Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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            <s xml:id="echoid-s3033" xml:space="preserve">
              <pb o="73" file="0125" n="136" rhead="MATHEMATICA. LIB. I. CAP. XIX."/>
            dem tempore corpus hoc percurreret Eb & </s>
            <s xml:id="echoid-s3034" xml:space="preserve">quæ exprimitur per Q x E b .</s>
            <s xml:id="echoid-s3035" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">108.</note>
            Potentia autem, quæ in P agit, augetur quantitate, qua P eodem tempore
              <lb/>
            transfertur per aD, & </s>
            <s xml:id="echoid-s3036" xml:space="preserve">quæ exprimitur per P x a D ; </s>
            <s xml:id="echoid-s3037" xml:space="preserve">ponimus enim
              <note symbol="*" position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">128.</note>
            rallelas Bb, Oo, Aa; </s>
            <s xml:id="echoid-s3038" xml:space="preserve">potentia ergo quæ retardat motum corporis Q, eſt ad
              <lb/>
            potentiam, quæ accelerat motum corporis P, ut Q x E b ad P x a D: </s>
            <s xml:id="echoid-s3039" xml:space="preserve">Sed po-
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            tentiæ hæapplicantur vecti, cujusfulcrum eſt C; </s>
            <s xml:id="echoid-s3040" xml:space="preserve">idcirco harum actiones, quas
              <lb/>
            æquales demonſtravimus, ſunt ut CB x E b x Q ad CA x a D x P . </s>
            <s xml:id="echoid-s3041" xml:space="preserve">Ideo CB x
              <note symbol="*" position="right" xlink:label="note-0125-03" xlink:href="note-0125-03a" xml:space="preserve">175.</note>
            ad CA x P, ut aD ad Eb, aut AO ad OB. </s>
            <s xml:id="echoid-s3042" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3043" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3044" xml:space="preserve">D. </s>
            <s xml:id="echoid-s3045" xml:space="preserve">Patet etiam in pendu-
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            lo tali compoſito producta fore æqualia, ſi unumquodque pondus multipli-
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            cetur per ſuas diſtantias a centris ſuſpenſionis & </s>
            <s xml:id="echoid-s3046" xml:space="preserve">oſcillationis.</s>
            <s xml:id="echoid-s3047" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3048" xml:space="preserve">Si plura pondera dentur & </s>
            <s xml:id="echoid-s3049" xml:space="preserve">unumquodque per ſuas diſtantias a centris ſuſpenſio-
              <lb/>
              <note position="right" xlink:label="note-0125-04" xlink:href="note-0125-04a" xml:space="preserve">309.</note>
            nis & </s>
            <s xml:id="echoid-s3050" xml:space="preserve">oſcillationis multiplicetur, ſummæ productorum ab utraque parte centri o-
              <lb/>
            ſcillationis æquales ſunt. </s>
            <s xml:id="echoid-s3051" xml:space="preserve">Quod demonſtratione ſimili evincitur.</s>
            <s xml:id="echoid-s3052" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3053" xml:space="preserve">Unde deducimus Methodum computatione determinandi centrum oſcil-
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            lationis.</s>
            <s xml:id="echoid-s3054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3055" xml:space="preserve">Sint corpora quæcunque A, B, C, D, E, horum diſtantiæ a centro ſuſpen-
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              <note position="right" xlink:label="note-0125-05" xlink:href="note-0125-05a" xml:space="preserve">310.</note>
            ſionis reſpectivè litteris a, b, c, d, e, exprimuntur; </s>
            <s xml:id="echoid-s3056" xml:space="preserve">ſit diſtantia centri oſcilla-
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            tionis a centro ſufpenſionis x. </s>
            <s xml:id="echoid-s3057" xml:space="preserve">Ponamus a, b, c, minores eſſe x, d & </s>
            <s xml:id="echoid-s3058" xml:space="preserve">e autern
              <lb/>
            majores.</s>
            <s xml:id="echoid-s3059" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3060" xml:space="preserve">Corporum A, B, C, diſtantiæ a centro oſcillationis ſunt x-a, x-b,
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            x-c, & </s>
            <s xml:id="echoid-s3061" xml:space="preserve">corporum reliquorum diſtantiæ ab eodem centro ſunt d-x,
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            e-x, multiplicando corpora ſingula per ſuas diſtantias ab utroque cen-
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            tro, habemus Aax - Aaa + Bbx - Bbb + Ccx - Ccc = Ddd - Ddx + Eee - Eex unde
              <note symbol="*" position="right" xlink:label="note-0125-06" xlink:href="note-0125-06a" xml:space="preserve">309.</note>
            ducimus x = {Aaa + Bbb + Ccc + Ddd + Eee/Aa + Bb + Cc + Dd + Ee}, quam eandem æquationem ha-
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            bemus quæcunque ex diſtantiis a, b, c, d, e, ſuperent x; </s>
            <s xml:id="echoid-s3062" xml:space="preserve">quare generalem hanc
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            detegimus regulam.</s>
            <s xml:id="echoid-s3063" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3064" xml:space="preserve">Si ſingula corpora multiplicentur per quadrata ſuarum diſtantiarum à centro ſu-
              <lb/>
              <note position="right" xlink:label="note-0125-07" xlink:href="note-0125-07a" xml:space="preserve">311.</note>
            ſpenſionis, & </s>
            <s xml:id="echoid-s3065" xml:space="preserve">ſumma productorum dividatur per ſummam productorum ſingulorum
              <lb/>
            corporum raultiplicatorum per ſuas diſtantias ab eodem centro ſuſpenſionis, quotiens
              <lb/>
            diviſionis dabit diſtantiam inter centra ſuſpenſionis & </s>
            <s xml:id="echoid-s3066" xml:space="preserve">oſcillationis.</s>
            <s xml:id="echoid-s3067" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3068" xml:space="preserve">Si, continuato pendulo ultra centrum ſuſpenſionis, corpora quædam
              <lb/>
              <note position="right" xlink:label="note-0125-08" xlink:href="note-0125-08a" xml:space="preserve">312.</note>
            ſupra punctum ſuſpenſionis applicentur, horum diſtantia erit negativa; </s>
            <s xml:id="echoid-s3069" xml:space="preserve">Si
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            Ex. </s>
            <s xml:id="echoid-s3070" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">talia forent corpora A&</s>
            <s xml:id="echoid-s3072" xml:space="preserve">B, pro + a & </s>
            <s xml:id="echoid-s3073" xml:space="preserve">+ b computatio ineunda foret
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            cum -a, -b, quorum quadrata cum etiam ſint + aa & </s>
            <s xml:id="echoid-s3074" xml:space="preserve">+ bb, diſtantia x in hoc ca-
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            ſu erit {Aaa + Bbb + Ccc + Ddd + Eee/-Aa-Bb + Cc + Dd + Ee.</s>
            <s xml:id="echoid-s3075" xml:space="preserve">}</s>
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          <p>
            <s xml:id="echoid-s3076" xml:space="preserve">Ut memoratam regulam applicemus lineæ cujus extremitas eſt
              <note position="right" xlink:label="note-0125-09" xlink:href="note-0125-09a" xml:space="preserve">313.</note>
            fionis centrum, ſingula ipſius puncta, aut potius partes minimæ, multipli-
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              <note symbol="*" position="right" xlink:label="note-0125-10" xlink:href="note-0125-10a" xml:space="preserve">311.</note>
            candæ ſunt per quadrata diſtantiarum ſuarum ab extremitate, ſumma horum
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              <note symbol="*" position="right" xlink:label="note-0125-11" xlink:href="note-0125-11a" xml:space="preserve">7.6. El. XII</note>
            productorum eſt pyramis, cujus baſis eſt lineæ quadratum, & </s>
            <s xml:id="echoid-s3077" xml:space="preserve">altitudo ipſa
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            linea, ſi linea dicatur a, pyramis hæc valet {1/3}a
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s3078" xml:space="preserve">Dividenda hæc eſt per ſummam partium minimarum multiplicatarum per ſuas diſtantias ab extre-
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              <note symbol="*" position="right" xlink:label="note-0125-12" xlink:href="note-0125-12a" xml:space="preserve">34. El. I.</note>
            mitate, quorum productorum ſumma eſt area trianguli cujus baſis eſt a, & </s>
            <s xml:id="echoid-s3079" xml:space="preserve">
              <lb/>
            altitudo etiam a; </s>
            <s xml:id="echoid-s3080" xml:space="preserve">quæ area valet {1/2}aa . </s>
            <s xml:id="echoid-s3081" xml:space="preserve">Dividendo autem {1/3}a
              <emph style="super">3</emph>
            per {1/2}a
              <emph style="super">2</emph>
            quo- tiens eſt {2/3}a diſtantia centri oſcillationis a centro ſuſpenſionis, ut ſuperius ex-
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            perimento confirmavimus .</s>
            <s xml:id="echoid-s3082" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">298.</note>
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