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-div542" type="section" level="1" n="542">
          <p style="it">
            <s xml:id="echoid-s14478" xml:space="preserve">
              <pb o="589" file="0605" n="606" rhead="CORPORUM FIRMORUM."/>
            babeat angulum ſolidum C minorem, quam eſt longioris E D F an-
              <lb/>
            gulus F, ſitque ex C pondus P maximum ſuſpenſum, invenire
              <lb/>
            pondus Q maximum applicandum angulo ſolido F.</s>
            <s xml:id="echoid-s14479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14480" xml:space="preserve">Ponatur radius G A baſeos = a. </s>
            <s xml:id="echoid-s14481" xml:space="preserve">peripheria = c. </s>
            <s xml:id="echoid-s14482" xml:space="preserve">longitudo G C
              <lb/>
            = b. </s>
            <s xml:id="echoid-s14483" xml:space="preserve">pondus P = p, Radius baſeos H D = r, ejus circumferentia
              <lb/>
            = {cr/a}. </s>
            <s xml:id="echoid-s14484" xml:space="preserve">longitudo H F = l. </s>
            <s xml:id="echoid-s14485" xml:space="preserve">pondus Q quæſitum = x.</s>
            <s xml:id="echoid-s14486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14487" xml:space="preserve">Erit ſoliditas Coni A B C = {abc/6}. </s>
            <s xml:id="echoid-s14488" xml:space="preserve">ejus momentum ex gravitate
              <lb/>
            = {abbc/24}. </s>
            <s xml:id="echoid-s14489" xml:space="preserve">momentum ponderis ipſi appenſi = bp. </s>
            <s xml:id="echoid-s14490" xml:space="preserve">ſoliditas vero
              <lb/>
            Coni E D F = {crrl/6a} ejuſque momentum ex gravitate = {cllrr/24a}. </s>
            <s xml:id="echoid-s14491" xml:space="preserve">mo-
              <lb/>
            mentum ponderis appendendi = lx. </s>
            <s xml:id="echoid-s14492" xml:space="preserve">Cohærentia baſeos A B eſt ad
              <lb/>
            eam baſeos E D, uti 8a
              <emph style="super">3</emph>
            , ad 8r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14493" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14494" xml:space="preserve">Quia momenta gravitatum tam Conorum, quam ponderum ap-
              <lb/>
            penſorum debent ad Cohærentias eandem habere rationem, nam
              <lb/>
            uti pondus P eſt maximum, ita Q debet eſſe maximum, ordine-
              <lb/>
            tur hæc proportio.
              <lb/>
            </s>
            <s xml:id="echoid-s14495" xml:space="preserve">{abbc/24} + bp. </s>
            <s xml:id="echoid-s14496" xml:space="preserve">8a
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14497" xml:space="preserve">: {cllrr/24a} + lx, 8r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14498" xml:space="preserve">
              <lb/>
            unde erit x = {bbcr
              <emph style="super">3</emph>
            /24aal} + {bpr/a
              <emph style="super">3</emph>
            l} - {clrr/24a}.</s>
            <s xml:id="echoid-s14499" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div543" type="section" level="1" n="543">
          <head xml:id="echoid-head656" style="it" xml:space="preserve">De Conidibus Parabolicis.</head>
          <head xml:id="echoid-head657" xml:space="preserve">PROPOSITIO LXIV.</head>
          <p style="it">
            <s xml:id="echoid-s14500" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14501" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14502" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14503" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14504" xml:space="preserve">Sit Conois Parabolica A B C, & </s>
            <s xml:id="echoid-s14505" xml:space="preserve">portio ex ea
              <lb/>
            abſciſſa D B E, quarum axes ſint B F, B G, erit momentum ponderis
              <lb/>
            A B C ad momentum ponderis D B E uti Cubus ex F B, ad Cubum
              <lb/>
            ex G B.</s>
            <s xml:id="echoid-s14506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14507" xml:space="preserve">Vocetur C F, r. </s>
            <s xml:id="echoid-s14508" xml:space="preserve">peripheria ejus circuli c. </s>
            <s xml:id="echoid-s14509" xml:space="preserve">F B, a. </s>
            <s xml:id="echoid-s14510" xml:space="preserve">tum radius al-
              <lb/>
            terius circuli G E, b. </s>
            <s xml:id="echoid-s14511" xml:space="preserve">erit axis G B = {abb/rr}. </s>
            <s xml:id="echoid-s14512" xml:space="preserve">ex natura Parabolæ, &</s>
            <s xml:id="echoid-s14513" xml:space="preserve"/>
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