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

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          <pb o="143" file="0211" n="230" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/>
        </div>
        <div xml:id="echoid-div810" type="section" level="1" n="211">
          <head xml:id="echoid-head298" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head299" xml:space="preserve">De percuſſione corporum lineis rigidis inter ſe cohæ-
            <lb/>
          rentium, & circa centra agitatorum.</head>
          <p style="it">
            <s xml:id="echoid-s5650" xml:space="preserve">Sint corpora A & </s>
            <s xml:id="echoid-s5651" xml:space="preserve">C, lineâ inflexili conjuncta, & </s>
            <s xml:id="echoid-s5652" xml:space="preserve">circa centrum H agitata; </s>
            <s xml:id="echoid-s5653" xml:space="preserve">fint
              <lb/>
              <note position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">531.</note>
            etiam corpora alia B & </s>
            <s xml:id="echoid-s5654" xml:space="preserve">D eodem modo juncta & </s>
            <s xml:id="echoid-s5655" xml:space="preserve">circa I agitata.</s>
            <s xml:id="echoid-s5656" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <emph style="sc">TAB. XX.</emph>
            <lb/>
          fig. 3.</note>
          <p>
            <s xml:id="echoid-s5657" xml:space="preserve">Ponamus darihorum corporum percuſſionem directam, quod obtinebit ſi in ſemu-
              <lb/>
            tuo impingant, unum ex corporibus adhærentibus uni lineæ, cum corpore quo-
              <lb/>
            cunque ex illis quæ cum alia cohærent lineâ, ut A & </s>
            <s xml:id="echoid-s5658" xml:space="preserve">B. </s>
            <s xml:id="echoid-s5659" xml:space="preserve">Impactio erit di-
              <lb/>
            recta ſi hæc corpora directè in ſe mutuo incurrant, quod fieri non poterit
              <lb/>
            niſi in momento incurſus lineæ quibus corpora cohærent ſint parallelæ in-
              <lb/>
            ter ſe.</s>
            <s xml:id="echoid-s5660" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5661" xml:space="preserve">Si in momento incurſus in quo in eâdem lineâ ambo moventur corpora,
              <lb/>
            motu quodam communi ferantur non hoc motu in ſe mutuo agent; </s>
            <s xml:id="echoid-s5662" xml:space="preserve">impactio
              <lb/>
            ergo pendebit â velocitate reſpectivâ, qua manente eadem datur partium intro-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0211-03" xlink:href="note-0211-03a" xml:space="preserve">495.</note>
            ceſſio , & </s>
            <s xml:id="echoid-s5663" xml:space="preserve">eadem vis amiſſa , quibuſcunque velocitatibus corpora
              <note symbol="*" position="right" xlink:label="note-0211-04" xlink:href="note-0211-04a" xml:space="preserve">497</note>
            tentur.</s>
            <s xml:id="echoid-s5664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5665" xml:space="preserve">Dari caſum in quo corpora in partes contrarias lata, poſtictum quieſcunt faci-
              <lb/>
              <note position="right" xlink:label="note-0211-05" xlink:href="note-0211-05a" xml:space="preserve">532.</note>
            le patet; </s>
            <s xml:id="echoid-s5666" xml:space="preserve">& </s>
            <s xml:id="echoid-s5667" xml:space="preserve">in hoc caſu, datâ velocitate reſpectivâ, ſummam virium eſſeomnium
              <lb/>
            minimam etiam liquet, tota enim vis deſtruitur & </s>
            <s xml:id="echoid-s5668" xml:space="preserve">minor quantitas nunquam
              <lb/>
            poteſt deſtrui ; </s>
            <s xml:id="echoid-s5669" xml:space="preserve">quænam autem ſit ratio velocitatum in hoc caſu
              <note symbol="*" position="right" xlink:label="note-0211-06" xlink:href="note-0211-06a" xml:space="preserve">531.</note>
            cam.</s>
            <s xml:id="echoid-s5670" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5671" xml:space="preserve">Sit a diſtantia corporis A â centro H, circa quod rotatur, & </s>
            <s xml:id="echoid-s5672" xml:space="preserve">c diſtantia
              <lb/>
            corporis C ab eodem centro. </s>
            <s xml:id="echoid-s5673" xml:space="preserve">Eodem modo ſit b diſtantia corporis B, & </s>
            <s xml:id="echoid-s5674" xml:space="preserve">c
              <lb/>
            diſtantia corporis D, â centro I, circa quod hæc corpora agitantur. </s>
            <s xml:id="echoid-s5675" xml:space="preserve">Sit ulte-
              <lb/>
            rius m velocitas corporis A; </s>
            <s xml:id="echoid-s5676" xml:space="preserve">& </s>
            <s xml:id="echoid-s5677" xml:space="preserve">n velocitas corporis B.</s>
            <s xml:id="echoid-s5678" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5679" xml:space="preserve">In caſu in quo corpora poſt ictum quieſcunt demonſtramus, poſitis motibus con-
              <lb/>
              <note position="right" xlink:label="note-0211-07" xlink:href="note-0211-07a" xml:space="preserve">533.</note>
            trariis m, n:</s>
            <s xml:id="echoid-s5680" xml:space="preserve">:Bbb + Dddxaa, Aaa + Cccxbb. </s>
            <s xml:id="echoid-s5681" xml:space="preserve">id eſt, Aaa + Cccx
              <lb/>
            bbm = Bbb + Dddxaan.</s>
            <s xml:id="echoid-s5682" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5683" xml:space="preserve">In hoc enim caſu ſumma virium, manente velocitate reſpectivâ m + n, eſt o-
              <lb/>
              <note position="right" xlink:label="note-0211-08" xlink:href="note-0211-08a" xml:space="preserve">534.</note>
            mnium minima.</s>
            <s xml:id="echoid-s5684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5685" xml:space="preserve">Summa virium eſt Amm + {Cccmm/aa} + Bnn + {Dddnn/bb} ; </s>
            <s xml:id="echoid-s5686" xml:space="preserve">nam a, c:</s>
            <s xml:id="echoid-s5687" xml:space="preserve">
              <note position="right" xlink:label="note-0211-09" xlink:href="note-0211-09a" xml:space="preserve">535.</note>
            {mc/a} = velocitati corporis C; </s>
            <s xml:id="echoid-s5688" xml:space="preserve">& </s>
            <s xml:id="echoid-s5689" xml:space="preserve">b, d, :</s>
            <s xml:id="echoid-s5690" xml:space="preserve">:n, {dn/b} = velocitati corporis D.</s>
            <s xml:id="echoid-s5691" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">470.</note>
          <p>
            <s xml:id="echoid-s5692" xml:space="preserve">Ponamus nunc velocitatem m augeri quantitate e, & </s>
            <s xml:id="echoid-s5693" xml:space="preserve">eadern quantitate mi-
              <lb/>
            nui velocitatem n, ut velocitas reſpectiva maneat; </s>
            <s xml:id="echoid-s5694" xml:space="preserve">videbimus ſummam eſſe
              <lb/>
            majorem.</s>
            <s xml:id="echoid-s5695" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5696" xml:space="preserve">Velocitas corporis A nunc eſt m + e; </s>
            <s xml:id="echoid-s5697" xml:space="preserve">Corporis C eſt {mc + ec/a}; </s>
            <s xml:id="echoid-s5698" xml:space="preserve">corporis </s>
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