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

Table of Notes

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          <pb o="607" file="0623" n="624" rhead="CORPORUM FIRMORUM."/>
          <p>
            <s xml:id="echoid-s15154" xml:space="preserve">Vocetur C A, a. </s>
            <s xml:id="echoid-s15155" xml:space="preserve">CD, b. </s>
            <s xml:id="echoid-s15156" xml:space="preserve">circumferentia deſcripta a puncto B
              <lb/>
            ſit c. </s>
            <s xml:id="echoid-s15157" xml:space="preserve">invenietur ſoliditas corporis generati = {bcr/3}. </s>
            <s xml:id="echoid-s15158" xml:space="preserve">centrum gravi-
              <lb/>
            tatis in axe CD diſtat a puncto D = {7/16} D C = {7/16}b. </s>
            <s xml:id="echoid-s15159" xml:space="preserve">quare momen-
              <lb/>
            tum ex gravitate erit {7bbcr/48}. </s>
            <s xml:id="echoid-s15160" xml:space="preserve">quia autem D B eſt = 2a
              <emph style="super">a</emph>
              <lb/>
            erit Cohærentia = 8 a
              <emph style="super">3</emph>
            2.</s>
            <s xml:id="echoid-s15161" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div568" type="section" level="1" n="568">
          <head xml:id="echoid-head683" xml:space="preserve">PROPOSITIO LXXXIX.</head>
          <p>
            <s xml:id="echoid-s15162" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15163" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15164" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15165" xml:space="preserve">12. </s>
            <s xml:id="echoid-s15166" xml:space="preserve">Sit ſolidum Hyperbolicum ABCE, in quo
              <lb/>
            ſegmentum LIKM baſi parallelum, erit Cohærentia ſolidi ABC
              <lb/>
            ad eam ſegmenti LIKMC, utirectangulumex GC, GH ad rectan-
              <lb/>
            gulum ex NC, NH.</s>
            <s xml:id="echoid-s15167" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15168" xml:space="preserve">Sit C H axis Hyperbolæ primus, quo ducto erit Cohærentia
              <lb/>
            baſeos A B F E ad Cohærentiam baſeos LIKM, in ratione dupli-
              <lb/>
            cata E A ad LI. </s>
            <s xml:id="echoid-s15169" xml:space="preserve">ſed eſt quadratum E A ad quadratum LI, uti re-
              <lb/>
            ctangulum ex abſciſſa G C X per G H, ad rectangulum ex abſciſſa-
              <lb/>
            N C in N H. </s>
            <s xml:id="echoid-s15170" xml:space="preserve">quare patet propoſitum.</s>
            <s xml:id="echoid-s15171" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div569" type="section" level="1" n="569">
          <head xml:id="echoid-head684" xml:space="preserve">De Hemisphæriis.</head>
          <head xml:id="echoid-head685" xml:space="preserve">PROPOSITIO XC.</head>
          <p>
            <s xml:id="echoid-s15172" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15173" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15174" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15175" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15176" xml:space="preserve">Momentum Hemisphærii inſcripti cylindro,
              <lb/>
            baſi affixa parieti, eſt dimidium momenti ipſius Cylindri habentis
              <lb/>
            eandem baſin & </s>
            <s xml:id="echoid-s15177" xml:space="preserve">altitudinem.</s>
            <s xml:id="echoid-s15178" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15179" xml:space="preserve">Vocetur enim radius A D baſeos, r. </s>
            <s xml:id="echoid-s15180" xml:space="preserve">& </s>
            <s xml:id="echoid-s15181" xml:space="preserve">peripheria circuli, c. </s>
            <s xml:id="echoid-s15182" xml:space="preserve">erit
              <lb/>
            ipſa baſis = {cr/2} hæc multiplicata per A E = r. </s>
            <s xml:id="echoid-s15183" xml:space="preserve">dat ſoliditatem Cylin-
              <lb/>
            dri circumſcripti C A E = {crr/2}, cujus centrum gravitatis eſt in me-
              <lb/>
            dio ſive in {1/2} r. </s>
            <s xml:id="echoid-s15184" xml:space="preserve">adeoque erit momentum cylindri ={cr
              <emph style="super">3</emph>
            /4}. </s>
            <s xml:id="echoid-s15185" xml:space="preserve">Eſt au-
              <lb/>
            tem ſoliditas Cylindri ad eam hemisphærii, uti 3 ad 2, </s>
          </p>
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