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

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          <pb o="183" file="0261" n="285" rhead="MATHEMATICA. Lib. I. Cap. XXVII."/>
          <p>
            <s xml:id="echoid-s7209" xml:space="preserve">Dum elaſteria actionibus æqualibus in ſe mutuo premunt, utrumque agit
              <lb/>
            quaſi obſtaculo immobili inſiſteret; </s>
            <s xml:id="echoid-s7210" xml:space="preserve">& </s>
            <s xml:id="echoid-s7211" xml:space="preserve">integram ſuam vim in partem oppoſitam
              <lb/>
            exerit ; </s>
            <s xml:id="echoid-s7212" xml:space="preserve">id eſt elaſteria agunt in corpora A & </s>
            <s xml:id="echoid-s7213" xml:space="preserve">C ita, ut ſingulis, præter
              <note symbol="*" position="right" xlink:label="note-0261-01" xlink:href="note-0261-01a" xml:space="preserve">561.</note>
            moratas vires, communicent vim C ff; </s>
            <s xml:id="echoid-s7214" xml:space="preserve">quare vis corpori A communicata va-
              <lb/>
            let B ff + 2C ff, & </s>
            <s xml:id="echoid-s7215" xml:space="preserve">C movetur vi A ff + B ff + Cff, dum B ad par-
              <lb/>
            tem Cpellitur actione quæ valet A ff-C ff.</s>
            <s xml:id="echoid-s7216" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7217" xml:space="preserve">Sed B non poteſt moveri, quin eâdem velocitate propellatur elaſterium
              <lb/>
            inter B & </s>
            <s xml:id="echoid-s7218" xml:space="preserve">C, & </s>
            <s xml:id="echoid-s7219" xml:space="preserve">ab elaſterio ita agitato accipit corpus C vim ftatim memo-
              <lb/>
            ratam eodem modo ac in nave, in qua elaſterium obſtaculo cede-
              <lb/>
            re neſcio inſiſteret, actione elaſterii moveretur; </s>
            <s xml:id="echoid-s7220" xml:space="preserve">id eſt velocitas qua
              <lb/>
            corpus C a B recedit, aut B celerius movetur, illa eſt quæ competit impreſſio-
              <lb/>
            ni ſtatim memoratæ, quæ velocitas eſt f {√A + B + C\x{0020}/C} . </s>
            <s xml:id="echoid-s7221" xml:space="preserve">Si corporis B
              <note symbol="*" position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">470.</note>
            locitas dicatur x, erit x + f {√A + B + C\x{0020}/C} velocitas corporis C. </s>
            <s xml:id="echoid-s7222" xml:space="preserve">Summa viri-
              <lb/>
            um horum corporum eſt A ff + B ff + C ff & </s>
            <s xml:id="echoid-s7223" xml:space="preserve">præterea A ff-C ff, ideſt
              <lb/>
            valet ſumma hæc 2 A ff + B ff; </s>
            <s xml:id="echoid-s7224" xml:space="preserve">Unde deducimus {B xx + C xx +
              <lb/>
            2fx √AC + BC + CC\x{0020} + A ff + B ff + C ff = 2Aff + Bff ;</s>
            <s xml:id="echoid-s7225" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">479.</note>
            aut {x x + 2f x √AC + BC + CC\x{0020}/B + C = Aff-Cff/B + C}; </s>
            <s xml:id="echoid-s7226" xml:space="preserve">& </s>
            <s xml:id="echoid-s7227" xml:space="preserve">
              <lb/>
            {x = f√AB + 2AC\x{0020}-f√AC + BC + CC\x{0020}/B + C}: </s>
            <s xml:id="echoid-s7228" xml:space="preserve">additâ velocitate
              <lb/>
            f√A + B + C\x{0020}/C} qua C recedit à B habemus ipſius C velocitatem
              <lb/>
            {fC √AB + 2AC\x{0020} + fB √AC + BC + CC\x{0020}/BC + CC}</s>
          </p>
          <p>
            <s xml:id="echoid-s7229" xml:space="preserve">Corporis autem A velocitas ex ipſius vi ante determinata detegitur eſtque
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            velocitas hæc {f√AB + 2AC\x{0020}/A}.</s>
            <s xml:id="echoid-s7230" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7231" xml:space="preserve">Velocitates hæ ex velocitate v ſunt ſubtrahendæ, aut ipſi ſunt addendæ,
              <lb/>
              <note position="right" xlink:label="note-0261-04" xlink:href="note-0261-04a" xml:space="preserve">647.</note>
            pro ut cum motu navis conſpirant aut contrariæ agunt.</s>
            <s xml:id="echoid-s7232" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7233" xml:space="preserve">Si in primo motu A celerius B feratur, id eſt m ſuperet n, velocitas cor-
              <lb/>
            poris A poſt ictum erit {v-f√AB + 2AC\x{0020}/A}; </s>
            <s xml:id="echoid-s7234" xml:space="preserve">reliquæ velocitates detectæ
              <lb/>
            corporum B & </s>
            <s xml:id="echoid-s7235" xml:space="preserve">C ipſi v addendæ ſunt.</s>
            <s xml:id="echoid-s7236" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7237" xml:space="preserve">In ſcholio 2. </s>
            <s xml:id="echoid-s7238" xml:space="preserve">Capitis ſequentis demonſtrabimus ſummam virium poſt ictum
              <lb/>
              <note position="right" xlink:label="note-0261-05" xlink:href="note-0261-05a" xml:space="preserve">648.</note>
            æqualem eſſe A mm + B nn + C pp; </s>
            <s xml:id="echoid-s7239" xml:space="preserve">quod cum ante demonſtratis congruit .</s>
            <s xml:id="echoid-s7240" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">558.</note>
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