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

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            <s xml:id="echoid-s5612" xml:space="preserve">
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            mutatio ergo eſt {Aa - Ab/A + B}; </s>
            <s xml:id="echoid-s5613" xml:space="preserve">cum velocitas b minor ſit velocitate a, auge-
              <lb/>
            tur illa in percuſſione: </s>
            <s xml:id="echoid-s5614" xml:space="preserve">ideò velocitas corporis B, id eſt velocitas utriuſ-
              <lb/>
            que corporis poſt impactionem, eſt b + {Aa - Ab/A + B} = {Bb + Aa/A + B} ut
              <note symbol="*" position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve"> 484.</note>
            betur in n. </s>
            <s xml:id="echoid-s5615" xml:space="preserve">513.</s>
            <s xml:id="echoid-s5616" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5617" xml:space="preserve">Poſitâ velocitate reſpectiva a + b, tendentibus nempe corporibus in con-
              <lb/>
              <note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">527.</note>
            trarias partes , ſimili ratiocinio regula n. </s>
            <s xml:id="echoid-s5618" xml:space="preserve">516. </s>
            <s xml:id="echoid-s5619" xml:space="preserve">detegitur.</s>
            <s xml:id="echoid-s5620" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">475.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s5621" xml:space="preserve">Haſce ambas regulas de colliſione corporum etiam ex demonſtratis
              <note symbol="*" position="left" xlink:label="note-0210-04" xlink:href="note-0210-04a" xml:space="preserve">510. 525.</note>
            ca quantitatem vis amiſſæ deduci poſſunt, quam demonſtrationem hìc ſub-
              <lb/>
            jiciam, ut ſirmitas illorum quæ de viribus inſitis ſuperius demonſtra-
              <lb/>
            ta ſunt clarius pateat, dum ex ipſis, per vias omnino diverſas, deducimus
              <lb/>
            regulas experimentis conſirmatas.</s>
            <s xml:id="echoid-s5622" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5623" xml:space="preserve">Sint iterum corpora A & </s>
            <s xml:id="echoid-s5624" xml:space="preserve">B; </s>
            <s xml:id="echoid-s5625" xml:space="preserve">hujus velocitas b illius a; </s>
            <s xml:id="echoid-s5626" xml:space="preserve">tendant ad eandem
              <lb/>
              <note position="left" xlink:label="note-0210-05" xlink:href="note-0210-05a" xml:space="preserve">528.</note>
            partem, & </s>
            <s xml:id="echoid-s5627" xml:space="preserve">velocitas reſpectiva erit a - b.</s>
            <s xml:id="echoid-s5628" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5629" xml:space="preserve">Summa virium ante ictum eſt Aaa + Bbb ; </s>
            <s xml:id="echoid-s5630" xml:space="preserve">vis ictu deſtructa
              <note symbol="*" position="left" xlink:label="note-0210-06" xlink:href="note-0210-06a" xml:space="preserve">470.</note>
            {ABaa - 2ABab + ABbb/A + B} , ſubtrahendo hancex ſumma virium
              <note symbol="*" position="left" xlink:label="note-0210-07" xlink:href="note-0210-07a" xml:space="preserve">510. 525.</note>
            vim poſt ictum ſuperſtitem {AAaa + 2ABab + BBbb/A + B}; </s>
            <s xml:id="echoid-s5631" xml:space="preserve">corpora poſt i-
              <lb/>
            ctum non ſeparantur , & </s>
            <s xml:id="echoid-s5632" xml:space="preserve">maſſa eſt A + B, per quam ſi dividamus vim
              <note symbol="*" position="left" xlink:label="note-0210-08" xlink:href="note-0210-08a" xml:space="preserve">484</note>
            ſtitem poſt ictum, habemus quadratum velocitatis poſt colliſionem; </s>
            <s xml:id="echoid-s5633" xml:space="preserve">quod
              <lb/>
            quadratum ergo eſt {A Aaa + 2A Bab + BBbb/
              <emph style="ol">A + B</emph>
              <emph style="super">q</emph>
            } = {
              <emph style="ol">Aa + Bb</emph>
              <emph style="super">q</emph>
            /
              <emph style="ol">A + B</emph>
              <emph style="super">q</emph>
            }. </s>
            <s xml:id="echoid-s5634" xml:space="preserve">cujus radix
              <lb/>
            {Aa + Bb/A + B} dat velocitatem quæſitam.</s>
            <s xml:id="echoid-s5635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5636" xml:space="preserve">Si adhibita velocitate reſpectiva a + b computatio ineatur regula n. </s>
            <s xml:id="echoid-s5637" xml:space="preserve">516.
              <lb/>
            </s>
            <s xml:id="echoid-s5638" xml:space="preserve">
              <note position="left" xlink:label="note-0210-09" xlink:href="note-0210-09a" xml:space="preserve">529.</note>
            detegitur.</s>
            <s xml:id="echoid-s5639" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5640" xml:space="preserve">Vulgo quantitas motus, quam ipſius vis inſitæ proportionem ſequi ponunt,
              <lb/>
              <note position="left" xlink:label="note-0210-10" xlink:href="note-0210-10a" xml:space="preserve">530.</note>
            determinatur multiplicando maſſam non per quadratum velocitatis, ſed per
              <lb/>
            ipſam velocitatem, ex hocprincipio deduxere Philoſophiipſas illas regulas n.
              <lb/>
            </s>
            <s xml:id="echoid-s5641" xml:space="preserve">513. </s>
            <s xml:id="echoid-s5642" xml:space="preserve">516. </s>
            <s xml:id="echoid-s5643" xml:space="preserve">quas nos variis methodis ex principiis noſtris deduximus; </s>
            <s xml:id="echoid-s5644" xml:space="preserve">mirum
              <lb/>
            hìc quid contigit, error erroris ſuit deſtructio, & </s>
            <s xml:id="echoid-s5645" xml:space="preserve">duplex error ad veritatem
              <lb/>
            conduxit; </s>
            <s xml:id="echoid-s5646" xml:space="preserve">falſum de menſura virium ſecuti ſunt principium, & </s>
            <s xml:id="echoid-s5647" xml:space="preserve">quod veri-
              <lb/>
            tati etiam minime congruum eſt, nullam vim intropremendo partes & </s>
            <s xml:id="echoid-s5648" xml:space="preserve">ha-
              <lb/>
            rum ſuperando cohæſionem corpora amittere poſuere.</s>
            <s xml:id="echoid-s5649" xml:space="preserve"/>
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