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-div540" type="section" level="1" n="540">
          <p>
            <s xml:id="echoid-s14443" xml:space="preserve">
              <pb o="588" file="0604" n="605" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            vitate & </s>
            <s xml:id="echoid-s14444" xml:space="preserve">pondere, ſit ſummum quod ferri poſſit, alterum momen-
              <lb/>
            tum in breviori cono quod ſummum erit, debebit eſſe illi æquale
              <lb/>
            unde {acbb/24}+qb = {acdd/24}+dx.
              <lb/>
            </s>
            <s xml:id="echoid-s14445" xml:space="preserve">ex quibus eruitur x = {acbb/24d} + {qb/d} - {acd/24}.</s>
            <s xml:id="echoid-s14446" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div541" type="section" level="1" n="541">
          <head xml:id="echoid-head654" xml:space="preserve">PROPOSITIO LXII.</head>
          <p style="it">
            <s xml:id="echoid-s14447" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14448" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s14449" xml:space="preserve">ſig. </s>
            <s xml:id="echoid-s14450" xml:space="preserve">14. </s>
            <s xml:id="echoid-s14451" xml:space="preserve">Datis duobus Conis A B G, C D K gravibus,
              <lb/>
            ejusdem materiæ, & </s>
            <s xml:id="echoid-s14452" xml:space="preserve">æque altis, ſed diverſarum baſium, appenſo-
              <lb/>
            que pondere maximo Qex vertice Coni minoris, invenire pondus
              <lb/>
            maximum P, quod geſtari poſſit ex vertice G Coni craſſioris.</s>
            <s xml:id="echoid-s14453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14454" xml:space="preserve">Vocetur radius baſeos A B, a. </s>
            <s xml:id="echoid-s14455" xml:space="preserve">peripheria, p. </s>
            <s xml:id="echoid-s14456" xml:space="preserve">longitudo G M b.
              <lb/>
            </s>
            <s xml:id="echoid-s14457" xml:space="preserve">pondus P quæſitum ſit = x. </s>
            <s xml:id="echoid-s14458" xml:space="preserve">Radius baſeos D C = r. </s>
            <s xml:id="echoid-s14459" xml:space="preserve">ejus circumferentia
              <lb/>
            {pr/a}. </s>
            <s xml:id="echoid-s14460" xml:space="preserve">longitudo K L = d. </s>
            <s xml:id="echoid-s14461" xml:space="preserve">pondus Q =q.</s>
            <s xml:id="echoid-s14462" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14463" xml:space="preserve">Erit ſoliditas coni C D K = {dprr/6a}. </s>
            <s xml:id="echoid-s14464" xml:space="preserve">ejuſque momentum ex gravi-
              <lb/>
            tate = {ddprr/24a}. </s>
            <s xml:id="echoid-s14465" xml:space="preserve">momentum ponderis Q =dq. </s>
            <s xml:id="echoid-s14466" xml:space="preserve">ſoliditas vero Coni
              <lb/>
            A B G = {abp/6} ejusque momentum ex gravitate = {abbp/24}. </s>
            <s xml:id="echoid-s14467" xml:space="preserve">momen-
              <lb/>
            tum ponderis P = bx. </s>
            <s xml:id="echoid-s14468" xml:space="preserve">Debent ſummæ momentorum in ſingulo
              <lb/>
            Cono ad Cohærentias ſuarum baſium habere eandem rationem, qua-
              <lb/>
            re ſtabunt quantitates in hac proportione
              <lb/>
            {ddprr/24a} + dq. </s>
            <s xml:id="echoid-s14469" xml:space="preserve">8r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14470" xml:space="preserve">: {abbp/24} + bx, 8a
              <emph style="super">3</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s14471" xml:space="preserve">unde eruitur X = {aaddp/24br} + {a
              <emph style="super">3</emph>
            dq/br
              <emph style="super">3</emph>
            } - {abp/24}.</s>
            <s xml:id="echoid-s14472" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div542" type="section" level="1" n="542">
          <head xml:id="echoid-head655" xml:space="preserve">PROPOSITIO LXIII.</head>
          <p style="it">
            <s xml:id="echoid-s14473" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14474" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s14475" xml:space="preserve">ſig. </s>
            <s xml:id="echoid-s14476" xml:space="preserve">15. </s>
            <s xml:id="echoid-s14477" xml:space="preserve">Datis duobus Conis A B C, D E F gravi-
              <lb/>
            bus, diverſæ longitudinis & </s>
            <s xml:id="echoid-s14478" xml:space="preserve">non ſimilibus, quorum brevior A B </s>
          </p>
        </div>
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