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 contents

< >
[611.] PROPOSITIO CVIII.
Page: 650 (633)
[612.] PROPOSITIO CIX.
Page: 650 (633)
[613.] PROPOSITIO CX.
Page: 651 (634)
[614.] PROPOSITIO CXI.
Page: 652 (635)
[615.] PROPOSITIO CXII.
Page: 653 (636)
[616.] PROPOSITIO CXIII.
Page: 653 (636)
[617.] PROPOSITIO CXIV.
Page: 654 (637)
[618.] PROPOSITIO CXV.
Page: 654 (637)
[619.] PROPOSITIO CXVI.
Page: 655 (638)
[620.] PROPOSITIO CXVII.
Page: 655 (638)
[621.] CAPUT OCTAVUM. De Cohærentia ſolidorum utrimque a foramine arcto exceptorum.
Page: 656 (639)
[622.] EXPERIMENTUM CCIX.
Page: 657 (640)
[623.] EXPERIMENTUM CCX.
Page: 657 (640)
[624.] EXPERIMENTUM CCXI.
Page: 658 (641)
[625.] EXPERIMENTUM CCXII.
Page: 658 (641)
[626.] EXPERIMENTUM CCXIII.
Page: 659 (642)
[627.] EXPERIMENTUM CCXIV.
Page: 659 (642)
[628.] EXPERIMENTUM CCXV.
Page: 659 (642)
[629.] EXPERIMENTUM CCXVI.
Page: 660 (643)
[630.] EXPERIMENTUM CCXVII.
Page: 660 (643)
[631.] EXPERIMENTUM CCXVIII.
Page: 660 (643)
[632.] EXPERIMENTUM CCXIX.
Page: 660 (643)
[633.] EXPERIMENTUM CCXX.
Page: 661 (644)
[634.] TABULA
Page: 664 (647)
[635.] EXPERIMENTUM CCXXI.
Page: 668 (651)
[636.] CAPUT NONUM. De Cohærentia corporum compreſſorum.
Page: 669 (652)
[637.] EXPERIMENTUM CCXXII.
Page: 672 (655)
[638.] EXPERIMENTUM CCXXIII.
Page: 672 (655)
[639.] EXPERIMENTUM CCXXIV.
Page: 672 (655)
[640.] EXPERIMENTUM CCXXV.
Page: 672 (655)
< >
page |< < (601) of 795 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div557" type="section" level="1" n="557">
          <p>
            <s xml:id="echoid-s14932" xml:space="preserve">
              <pb o="601" file="0617" n="618" rhead="CORPORUM FIRMORUM."/>
            quare momentum ponderis P habet ad utriuſque ſolidi Cohæren-
              <lb/>
            tiam eandem rationem.</s>
            <s xml:id="echoid-s14933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14934" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14935" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14936" xml:space="preserve">Si dimidii ſolidi parabolici E B A M E ſuperficiei ſupe-
              <lb/>
            riori E B E imponatur aliquod parallelopipedum grave, aut pon-
              <lb/>
            dus æquabiliter ſuper eam diſperſum, erit uti quantitas ponderis
              <lb/>
            ſupra B E, ad eam ſupra portionem C E E, ita Cohærentia ſolidi
              <lb/>
            E A B E ad Cohærentiam ſolidi E D C E: </s>
            <s xml:id="echoid-s14937" xml:space="preserve">quamobrem erit Cohæren-
              <lb/>
            tia proportionalis ponderi impoſito, & </s>
            <s xml:id="echoid-s14938" xml:space="preserve">ſolidum æquabilis Cohæren-
              <lb/>
            tiæ per totam longitudinem.</s>
            <s xml:id="echoid-s14939" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div558" type="section" level="1" n="558">
          <head xml:id="echoid-head672" xml:space="preserve">PROPOSITIO LXXIX.</head>
          <p>
            <s xml:id="echoid-s14940" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14941" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14942" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14943" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14944" xml:space="preserve">Solidi Parabolici F O E M A E momentum
              <lb/>
            ex gravitate ad Cohærentiam baſeos A F O M majorem rationem
              <lb/>
            habet, quam portionis D G P E H momentum ex gravitate ad Co-
              <lb/>
            hærentiam baſeos D G P H.</s>
            <s xml:id="echoid-s14945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14946" xml:space="preserve">Vocetur F A, a. </s>
            <s xml:id="echoid-s14947" xml:space="preserve">E B, b. </s>
            <s xml:id="echoid-s14948" xml:space="preserve">D G, c. </s>
            <s xml:id="echoid-s14949" xml:space="preserve">erit C E = {bcc.</s>
            <s xml:id="echoid-s14950" xml:space="preserve">/aa} Sit F O = d.
              <lb/>
            </s>
            <s xml:id="echoid-s14951" xml:space="preserve">erit ſoliditas corporis A F E = {2/3} a b d. </s>
            <s xml:id="echoid-s14952" xml:space="preserve">& </s>
            <s xml:id="echoid-s14953" xml:space="preserve">ſoliditas corporis D G P E
              <lb/>
            = 2{b c
              <emph style="super">3</emph>
            d.</s>
            <s xml:id="echoid-s14954" xml:space="preserve">/3 aa} diſtat autem centrum gravitatis in plano parabolico
              <lb/>
            A F E {2/5} b, a puncto B in axe B E, adeoque diſtabit tantundem in
              <lb/>
            ſegmenti E E B medio a baſi A M F O. </s>
            <s xml:id="echoid-s14955" xml:space="preserve">hinc erit momentum
              <lb/>
            ſolidi Parabolici A F O E M = {4/15} a b b d. </s>
            <s xml:id="echoid-s14956" xml:space="preserve">& </s>
            <s xml:id="echoid-s14957" xml:space="preserve">momentum ſolidi
              <lb/>
            D G P E = {4 b b c
              <emph style="super">5</emph>
            d.</s>
            <s xml:id="echoid-s14958" xml:space="preserve">/15 a
              <emph style="super">4</emph>
            } Cohærentia baſeos ſolidi A F O E M eſt = a a d. </s>
            <s xml:id="echoid-s14959" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s14960" xml:space="preserve">Cohærentia ſolidi D G P E H = c c d. </s>
            <s xml:id="echoid-s14961" xml:space="preserve">quare erit momen-
              <lb/>
            tum ſolidi A F O E M ad ſuam Cohærentiam, uti {4/15} a b b d. </s>
            <s xml:id="echoid-s14962" xml:space="preserve">
              <lb/>
            ad a a d. </s>
            <s xml:id="echoid-s14963" xml:space="preserve">= {4/15} b b, ad a. </s>
            <s xml:id="echoid-s14964" xml:space="preserve">Et Momentum ſolidi D G P E H ad
              <lb/>
            ſuam Cohærentiam uti 4{b b c
              <emph style="super">5</emph>
            d/15 a
              <emph style="super">4</emph>
            } ad c c d. </s>
            <s xml:id="echoid-s14965" xml:space="preserve">= {4/15} b b c
              <emph style="super">3</emph>
            , ad a
              <emph style="super">4</emph>
            . </s>
            <s xml:id="echoid-s14966" xml:space="preserve">Sed
              <lb/>
            eſt b b ad a in majori ratione, quam b b c
              <emph style="super">3</emph>
            ad a
              <emph style="super">4</emph>
            . </s>
            <s xml:id="echoid-s14967" xml:space="preserve">quia a eſt major
              <lb/>
            quam c. </s>
            <s xml:id="echoid-s14968" xml:space="preserve">Ergo eſt momentum ex gravitate in ſolido A F E O M ad
              <lb/>
            ſuam Cohærentiam in majori ratione, quam eſt momentum gra-
              <lb/>
            vitatis in ſolido D G P H ad ſuam.</s>
            <s xml:id="echoid-s14969" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum