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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          <pb o="587" file="0603" n="604" rhead="CORPORUM FIRMORUM."/>
          <p>
            <s xml:id="echoid-s14417" xml:space="preserve">Momentum coni integri B G A eſt = {aabb/12}. </s>
            <s xml:id="echoid-s14418" xml:space="preserve">& </s>
            <s xml:id="echoid-s14419" xml:space="preserve">pondere appenſo
              <lb/>
            ex G vocato p. </s>
            <s xml:id="echoid-s14420" xml:space="preserve">cujus momentum eſt = pb. </s>
            <s xml:id="echoid-s14421" xml:space="preserve">erit momentorum
              <lb/>
            horum ſumma = {aabb/12}+pb. </s>
            <s xml:id="echoid-s14422" xml:space="preserve">quia momenta hæc, tum momenta
              <lb/>
            coni truncati ſimul cum pondere incognito ad Cohærentiam baſeos
              <lb/>
            ejuſdem A B eandem debent habere rationem, debent momenta
              <lb/>
            eſſe æqualia, adeoque {aabb/12}+pb = 4aab-{4bc
              <emph style="super">3</emph>
            -9a
              <emph style="super">3</emph>
            b/4aa-4c
              <emph style="super">3</emph>
            }
              <lb/>
            X {aab/3}-{bc
              <emph style="super">3</emph>
            /3a + bx - {bcx/a} unde eruitur quantitas incognita
              <lb/>
            x = {aabb/12} + pb - {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}/b-{bc/a}}.</s>
            <s xml:id="echoid-s14423" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div540" type="section" level="1" n="540">
          <head xml:id="echoid-head653" xml:space="preserve">PROPOSITIO LXI.</head>
          <p style="it">
            <s xml:id="echoid-s14424" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14425" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s14426" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14427" xml:space="preserve">13. </s>
            <s xml:id="echoid-s14428" xml:space="preserve">Datis duobus Conis A B G, C D K gravibus,
              <lb/>
            ejuſdem materiæ & </s>
            <s xml:id="echoid-s14429" xml:space="preserve">æqualium baſium, ſed diverſæ longitudinis,
              <lb/>
            datoque maximo pondere Q appenſo ex longiſſimo cono A B G, in-
              <lb/>
            venire pondus P, appendendum ex vertice K brevioris coni, quod
              <lb/>
            etiam ſit maximum.</s>
            <s xml:id="echoid-s14430" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14431" xml:space="preserve">Vocetur A B, 2a. </s>
            <s xml:id="echoid-s14432" xml:space="preserve">peripheria baſeos, c. </s>
            <s xml:id="echoid-s14433" xml:space="preserve">M G, b. </s>
            <s xml:id="echoid-s14434" xml:space="preserve">Q pondus, q. </s>
            <s xml:id="echoid-s14435" xml:space="preserve">C D
              <lb/>
            2a. </s>
            <s xml:id="echoid-s14436" xml:space="preserve">K L, d. </s>
            <s xml:id="echoid-s14437" xml:space="preserve">pondus quæſitum P ſit = x.</s>
            <s xml:id="echoid-s14438" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14439" xml:space="preserve">Erit ſoliditas Coni A B G = {acb/6}. </s>
            <s xml:id="echoid-s14440" xml:space="preserve">ejuſque momentum ex gravitate
              <lb/>
            = {acbb/24}. </s>
            <s xml:id="echoid-s14441" xml:space="preserve">momentum ponderis Q = qb. </s>
            <s xml:id="echoid-s14442" xml:space="preserve">ſoliditas coni brevioris
              <lb/>
            ={acd/6} ejus momentum {acdd/24} momentum ponderis P = d x & </s>
            <s xml:id="echoid-s14443" xml:space="preserve">
              <lb/>
            quia baſes conorum ponuntur æquales, erunt Cohærentiæ æquales,
              <lb/>
            adeoque cum momentum in uno cono, quod oritur ex propria </s>
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