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

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        <div xml:id="echoid-div987" type="section" level="1" n="244">
          <p>
            <s xml:id="echoid-s7165" xml:space="preserve">
              <pb o="182" file="0260" n="284" rhead="PHYSICES ELEMENTA"/>
            inter ſeut A per f b ad B per g i, erit i m velocitas communicata actione cor-
              <lb/>
            poris A.</s>
            <s xml:id="echoid-s7166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7167" xml:space="preserve">Multiplicando i m & </s>
            <s xml:id="echoid-s7168" xml:space="preserve">m l per C, quo ratio non mutatur, habemus i m per
              <lb/>
            C ad m l per C, ut A per f b ad B per g i; </s>
            <s xml:id="echoid-s7169" xml:space="preserve">unde deducimus i m per C plus
              <lb/>
            m l per C, id eſt C per i l, ad i m per C, ut A per f b plus B per g i ad Aper
              <lb/>
            f b: </s>
            <s xml:id="echoid-s7170" xml:space="preserve">antecedentia autem ſunt æqualia ergo & </s>
            <s xml:id="echoid-s7171" xml:space="preserve">conſequentia.</s>
            <s xml:id="echoid-s7172" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7173" xml:space="preserve">Idcirco A ad C. </s>
            <s xml:id="echoid-s7174" xml:space="preserve">ut i m mutatio velocitatis in corpore C ex actione cor-
              <lb/>
            poris A, ad f b mutationem in velocitate corporis A. </s>
            <s xml:id="echoid-s7175" xml:space="preserve">Id eſt, mutationes
              <lb/>
            in velocitatibus horum corporum oriundæ ex actione mutua in colliſione.
              <lb/>
            </s>
            <s xml:id="echoid-s7176" xml:space="preserve">ſunt inverſè ut maſſæ, ut hoc notavimus in num. </s>
            <s xml:id="echoid-s7177" xml:space="preserve">627.</s>
            <s xml:id="echoid-s7178" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div993" type="section" level="1" n="245">
          <head xml:id="echoid-head346" xml:space="preserve">SCHOLIUM 2.</head>
          <head xml:id="echoid-head347" xml:space="preserve">Inveſtigatio motus memorati in n. 633.</head>
          <p>
            <s xml:id="echoid-s7179" xml:space="preserve">Concipiamus tria corpora A, B, C, perfecte elaſtica; </s>
            <s xml:id="echoid-s7180" xml:space="preserve">ſit primi velocitas m,
              <lb/>
              <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">645.</note>
            ſecundi n; </s>
            <s xml:id="echoid-s7181" xml:space="preserve">tertii p; </s>
            <s xml:id="echoid-s7182" xml:space="preserve">tendant hæc ad eandem partem: </s>
            <s xml:id="echoid-s7183" xml:space="preserve">Poſt ictum ante in-
              <lb/>
            ſtauratam figuram velocitas eſt {Am + Bn + Cp/A + B + C} , dicatur hæc v.</s>
            <s xml:id="echoid-s7184" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">626. 643.</note>
          <p>
            <s xml:id="echoid-s7185" xml:space="preserve">Vis ictu deſtructa eſt {ABx
              <emph style="ol">m-n</emph>
              <emph style="super">2</emph>
            + ACx
              <emph style="ol">m-p</emph>
              <emph style="super">2</emph>
            + BCx
              <emph style="ol">n-p</emph>
              <emph style="super">2</emph>
            /A + B + C}
              <note symbol="*" position="left" xlink:label="note-0260-03" xlink:href="note-0260-03a" xml:space="preserve">625. 641.</note>
            Sit hæc æqualis 2Aff + 2Bff + 2Cff.</s>
            <s xml:id="echoid-s7186" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7187" xml:space="preserve">Si non omnia corpora ad eandem partem tenderent velocitas poſt ictum,
              <lb/>
            & </s>
            <s xml:id="echoid-s7188" xml:space="preserve">vis deſtructa, iiſdem regulis determinari poſſent,</s>
          </p>
          <p>
            <s xml:id="echoid-s7189" xml:space="preserve">Sepoſito elaſterio poſt ictum corpora in nave, velocitate v motâ, quie-
              <lb/>
            ſcerent, ſolo ergo elaſterio in hac poſt ictum moventur & </s>
            <s xml:id="echoid-s7190" xml:space="preserve">iiſdem velocitati-
              <lb/>
            bus in nave moventur, quibus iiſdem elaſteriis corpora ſi revera quieſce-
              <lb/>
            rent, agitarentur; </s>
            <s xml:id="echoid-s7191" xml:space="preserve">determinatis ergo motibus in hoc ultimo caſu habebimus
              <lb/>
            motus in nave, unde motus abſoluti facile deducuntur.</s>
            <s xml:id="echoid-s7192" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7193" xml:space="preserve">Ponimus igitur corpora quieſcentia A, B, C, & </s>
            <s xml:id="echoid-s7194" xml:space="preserve">inter hæc elaſteria flexa
              <lb/>
              <note position="left" xlink:label="note-0260-04" xlink:href="note-0260-04a" xml:space="preserve">646.</note>
            viribus quibus in ictu partes fuere compreſſæ, quæ valent 2 A ff + 2 B ff +
              <lb/>
            2C ff. </s>
            <s xml:id="echoid-s7195" xml:space="preserve">Cum agatur de caſu in quo inter A & </s>
            <s xml:id="echoid-s7196" xml:space="preserve">B, & </s>
            <s xml:id="echoid-s7197" xml:space="preserve">inter B & </s>
            <s xml:id="echoid-s7198" xml:space="preserve">C, partes
              <lb/>
            æqualiter inflectuntur, vis qua elaſterium utrumque comprimitur eſt A ff
              <lb/>
            + B ff + C ff talemque vim dum elaſterium ſeſe expandit corporibus com-
              <lb/>
            municat ,</s>
          </p>
          <note symbol="*" position="left" xml:space="preserve">560.</note>
          <p>
            <s xml:id="echoid-s7199" xml:space="preserve">Elaſterium inter A & </s>
            <s xml:id="echoid-s7200" xml:space="preserve">B ſeſe expandens Corpori A communicat vim B ff
              <lb/>
            + C ff, & </s>
            <s xml:id="echoid-s7201" xml:space="preserve">in corpus B actionem exerit, quæ valet vim A ff . </s>
            <s xml:id="echoid-s7202" xml:space="preserve">Eodem
              <note symbol="*" position="left" xlink:label="note-0260-06" xlink:href="note-0260-06a" xml:space="preserve">561.</note>
            do elaſterium aliud corpori C communicat vim A ff + B ff & </s>
            <s xml:id="echoid-s7203" xml:space="preserve">in Bexerit a-
              <lb/>
            ctionem quæ valet vim C ff .</s>
            <s xml:id="echoid-s7204" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">561.</note>
          <p>
            <s xml:id="echoid-s7205" xml:space="preserve">Corpus B premitur ergo duabus actionibus in partes oppoſitas, ſi A ſuperet
              <lb/>
            C, magis hoc corpus verſus premitur corpus B, actione quæ valet differen-
              <lb/>
            tiam actionum A ff & </s>
            <s xml:id="echoid-s7206" xml:space="preserve">C ff, de cætero actiones in utramque partem ſunt æ-
              <lb/>
            quales inter ſe & </s>
            <s xml:id="echoid-s7207" xml:space="preserve">valent C ff.</s>
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