Musschenbroek, Petrus van, Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae

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        <div xml:id="echoid-div561" type="section" level="1" n="561">
          <p>
            <s xml:id="echoid-s15008" xml:space="preserve">
              <pb o="603" file="0619" n="620" rhead="CORPORUM FIRMORUM."/>
            ad horizontem perpendiculari, erit momentum gravitatis in ſolido
              <lb/>
            A T C K B, ad momentum gravitatis in ſegmento A O F M B, poſi-
              <lb/>
            tâ ſectione O F M parallela ad T C K, uti Cohærentia baſeos
              <lb/>
            T C K ad Cohærentiam baſeos O F M.</s>
            <s xml:id="echoid-s15009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15010" xml:space="preserve">Vocetur C T, r. </s>
            <s xml:id="echoid-s15011" xml:space="preserve">A T, a. </s>
            <s xml:id="echoid-s15012" xml:space="preserve">O A, b. </s>
            <s xml:id="echoid-s15013" xml:space="preserve">O F, {b br.</s>
            <s xml:id="echoid-s15014" xml:space="preserve">/a a} C K, c. </s>
            <s xml:id="echoid-s15015" xml:space="preserve">Eſt ſpatium
              <lb/>
            O F A = {1/3} O F X O A = {1/3} {b
              <emph style="super">3</emph>
            r,/a a} & </s>
            <s xml:id="echoid-s15016" xml:space="preserve">ſpatium T C A = {1/3} a r: </s>
            <s xml:id="echoid-s15017" xml:space="preserve">adeo-
              <lb/>
            que ſoliditas O F M A B eſt = {b
              <emph style="super">3</emph>
            c r.</s>
            <s xml:id="echoid-s15018" xml:space="preserve">/3 a a} & </s>
            <s xml:id="echoid-s15019" xml:space="preserve">ſoliditas T C K A B = {1/3} a r c.
              <lb/>
            </s>
            <s xml:id="echoid-s15020" xml:space="preserve">diſtantia autem centri gravitatis ab O F in plano O F A eſt = {3/10} A O. </s>
            <s xml:id="echoid-s15021" xml:space="preserve">
              <lb/>
            adeoque erit in corpore O F A M. </s>
            <s xml:id="echoid-s15022" xml:space="preserve">a ſectione O F M remotum {3/10} A O. </s>
            <s xml:id="echoid-s15023" xml:space="preserve">
              <lb/>
            hinc momentum ſolidi O A B M F, erit = {b
              <emph style="super">4</emph>
            c r.</s>
            <s xml:id="echoid-s15024" xml:space="preserve">/10 a a} & </s>
            <s xml:id="echoid-s15025" xml:space="preserve">momentum ſo-
              <lb/>
            lidi T C K A B ex gravitate erit = {a a r c.</s>
            <s xml:id="echoid-s15026" xml:space="preserve">/10} Eſt autem Cohærentia
              <lb/>
            baſeos O F M = {b
              <emph style="super">4</emph>
            r r c.</s>
            <s xml:id="echoid-s15027" xml:space="preserve">/a
              <emph style="super">4</emph>
            } & </s>
            <s xml:id="echoid-s15028" xml:space="preserve">Cohærentia baſeos T C K = r r c: </s>
            <s xml:id="echoid-s15029" xml:space="preserve">ordi-
              <lb/>
            nentur momenta gravitatis & </s>
            <s xml:id="echoid-s15030" xml:space="preserve">Cohærentiæ in proportionem, erit
              <lb/>
            {b
              <emph style="super">4</emph>
            c r.</s>
            <s xml:id="echoid-s15031" xml:space="preserve">/10 a a} {b
              <emph style="super">4</emph>
            r r c/a
              <emph style="super">4</emph>
            }:</s>
            <s xml:id="echoid-s15032" xml:space="preserve">: {a a r c.</s>
            <s xml:id="echoid-s15033" xml:space="preserve">/10} r r c. </s>
            <s xml:id="echoid-s15034" xml:space="preserve">
              <lb/>
            multiplicando enim extrema & </s>
            <s xml:id="echoid-s15035" xml:space="preserve">media per ſe habentur producta
              <lb/>
            utrimque æqualia. </s>
            <s xml:id="echoid-s15036" xml:space="preserve">{b
              <emph style="super">4</emph>
            c c r
              <emph style="super">3</emph>
            /10 a a} = {a a b
              <emph style="super">4</emph>
            c c r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s15037" xml:space="preserve">/10 a
              <emph style="super">4</emph>
            } adeoque quantitates an-
              <lb/>
            tea fuerunt proportionales, unde momenta gravium ſunt inter
              <lb/>
            ſe veluti Cohærentiæ: </s>
            <s xml:id="echoid-s15038" xml:space="preserve">hoc etiam alio modo demonſtravit Cl. </s>
            <s xml:id="echoid-s15039" xml:space="preserve">
              <lb/>
            Leibnitſius.</s>
            <s xml:id="echoid-s15040" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div562" type="section" level="1" n="562">
          <head xml:id="echoid-head676" xml:space="preserve">PROPOSITIO LXXXIII.</head>
          <p>
            <s xml:id="echoid-s15041" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15042" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15043" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15044" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15045" xml:space="preserve">Sit ſolidum B R S A a D C parallelopipedum
              <lb/>
            rectangulum, cujus latus B D C E ad horizontem perpendiculare:
              <lb/>
            </s>
            <s xml:id="echoid-s15046" xml:space="preserve">ſit ſolidum parabolicum A a B E R S ex priori abſciſſum, atque ver-
              <lb/>
            tex parabolæ in a & </s>
            <s xml:id="echoid-s15047" xml:space="preserve">A, axes in a R, A S. </s>
            <s xml:id="echoid-s15048" xml:space="preserve">ordinatæ B R, E S: </s>
            <s xml:id="echoid-s15049" xml:space="preserve">tum
              <lb/>
            ſolidum reliquum B D C E a A baſi B D C E applicatum parieti </s>
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