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

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            <s xml:id="echoid-s6836" xml:space="preserve">
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            porum colliſionem in cap. </s>
            <s xml:id="echoid-s6837" xml:space="preserve">
              <emph style="sc">XXIII.</emph>
            adhibuimus. </s>
            <s xml:id="echoid-s6838" xml:space="preserve">Vbitria dantur
              <lb/>
              <note position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">621.</note>
            corpora duæ dantur velocitates reſpectivæ à quibus pendent
              <lb/>
            actiones corporum in ſe mutuo , & </s>
            <s xml:id="echoid-s6839" xml:space="preserve">partium
              <note symbol="*" position="left" xlink:label="note-0250-02" xlink:href="note-0250-02a" xml:space="preserve">494.</note>
            nes, quæ manentibus corporibus, & </s>
            <s xml:id="echoid-s6840" xml:space="preserve">hiſce duabus velocita-
              <lb/>
            tibus, eadem ſemper eſt, ideoque & </s>
            <s xml:id="echoid-s6841" xml:space="preserve">vis ictu deſtructa . </s>
            <s xml:id="echoid-s6842" xml:space="preserve">
              <note position="left" xlink:label="note-0250-03" xlink:href="note-0250-03a" xml:space="preserve">622</note>
            do corpora poſt ictum quieſcunt ſumma virium eſt, datis ve-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0250-04" xlink:href="note-0250-04a" xml:space="preserve">488.</note>
            locitatibus reſpectivis, omnium minima; </s>
            <s xml:id="echoid-s6843" xml:space="preserve">ſi enim ſumma mi-
              <lb/>
            nor daretur minor vis ictu deſtruetur, quod fieri non pot-
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s6844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6845" xml:space="preserve">Demonſtramus autem in Scholio 1. </s>
            <s xml:id="echoid-s6846" xml:space="preserve">hujus cap. </s>
            <s xml:id="echoid-s6847" xml:space="preserve">vim, datis ve-
              <lb/>
              <note position="left" xlink:label="note-0250-05" xlink:href="note-0250-05a" xml:space="preserve">623</note>
            locitatibus reſpectivis, eſſe omnium minimam, ſi motis duobus
              <lb/>
            corporibus unam partem verſus, aliud in contrariam partem
              <lb/>
            ita feratur, ut bujus maſſæ productum per ſuam velocitatem
              <lb/>
            valeat ſummam productorum maſſarum reliquorum duo-
              <lb/>
            rum, ſingularum multiplicatarum per ſuas velocita-
              <lb/>
            tes.</s>
            <s xml:id="echoid-s6848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6849" xml:space="preserve">In hoc autem caſu corpora poſt ictum quieſcere, & </s>
            <s xml:id="echoid-s6850" xml:space="preserve">ideo
              <lb/>
            ſummam virium eſſe omnium minimam etiam deducimus ex
              <lb/>
            demonſtratis circa colliſionem corporum duorum, ad quam
              <lb/>
            trium corporum colliſionem referimus.</s>
            <s xml:id="echoid-s6851" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6852" xml:space="preserve">Sint corpora tria A, B, C; </s>
            <s xml:id="echoid-s6853" xml:space="preserve">velocitas primi f b; </s>
            <s xml:id="echoid-s6854" xml:space="preserve">ſecundi
              <lb/>
              <note position="left" xlink:label="note-0250-06" xlink:href="note-0250-06a" xml:space="preserve">624</note>
            g i; </s>
            <s xml:id="echoid-s6855" xml:space="preserve">tertii l i. </s>
            <s xml:id="echoid-s6856" xml:space="preserve">Ponimus producta A per f b & </s>
            <s xml:id="echoid-s6857" xml:space="preserve">B per g i,
              <lb/>
              <note position="left" xlink:label="note-0250-07" xlink:href="note-0250-07a" xml:space="preserve">
                <emph style="sc">TAB XXV.</emph>
                <lb/>
              fig. 4.</note>
            ſimul ſumta, valere productum C per l i.</s>
            <s xml:id="echoid-s6858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6859" xml:space="preserve">Concipiamus corpus C in duas partes reſolvi D & </s>
            <s xml:id="echoid-s6860" xml:space="preserve">E ita,
              <lb/>
              <note position="left" xlink:label="note-0250-08" xlink:href="note-0250-08a" xml:space="preserve">
                <emph style="sc">TAB. XXV.</emph>
                <lb/>
              fig. 5.</note>
            ut D per l i valeat A per f b, & </s>
            <s xml:id="echoid-s6861" xml:space="preserve">E per l i æquale ſit B per
              <lb/>
            g i; </s>
            <s xml:id="echoid-s6862" xml:space="preserve">id eſt ſit D ad E, ut A per f b ad B per g i. </s>
            <s xml:id="echoid-s6863" xml:space="preserve">In hoc
              <lb/>
            caſu A ad D, ut l i ad f b, & </s>
            <s xml:id="echoid-s6864" xml:space="preserve">corpora hæc concurrentia poſt
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0250-09" xlink:href="note-0250-09a" xml:space="preserve">500.</note>
            ictum quieſcunt : </s>
            <s xml:id="echoid-s6865" xml:space="preserve">quieſcunt etiam B & </s>
            <s xml:id="echoid-s6866" xml:space="preserve">E ; </s>
            <s xml:id="echoid-s6867" xml:space="preserve">quia B ad
              <note symbol="*" position="left" xlink:label="note-0250-10" xlink:href="note-0250-10a" xml:space="preserve">500.</note>
            ut l i ad g i. </s>
            <s xml:id="echoid-s6868" xml:space="preserve">Hæc autem quatuor corpora à tribus da-
              <lb/>
            tis, memoratis velocitatibus agitatis, non differunt.</s>
            <s xml:id="echoid-s6869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6870" xml:space="preserve">Vis in ictu quocunque amiſſa datis velocitatibus reſpectivis
              <lb/>
            valet ſummam virium in caſu in quo corpora quieſcunt ;</s>
            <s xml:id="echoid-s6871" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0250-11" xlink:href="note-0250-11a" xml:space="preserve">622.</note>
            hæc autem ſumma ſolis datis velocitatibus reſpectivis exprimi
              <lb/>
            poteſt &</s>
            <s xml:id="echoid-s6872" xml:space="preserve">, ut in Scholio 1. </s>
            <s xml:id="echoid-s6873" xml:space="preserve">demonſtramus. </s>
            <s xml:id="echoid-s6874" xml:space="preserve">In omni concurſu
              <lb/>
              <note position="left" xlink:label="note-0250-12" xlink:href="note-0250-12a" xml:space="preserve">625.</note>
            directo trium corporum, vis amiſſa proportionem ſequitur
              <lb/>
            ſummætrium productorum, quæ formantur multiplicatis </s>
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