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

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              <pb o="175" file="0251" n="274" rhead="MATHEMATICA. LIB. I. CAP XXVII."/>
            bus maſſis in ſe mutuo, & </s>
            <s xml:id="echoid-s6875" xml:space="preserve">per quadratum velocitatis reſpe-
              <lb/>
            ctivæ barum ipſarum, diviſâ ſummâ bacper ſummam trium
              <lb/>
            maſſarum.</s>
            <s xml:id="echoid-s6876" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6877" xml:space="preserve">Datis corporibus A, B, & </s>
            <s xml:id="echoid-s6878" xml:space="preserve">C; </s>
            <s xml:id="echoid-s6879" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6880" xml:space="preserve">multiplicari debet maſſa
              <lb/>
            A per maſſam B & </s>
            <s xml:id="echoid-s6881" xml:space="preserve">productum hoc per quadratum velocita-
              <lb/>
            tis reſpectivæ A & </s>
            <s xml:id="echoid-s6882" xml:space="preserve">B; </s>
            <s xml:id="echoid-s6883" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6884" xml:space="preserve">productum maſſæ A per maſſam C
              <lb/>
            multiplicandum eſt per quadratum velocitatis reſpectivæ ho-
              <lb/>
            rum corporum; </s>
            <s xml:id="echoid-s6885" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6886" xml:space="preserve">tandem ductis maſſis B & </s>
            <s xml:id="echoid-s6887" xml:space="preserve">C in ſe invi-
              <lb/>
            cem, productum multiplicari debet per quadratum velocita-
              <lb/>
            tis reſpectivæ horum corporum; </s>
            <s xml:id="echoid-s6888" xml:space="preserve">ſumma verò trium horum
              <lb/>
            productorum dividenda eſt per ſummam maſſarum, & </s>
            <s xml:id="echoid-s6889" xml:space="preserve">habe-
              <lb/>
            bimus vim ictu amiſſam.</s>
            <s xml:id="echoid-s6890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6891" xml:space="preserve">Si non fuerint elaſtica tria corpora, de talibus enim agi-
              <lb/>
              <note position="right" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">626</note>
            mus, poſt ictum eadem velocitate feruntur , & </s>
            <s xml:id="echoid-s6892" xml:space="preserve">hæc eſt
              <note symbol="*" position="right" xlink:label="note-0251-02" xlink:href="note-0251-02a" xml:space="preserve">484.</note>
            locitas quam navis haberet, in qua corpora juxta legem in
              <lb/>
            n. </s>
            <s xml:id="echoid-s6893" xml:space="preserve">610. </s>
            <s xml:id="echoid-s6894" xml:space="preserve">indicatam agitata forent; </s>
            <s xml:id="echoid-s6895" xml:space="preserve">quia poſt ictum in nave
              <lb/>
            corpora quieſcerent, translatis ipſis eadem cum nave ve-
              <lb/>
            locitate. </s>
            <s xml:id="echoid-s6896" xml:space="preserve">Navis velocitatem in Scholio 1. </s>
            <s xml:id="echoid-s6897" xml:space="preserve">detegimus, & </s>
            <s xml:id="echoid-s6898" xml:space="preserve">ha-
              <lb/>
            betur, multiplicando ſingulorum corporum maſſas per ſuas
              <lb/>
            velocitates & </s>
            <s xml:id="echoid-s6899" xml:space="preserve">dividendo per ſummam maſſarum ſummam
              <lb/>
            productorum, ſi tria corpora ad eandem partem tendant; </s>
            <s xml:id="echoid-s6900" xml:space="preserve">ſin
              <lb/>
            minus, motuum contrariorum producta à ſe invicem ſub-
              <lb/>
            trabi debent.</s>
            <s xml:id="echoid-s6901" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6902" xml:space="preserve">Videmus quæ ſpectant trium corporum colliſionem, in
              <lb/>
            multis cum iis quæ de duobus corporibus demonſtrata ſunt
              <lb/>
            convenire, quod etiam referri poteſt ad demonſtrata de mu-
              <lb/>
            tationibus velocitatum in ratione inverſa maſſarum . </s>
            <s xml:id="echoid-s6903" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0251-03" xlink:href="note-0251-03a" xml:space="preserve">512.</note>
            ut in Scholio 1. </s>
            <s xml:id="echoid-s6904" xml:space="preserve">demonſtramus; </s>
            <s xml:id="echoid-s6905" xml:space="preserve">Mutationes in velocitatibus
              <lb/>
              <note position="right" xlink:label="note-0251-04" xlink:href="note-0251-04a" xml:space="preserve">627</note>
            duorum corporum, oriundæ ex actione mutua borum corporum
              <lb/>
            in colliſione, ſunt inverſe ut corporum maſſæ, licet & </s>
            <s xml:id="echoid-s6906" xml:space="preserve">aliâ a-
              <lb/>
            ctione eodem tempore unius motus mutetur.</s>
            <s xml:id="echoid-s6907" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6908" xml:space="preserve">Si nunc concipiamus corpora perfectè elaſtica, hæc in
              <lb/>
              <note position="right" xlink:label="note-0251-05" xlink:href="note-0251-05a" xml:space="preserve">628</note>
            nave memoratâ, ſolâ elaſterii actione moventur, & </s>
            <s xml:id="echoid-s6909" xml:space="preserve">à ſe in-
              <lb/>
            vicem recedunt iiſdem celeritatibus, & </s>
            <s xml:id="echoid-s6910" xml:space="preserve">viribus, quibus ad
              <lb/>
            ſe invicem acceſſere; </s>
            <s xml:id="echoid-s6911" xml:space="preserve">in hoc enim caſu ſingula elaſteria,
              <lb/>
            quæ, dum relaxantur, vires generant æquales illis, </s>
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