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

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[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)
[641.] EXPERIMENTUM CCXXVI.
Page: 672 (655)
[642.] EXPERIMENTUM CCXXVII.
Page: 672 (655)
[643.] EXPERIMENTUM CCXXVIII.
Page: 673 (656)
[644.] EXPERIMENTUM CCXXIX.
Page: 673 (656)
[645.] EXPERIMENTUM CCXXX.
Page: 673 (656)
[646.] EXPERIMENTUM CCXXXI.
Page: 673 (656)
[647.] EXPERIMENTUM CCXXXII.
Page: 673 (656)
[648.] EXPERIMENTUM CCXXXIII.
Page: 673 (656)
[649.] EXPERIMENTUM CCXXXIV.
Page: 673 (656)
[650.] EXPERIMENTUM CCXXXV.
Page: 674 (657)
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            <s xml:id="echoid-s13932" xml:space="preserve">Vocetur radius baſeos A B, r, peripheria c. </s>
            <s xml:id="echoid-s13933" xml:space="preserve">longitudo A D, b. </s>
            <s xml:id="echoid-s13934" xml:space="preserve">lon-
              <lb/>
            gitudo E H, l. </s>
            <s xml:id="echoid-s13935" xml:space="preserve">radius baſeos E F, x.</s>
            <s xml:id="echoid-s13936" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13937" xml:space="preserve">Erit cylindrus A B C D = {1/2} b c r. </s>
            <s xml:id="echoid-s13938" xml:space="preserve">& </s>
            <s xml:id="echoid-s13939" xml:space="preserve">momentum ejus = {1/4} b b c r.
              <lb/>
            </s>
            <s xml:id="echoid-s13940" xml:space="preserve">Cohærentia 8 r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13941" xml:space="preserve">ut ſoliditas cylindri E F G H habeatur, pone
              <lb/>
            r.</s>
            <s xml:id="echoid-s13942" xml:space="preserve">c:</s>
            <s xml:id="echoid-s13943" xml:space="preserve">: x. </s>
            <s xml:id="echoid-s13944" xml:space="preserve">{c x.</s>
            <s xml:id="echoid-s13945" xml:space="preserve">/r} peripheria baſeos, unde {1/2} {c x x/r} = baſi, ſoliditas = {1/2} {c x x l.</s>
            <s xml:id="echoid-s13946" xml:space="preserve">/r}
              <lb/>
            & </s>
            <s xml:id="echoid-s13947" xml:space="preserve">momentum ex gravitate = {1/4} {c l l x x.</s>
            <s xml:id="echoid-s13948" xml:space="preserve">/r} Cohærentia baſeos E F uti
              <lb/>
            8 x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13949" xml:space="preserve">quarepoſtulatur proportio 8 x
              <emph style="super">3</emph>
            , {1/4} {c l l x x/r}:</s>
            <s xml:id="echoid-s13950" xml:space="preserve">: 8 r
              <emph style="super">3</emph>
            , {1/4} b b c r. </s>
            <s xml:id="echoid-s13951" xml:space="preserve">
              <lb/>
            unde x = {l l r/b b}</s>
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          <head xml:id="echoid-head641" xml:space="preserve">PROPOSITIO LI.</head>
          <p style="it">
            <s xml:id="echoid-s13952" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13953" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s13954" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13955" xml:space="preserve">37. </s>
            <s xml:id="echoid-s13956" xml:space="preserve">Dato Cylindro A B C D & </s>
            <s xml:id="echoid-s13957" xml:space="preserve">pondere I, quo-
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            rum momenta ex gravitate ad Cohærentiam habeant quamcunque
              <lb/>
            rationem, invenire alium cylindrum datæ longitudinis, in quo mo-
              <lb/>
            mentum gravitatis ad ſuam Cohærentiam habeat eandem rationem.</s>
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            <s xml:id="echoid-s13959" xml:space="preserve">Vocetur radius baſeos A B, r. </s>
            <s xml:id="echoid-s13960" xml:space="preserve">peripheria c. </s>
            <s xml:id="echoid-s13961" xml:space="preserve">longitudo A D, b. </s>
            <s xml:id="echoid-s13962" xml:space="preserve">pon-
              <lb/>
            dus I, p. </s>
            <s xml:id="echoid-s13963" xml:space="preserve">erit momentum Cylindri ex gravitate, una cum momento
              <lb/>
            ponderis I = {1/4} b b c r + p b. </s>
            <s xml:id="echoid-s13964" xml:space="preserve">Cohærentia ut 8 r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13965" xml:space="preserve">Vocetur E H, d.
              <lb/>
            </s>
            <s xml:id="echoid-s13966" xml:space="preserve">radius baſeos E F, x. </s>
            <s xml:id="echoid-s13967" xml:space="preserve">erit ejus peripheria = {c x/r}. </s>
            <s xml:id="echoid-s13968" xml:space="preserve">baſis = {1/2} {c x x.</s>
            <s xml:id="echoid-s13969" xml:space="preserve">/r} & </s>
            <s xml:id="echoid-s13970" xml:space="preserve">ſo-
              <lb/>
            liditas = {1/2} {c d x x.</s>
            <s xml:id="echoid-s13971" xml:space="preserve">/r} unde momentum eſt = {1/4} {c d d x x.</s>
            <s xml:id="echoid-s13972" xml:space="preserve">/r} & </s>
            <s xml:id="echoid-s13973" xml:space="preserve">Cohæren-
              <lb/>
            tia ut 8 x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13974" xml:space="preserve">hinc ſtabunt quantitates ordinatæ in proportionem
              <lb/>
            {1/4} {c d d x x,/r} 8 x
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s13975" xml:space="preserve">: {1/4} b b c r + b p. </s>
            <s xml:id="echoid-s13976" xml:space="preserve">8 r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13977" xml:space="preserve">
              <lb/>
            unde x ={{1/4} c d d r r.</s>
            <s xml:id="echoid-s13978" xml:space="preserve">/{1/4} b b c r + b p}</s>
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