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-div538" type="section" level="1" n="538">
          <p>
            <s xml:id="echoid-s14383" xml:space="preserve">
              <pb o="586" file="0602" n="603" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            Eſt autem demonſtratum in Prop. </s>
            <s xml:id="echoid-s14384" xml:space="preserve">XVI, Carrei de Centro
              <lb/>
            Gravitatis, in Conis & </s>
            <s xml:id="echoid-s14385" xml:space="preserve">Pyramidibus centrum gravitatis
              <lb/>
            dari in axe G E, ad {1/4} longitudinis G E a puncto baſeos E. </s>
            <s xml:id="echoid-s14386" xml:space="preserve">Qua
              <lb/>
            re momentum Coni aut Pyramidis A G B erit = {aab/3} X {1/4}b.
              <lb/>
            </s>
            <s xml:id="echoid-s14387" xml:space="preserve">& </s>
            <s xml:id="echoid-s14388" xml:space="preserve">momentum Coni aut Pyramidis C G D erit = {bc
              <emph style="super">3</emph>
            /3a} X {1/4} {bc/4a}. </s>
            <s xml:id="echoid-s14389" xml:space="preserve">quæ
              <lb/>
            momenta ſunt inter ſe veluti a
              <emph style="super">4</emph>
            ad c
              <emph style="super">4</emph>
            .</s>
            <s xml:id="echoid-s14390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14391" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14392" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14393" xml:space="preserve">Cumbaſes conorum & </s>
            <s xml:id="echoid-s14394" xml:space="preserve">pyramidum ſunt inter ſe uti a a
              <lb/>
            ad c c. </s>
            <s xml:id="echoid-s14395" xml:space="preserve">erunt momenta ex gravitate in ratione duplicata baſium
              <lb/>
            conorum & </s>
            <s xml:id="echoid-s14396" xml:space="preserve">pyramidum ſimilium.</s>
            <s xml:id="echoid-s14397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14398" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14399" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14400" xml:space="preserve">Et cum Cohærentiæ conorum & </s>
            <s xml:id="echoid-s14401" xml:space="preserve">pyramidum ſunt inter
              <lb/>
            ſe uti a
              <emph style="super">3</emph>
            ad c
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14402" xml:space="preserve">erunt momenta ex gravitate ad Cohærentiam uti
              <lb/>
            Surde ſolida ad Cubos.</s>
            <s xml:id="echoid-s14403" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div539" type="section" level="1" n="539">
          <head xml:id="echoid-head652" xml:space="preserve">PROPOSITIO LX.</head>
          <p style="it">
            <s xml:id="echoid-s14404" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14405" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s14406" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14407" xml:space="preserve">12. </s>
            <s xml:id="echoid-s14408" xml:space="preserve">Dato Cono Gravi A B G, maximoque ponde-
              <lb/>
            re, quod ab extremo G geſtari poſſit, invenire maximum pondus,
              <lb/>
            quod ab extremo C cjusdem Conitruncati C D B A geſtabitur.</s>
            <s xml:id="echoid-s14409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14410" xml:space="preserve">Quantitatibus deſignatis uti in Propoſitione LIX. </s>
            <s xml:id="echoid-s14411" xml:space="preserve">quæratur primo
              <lb/>
            centrum Gravitatis in cono truncato A B C D, cujus diſtantia a
              <lb/>
            puncto E baſeos eſt = {4aab-4bc
              <emph style="super">3</emph>
            -9a
              <emph style="super">3</emph>
            b/4aa-4c
              <emph style="super">3</emph>
            }. </s>
            <s xml:id="echoid-s14412" xml:space="preserve">eſt autem pondus ipſius
              <lb/>
            coni truncati = {aab/3}-{bc
              <emph style="super">3</emph>
            /3a}. </s>
            <s xml:id="echoid-s14413" xml:space="preserve">unde momentum coni truncati erit
              <lb/>
            = {4aab-4bc
              <emph style="super">3</emph>
            -9a
              <emph style="super">3</emph>
            b/4aa-4c
              <emph style="super">3</emph>
            } X {aab/3}-{bc
              <emph style="super">3</emph>
            /3a}
              <lb/>
            Eſt quoque longitudo E f, ex qua pondus ſuſpendetur =b-{bc/a}.
              <lb/>
            </s>
            <s xml:id="echoid-s14414" xml:space="preserve">vocatoque pondere incognito & </s>
            <s xml:id="echoid-s14415" xml:space="preserve">appendendo = x, erit momen-
              <lb/>
            tum ejus = bx-{bcx/a}.</s>
            <s xml:id="echoid-s14416" xml:space="preserve"/>
          </p>
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