem, uti ex computatione ipſa ſequitur, fuere ſeparata, id eſt, illa ipſa
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0266-05" xlink:href="note-0266-05a" xml:space="preserve">642. 654.</note>
            fuit ſumma virium quibus à centro gravitatis receſſere, cum hujus centri ve-
              <lb/>
            locitas ictu non fuerit mutatâ , unde ſequitur ſummam virium abſoluta- rum etiam eandem eſſe ante & </s>
            <s xml:id="echoid-s7405" xml:space="preserve">poſt ictum .</s>
            <s xml:id="echoid-s7406" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">664.</note>
          <p>
            <s xml:id="echoid-s7407" xml:space="preserve">In n. </s>
            <s xml:id="echoid-s7408" xml:space="preserve">658. </s>
            <s xml:id="echoid-s7409" xml:space="preserve">diximus etiam centrum commune gravitatis corporum in col-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0266-07" xlink:href="note-0266-07a" xml:space="preserve">661</note>
            liſionibus compoſitis in n. </s>
            <s xml:id="echoid-s7410" xml:space="preserve">634. </s>
            <s xml:id="echoid-s7411" xml:space="preserve">636 memoratis, eadem directione & </s>
            <s xml:id="echoid-s7412" xml:space="preserve">veloci-
              <lb/>
              <note position="left" xlink:label="note-0266-08" xlink:href="note-0266-08a" xml:space="preserve">666.</note>
            tate motum poſt corporum concurſum continuare.</s>
            <s xml:id="echoid-s7413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7414" xml:space="preserve">Si concipiamus corpora A & </s>
            <s xml:id="echoid-s7415" xml:space="preserve">B ultra K eadem velocitate, qua anteictum
              <lb/>
            movebantur, motum continuare quieſcente eodem modo corpore C, neque
              <lb/>
              <note position="left" xlink:label="note-0266-09" xlink:href="note-0266-09a" xml:space="preserve">
                <emph style="sc">TA. XXV</emph>
                <lb/>
              fig. 6. 7.</note>
            directio neque velocitas centri gravitatis communis mutata erit; </s>
            <s xml:id="echoid-s7416" xml:space="preserve">conſtabit
              <lb/>
            ergo propoſitum ſi demonſtremus in eodem puncto verſari centrum gravita-
              <lb/>
            tis, poſitis corporibus, C in K, A in D, & </s>
            <s xml:id="echoid-s7417" xml:space="preserve">B in E; </s>
            <s xml:id="echoid-s7418" xml:space="preserve">aut poſitis his, C in N,
              <lb/>
            A in I, & </s>
            <s xml:id="echoid-s7419" xml:space="preserve">B in M; </s>
            <s xml:id="echoid-s7420" xml:space="preserve">aut tandem poſitis, C in n, A in i, & </s>
            <s xml:id="echoid-s7421" xml:space="preserve">B in m. </s>
            <s xml:id="echoid-s7422" xml:space="preserve">Patebit
              <lb/>
            autem in hiſce tribus occaſionibus idem eſſe gravitatis centrum ſi demonſtre-
              <lb/>
            mus hujus diſtantias à lineis KF & </s>
            <s xml:id="echoid-s7423" xml:space="preserve">KG non mutari.</s>
            <s xml:id="echoid-s7424" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7425" xml:space="preserve">Reſpectu lineæ utriusque demonſtratio eadem eſt, quare de KF tantum a-
              <lb/>
            gam.</s>
            <s xml:id="echoid-s7426" xml:space="preserve"/>
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