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

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          <p>
            <s xml:id="echoid-s5698" xml:space="preserve">
              <pb o="144" file="0212" n="231" rhead="PHYSICES ELEMENTA"/>
            eſt m - e; </s>
            <s xml:id="echoid-s5699" xml:space="preserve">& </s>
            <s xml:id="echoid-s5700" xml:space="preserve">tandem celeritas corporis D eſt {nd - ed/b}. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">Summa virium nunc
              <lb/>
            erit Amm + 2Ame + Acc + {Cccmm + 2Cccme + Cccee/aa} + Bnn - 2Bne
              <lb/>
            + Bee + {Dddnn - 2Dddne + Dddee/bb}. </s>
            <s xml:id="echoid-s5702" xml:space="preserve">Sed
              <emph style="ol">Aaa + Ccc</emph>
            x bbm
              <lb/>
            =
              <emph style="ol">Bbb + Ddd</emph>
            x aan; </s>
            <s xml:id="echoid-s5703" xml:space="preserve">ponimus enim de hoc caſu agi; </s>
            <s xml:id="echoid-s5704" xml:space="preserve">dividendo hanc
              <lb/>
            æquationem per aabb, habemus Am + {Cccm/aa} = Bn + {Dddn/bb}; </s>
            <s xml:id="echoid-s5705" xml:space="preserve">idcirco
              <lb/>
            in ultima ſumma ſeſe mutuo deſtruunt + 2Ame + {2Cccme/aa} & </s>
            <s xml:id="echoid-s5706" xml:space="preserve">- 2Bne -
              <lb/>
            {2Dddne/bb} & </s>
            <s xml:id="echoid-s5707" xml:space="preserve">ſumma ad hanc reducitur Amm + Aee + {Cccmm + Cccee/aa}
              <lb/>
            + Bnn + Bee + {Dddnn + {Dddee/bb} quæ primâ memoratâ ſummâ major
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s5708" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s5709" xml:space="preserve">D. </s>
            <s xml:id="echoid-s5710" xml:space="preserve">E.</s>
            <s xml:id="echoid-s5711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5712" xml:space="preserve">Nec diverſa eſt demonſtratio ſi augeatur n, imminutâ velocitate m.</s>
            <s xml:id="echoid-s5713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5714" xml:space="preserve">Vis in colliſione quacunque, datâ velocitate reſpectivâ, deſtructa determi-
              <lb/>
              <note position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">536.</note>
            nari poteſt, nam valet ſummam virium in caſu in quo hæc minima eſt . </s>
            <s xml:id="echoid-s5715" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">531.</note>
            nunc m + n = r.</s>
            <s xml:id="echoid-s5716" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5717" xml:space="preserve">Datur ratio inter m & </s>
            <s xml:id="echoid-s5718" xml:space="preserve">n & </s>
            <s xml:id="echoid-s5719" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">533.</note>
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa,
              <emph style="ol">Aaa x Ccc</emph>
            x bb:</s>
            <s xml:id="echoid-s5720" xml:space="preserve">:
              <lb/>
            m + n = r, n;
              <lb/>
            </s>
            <s xml:id="echoid-s5721" xml:space="preserve">ergo n = {
              <emph style="ol">Aaa + Ccc</emph>
            x bbr/
              <emph style="ol">Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa}. </s>
            <s xml:id="echoid-s5722" xml:space="preserve">Eodem modo detegi-
              <lb/>
            mus m = {
              <emph style="ol">Bbb + Ddd</emph>
            x aar/Aaa x Ccc x bb +
              <emph style="ol">Bbb + Ddd</emph>
            x aa}. </s>
            <s xml:id="echoid-s5723" xml:space="preserve">Summa virium eſt
              <lb/>
            {
              <emph style="ol">Aaa + Ccc</emph>
            x mm/aa} + {
              <emph style="ol">Bbb + Ddd</emph>
            x nn/bb} , ſubſtituendo pro m & </s>
            <s xml:id="echoid-s5724" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0212-04" xlink:href="note-0212-04a" xml:space="preserve">535</note>
            valores ſumma hæc erit
              <lb/>
            {
              <emph style="ol">Aaa + Ccc</emph>
            x
              <emph style="ol">Bbb + Ddd</emph>
              <emph style="super">q</emph>
            x aarr +
              <emph style="ol">Bbb + Ddd</emph>
            x
              <emph style="ol">Aaa + Ccc</emph>
              <emph style="super">q</emph>
            x bbrr/{
              <emph style="ol">/Aaa + Ccc</emph>
            x bb +
              <emph style="ol">Bbb + Ddd x aa</emph>
              <emph style="super">q</emph>
            }
              <lb/>
            Dividendo numeratorem & </s>
            <s xml:id="echoid-s5725" xml:space="preserve">denominatorem per
              <emph style="ol">Aaa + Ccc</emph>
            x bb </s>
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