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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          <p>
            <s xml:id="echoid-s14513" xml:space="preserve">
              <pb o="590" file="0606" n="607" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            peripheria circuli D G E = {bc/r}. </s>
            <s xml:id="echoid-s14514" xml:space="preserve">Eſt vero Conoidis parabolicæ A B C
              <lb/>
            ſoliditas = {acr/4} per Prop. </s>
            <s xml:id="echoid-s14515" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s14516" xml:space="preserve">Carrei de Dimenſione Solidorum.
              <lb/>
            </s>
            <s xml:id="echoid-s14517" xml:space="preserve">& </s>
            <s xml:id="echoid-s14518" xml:space="preserve">quia centrum gravitatis eſt ad {1/3} F B a puncto F, in axe F B, per
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s14519" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s14520" xml:space="preserve">Carrei de Centro Gravitatis, erit momentum Conoi-
              <lb/>
            dis parabolicæ A B C = {aacr/12}. </s>
            <s xml:id="echoid-s14521" xml:space="preserve">ſed ſolidum D B E eſt = {ab
              <emph style="super">4</emph>
            c/4r
              <emph style="super">3</emph>
            } cujus
              <lb/>
            momentum ex gravitate eſt = {aab
              <emph style="super">6</emph>
            c/12r
              <emph style="super">5</emph>
            }. </s>
            <s xml:id="echoid-s14522" xml:space="preserve">datur in Propoſitione. </s>
            <s xml:id="echoid-s14523" xml:space="preserve">
              <lb/>
            {aab
              <emph style="super">6</emph>
            c/12r
              <emph style="super">5</emph>
            }. </s>
            <s xml:id="echoid-s14524" xml:space="preserve">{aacr/12}:</s>
            <s xml:id="echoid-s14525" xml:space="preserve">: {a
              <emph style="super">3</emph>
            b
              <emph style="super">6</emph>
            /r
              <emph style="super">6</emph>
            }a
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14526" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14527" xml:space="preserve">Quod patet multiplicando hujus Proportionis terminos medios & </s>
            <s xml:id="echoid-s14528" xml:space="preserve">
              <lb/>
            extremos per ſe, proveniuntque producta æqualia, nempe {a
              <emph style="super">5</emph>
            b
              <emph style="super">6</emph>
            c.</s>
            <s xml:id="echoid-s14529" xml:space="preserve">/12r
              <emph style="super">5</emph>
            }.</s>
            <s xml:id="echoid-s14530" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14531" xml:space="preserve">Coroll. </s>
            <s xml:id="echoid-s14532" xml:space="preserve">Sunt quadrata momentorum Cohærentiæ harum Conoi-
              <lb/>
            dum Parabolicarum inter ſe, uti momenta gravitatis ipſarum Co-
              <lb/>
            noidum. </s>
            <s xml:id="echoid-s14533" xml:space="preserve">Nam ſunt Cohærentiæ inter ſe uti r
              <emph style="super">3</emph>
            ad b
              <emph style="super">3</emph>
            , quarum qua-
              <lb/>
            drata ſunt r
              <emph style="super">6</emph>
            , b
              <emph style="super">6</emph>
            . </s>
            <s xml:id="echoid-s14534" xml:space="preserve">eſt vero {aab
              <emph style="super">6</emph>
            c/12r
              <emph style="super">5</emph>
            } {aacr/12}:</s>
            <s xml:id="echoid-s14535" xml:space="preserve">: b
              <emph style="super">6</emph>
            , r
              <emph style="super">6</emph>
            . </s>
            <s xml:id="echoid-s14536" xml:space="preserve">nam multipli-
              <lb/>
            catis extremis mediisque terminis per ſe, habentur producta utrim-
              <lb/>
            que æqualia, nempe{aab
              <emph style="super">6</emph>
            cr/12}</s>
          </p>
        </div>
        <div xml:id="echoid-div544" type="section" level="1" n="544">
          <head xml:id="echoid-head658" xml:space="preserve">PROPOSITIO LXV.</head>
          <p style="it">
            <s xml:id="echoid-s14537" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14538" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14539" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14540" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14541" xml:space="preserve">Datis duabus Conoidibus Parabolicis gravi-
              <lb/>
            bus D E F, A B C, ejusdem altitudinis ſed diverſarum baſium, at-
              <lb/>
            que pondere dato Q appenſo ex vertice F Conoidis gracilioris,
              <lb/>
            invenire pondus P appendendum ex vertice C Conoidis craſſioris,
              <lb/>
            ita ut momenta propriarum gravitatum inconoidibus, & </s>
            <s xml:id="echoid-s14542" xml:space="preserve">ponde-
              <lb/>
            rum appenſorum earum verticibus, ſint ad cohærentias baſium in
              <lb/>
            eadem proportione.</s>
            <s xml:id="echoid-s14543" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14544" xml:space="preserve">Vocetur A F, r. </s>
            <s xml:id="echoid-s14545" xml:space="preserve">C F, b. </s>
            <s xml:id="echoid-s14546" xml:space="preserve">peripheria baſeos, c, pondus P </s>
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