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">
          <pb o="189" file="0267" n="291" rhead="MATHEMATICA. LIB. I. CAP. XXVIII."/>
          <p>
            <s xml:id="echoid-s7427" xml:space="preserve">Diſtantia puncti N ab hac linea eſt NM; </s>
            <s xml:id="echoid-s7428" xml:space="preserve">puncti n eſt 2NM; </s>
            <s xml:id="echoid-s7429" xml:space="preserve">puncto-
              <lb/>
            rum D, I, & </s>
            <s xml:id="echoid-s7430" xml:space="preserve">i diſtantiæ ab cadem KF deteguntur hiſce proportionibus
              <lb/>
            PN, NM:</s>
            <s xml:id="echoid-s7431" xml:space="preserve">: { KD, {NM x KD/PN} \\ KI, {NM x KI/PN} \\ Ki, {NM x Ki/PN}
              <lb/>
            Quibus detectis, diſtantiæ centri gravitatis communis corporum, à memo-
              <lb/>
            ratâ lineâ KF, in tribus memoratis corporum diſpoſitionibus, deteguntur
              <lb/>
            {NM x KD x A/PN x A + B + C}, {NM x C/A + B + C} + {NM x KI x A/PN x A + B + C}, & </s>
            <s xml:id="echoid-s7432" xml:space="preserve">{2 NM x C/A + B + C}
              <lb/>
            + {NM x Ki + A/PN x A + B + C} quas æquales demonſtramus.</s>
            <s xml:id="echoid-s7433" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0267-01" xlink:href="note-0267-01a" xml:space="preserve">159.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s7434" xml:space="preserve">Ex conſtructione ſequitur PN ſe habere ad NQ, & </s>
            <s xml:id="echoid-s7435" xml:space="preserve">etiam 2 PN ad
              <lb/>
            2 NQ, ut A ad C; </s>
            <s xml:id="echoid-s7436" xml:space="preserve">NQ æqualis eſt ID, & </s>
            <s xml:id="echoid-s7437" xml:space="preserve">valet KD-KI ergo PN x C
              <lb/>
            = KD x A - KI x A, & </s>
            <s xml:id="echoid-s7438" xml:space="preserve">PN x C + KI x A = KD x A.</s>
            <s xml:id="echoid-s7439" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7440" xml:space="preserve">Eodem modo 2NQ valet 2ID, id eſt iD, & </s>
            <s xml:id="echoid-s7441" xml:space="preserve">æqualis eſt KD - Ki;
              <lb/>
            </s>
            <s xml:id="echoid-s7442" xml:space="preserve">unde deducimus 2PN x C + Ki x A = KD x A.</s>
            <s xml:id="echoid-s7443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7444" xml:space="preserve">Multiplicatis hiſce tribus quantitatibus æqualibus KD x A, PN x C +
              <lb/>
            KI x A, & </s>
            <s xml:id="echoid-s7445" xml:space="preserve">2PN x C + Ki x A, per NM & </s>
            <s xml:id="echoid-s7446" xml:space="preserve">diviſis productis per
              <lb/>
            PN x
              <emph style="ol">A + B + C</emph>
            , habebimus quotientes æquales, à diſtantiis detectis non di-
              <lb/>
            verſos. </s>
            <s xml:id="echoid-s7447" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s7448" xml:space="preserve">D. </s>
            <s xml:id="echoid-s7449" xml:space="preserve">E.</s>
            <s xml:id="echoid-s7450" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1030" type="section" level="1" n="251">
          <head xml:id="echoid-head357" xml:space="preserve">SCHOLIUM 3.</head>
          <p>
            <s xml:id="echoid-s7451" xml:space="preserve">SI demonſtratam in hoc capite propoſitionem, ante & </s>
            <s xml:id="echoid-s7452" xml:space="preserve">poſt colliſionem
              <lb/>
              <note position="right" xlink:label="note-0267-02" xlink:href="note-0267-02a" xml:space="preserve">667.</note>
            centrum gravitatis eâdem velocitate ferri, applicemus ad colliſionem in n.
              <lb/>
            </s>
            <s xml:id="echoid-s7453" xml:space="preserve">521. </s>
            <s xml:id="echoid-s7454" xml:space="preserve">memoratam, corporum poſt colliſionem velocitates determinare poſſu-
              <lb/>
            mus.</s>
            <s xml:id="echoid-s7455" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7456" xml:space="preserve">Tria corpora poſt ictum, juxta directionem primi motus feruntur veloci-
              <lb/>
            tate, qua ante ictum centrum gravitatis fertur ; </s>
            <s xml:id="echoid-s7457" xml:space="preserve">nam nulla datur actio
              <note symbol="*" position="right" xlink:label="note-0267-03" xlink:href="note-0267-03a" xml:space="preserve">652.</note>
            directe ſeparari poſſint; </s>
            <s xml:id="echoid-s7458" xml:space="preserve">velocitas hæc detegitur regulâ in n. </s>
            <s xml:id="echoid-s7459" xml:space="preserve">519. </s>
            <s xml:id="echoid-s7460" xml:space="preserve">traditâ.
              <lb/>
            </s>
            <s xml:id="echoid-s7461" xml:space="preserve">itaque moventur ut corpora mollia poſt impactionem directam, ſed quæ in
              <lb/>
            hac corporum mollium impactione deſtruitur, corpora impingentia vim ſer-
              <lb/>
            vant in caſu quem examinamus; </s>
            <s xml:id="echoid-s7462" xml:space="preserve">& </s>
            <s xml:id="echoid-s7463" xml:space="preserve">hac idcirco lateraliter feruntur quæ
              <note symbol="*" position="right" xlink:label="note-0267-04" xlink:href="note-0267-04a" xml:space="preserve">601.</note>
            datur quare lateralis velocitas, quæ nempe cum prima directione
              <note symbol="*" position="right" xlink:label="note-0267-05" xlink:href="note-0267-05a" xml:space="preserve">510. 525.</note>
            cit rectum, detegi poteſt: </s>
            <s xml:id="echoid-s7464" xml:space="preserve">ideoque directiones & </s>
            <s xml:id="echoid-s7465" xml:space="preserve">velocitates abſolutas qui-
              <lb/>
            bus corpora impingentia poſt ictum moventur facile determinantur.</s>
            <s xml:id="echoid-s7466" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7467" xml:space="preserve">Dicatur Q maſſa corporis quieſcentis; </s>
            <s xml:id="echoid-s7468" xml:space="preserve">ſint aliorum maſſæ P, P; </s>
            <s xml:id="echoid-s7469" xml:space="preserve">& </s>
            <s xml:id="echoid-s7470" xml:space="preserve">horum
              <lb/>
              <note position="right" xlink:label="note-0267-06" xlink:href="note-0267-06a" xml:space="preserve">
                <emph style="sc">TAB XXI.</emph>
                <lb/>
              fig. 4</note>
            volocitas v.</s>
            <s xml:id="echoid-s7471" xml:space="preserve"/>
          </p>
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