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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          <p>
            <s xml:id="echoid-s13477" xml:space="preserve">
              <pb o="563" file="0579" n="580" rhead="CORPORUM FIRMORUM."/>
            tudo data a k = e, latitudo e o = f. </s>
            <s xml:id="echoid-s13478" xml:space="preserve">altitudo a e = x pondus p
              <lb/>
            = p.</s>
            <s xml:id="echoid-s13479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13480" xml:space="preserve">Tum erit momentum parallelopipedi A E F D ex gravitate, =
              <lb/>
            {1/2} a b d d, & </s>
            <s xml:id="echoid-s13481" xml:space="preserve">momentum ponderis ſibiannexi = o d: </s>
            <s xml:id="echoid-s13482" xml:space="preserve">Cohærentia vero
              <lb/>
            = a a b. </s>
            <s xml:id="echoid-s13483" xml:space="preserve">præterea erit momentum ex gravitate parallelopipedi, a e o k,
              <lb/>
            = {1/2} e e f x. </s>
            <s xml:id="echoid-s13484" xml:space="preserve">& </s>
            <s xml:id="echoid-s13485" xml:space="preserve">momentum ponderis P appenſi = e p. </s>
            <s xml:id="echoid-s13486" xml:space="preserve">Cohærentia
              <lb/>
            = x x f. </s>
            <s xml:id="echoid-s13487" xml:space="preserve">proponitur vero {1/2} a b d d + d o, a a b:</s>
            <s xml:id="echoid-s13488" xml:space="preserve">: {1/2} e e f x + e p. </s>
            <s xml:id="echoid-s13489" xml:space="preserve">x x f
              <lb/>
            idcirco {1/2} a b d d f x x + d f o x x = {1/2} a a b e e f x + a a b e p tranſpoſito-
              <lb/>
            que {1/2} a a b e e f x. </s>
            <s xml:id="echoid-s13490" xml:space="preserve">fit {1/2} a b d d f x x + d f o x x - {1/2} a a b e e f x = a a b e p.
              <lb/>
            </s>
            <s xml:id="echoid-s13491" xml:space="preserve">factaque diviſione per {1/2} a b d d f + d f o
              <lb/>
            fit x x - {{1/2} a a b e e f x/{1/2} a b d d f + d f o} = {a a b e p/{1/2} a b d d f + d f o}
              <lb/>
            additiſque {{1/16} a
              <emph style="super">4</emph>
            b b e
              <emph style="super">4</emph>
            f f/{1/16} a a b b d
              <emph style="super">4</emph>
            f f+{1/4} a b d
              <emph style="super">3</emph>
            f o + {1/4} d d o o f f}. </s>
            <s xml:id="echoid-s13492" xml:space="preserve">
              <lb/>
            erit x x - {{1/2} a a b e e f x/{1/2} a b d d f + d f o} + {{1/16} a
              <emph style="super">4</emph>
            b b e
              <emph style="super">4</emph>
            f f/{1/16} a a b b d
              <emph style="super">4</emph>
            f f + {1/4} a b d
              <emph style="super">3</emph>
            f o + {1/4} d d o o f f}
              <lb/>
            = {a a b e p/{1/2} a b d d f + d f o.</s>
            <s xml:id="echoid-s13493" xml:space="preserve">} + {{1/16} a
              <emph style="super">4</emph>
            b b e
              <emph style="super">4</emph>
            f f/{1/16} a a b b d
              <emph style="super">4</emph>
            f f + {1/4} a b d
              <emph style="super">3</emph>
            f o + {1/4} d d f f o}
              <lb/>
            atque utrimque extrahendo radicem
              <lb/>
            x - {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} = {a a b e p/{1/2} a b d d f + d f o.</s>
            <s xml:id="echoid-s13494" xml:space="preserve">} + {{1/16} a
              <emph style="super">4</emph>
            b b e
              <emph style="super">4</emph>
            f f/{1/16} a a b b d
              <emph style="super">4</emph>
            f f + {1/4} a b d
              <emph style="super">3</emph>
            f o + {1/4} d d f f o o}
              <lb/>
            tranſpoſitisque - {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} habetur ſola quantitas
              <lb/>
            x = {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} + {a a b e p/{1/2} a b d d f + {1/2} d f o}. </s>
            <s xml:id="echoid-s13495" xml:space="preserve">+ {{1/16} a
              <emph style="super">4</emph>
            b b e
              <emph style="super">4</emph>
            f f/{1/16} a a b b d
              <emph style="super">4</emph>
            f f + {1/4} a b d
              <emph style="super">3</emph>
            f o + {1/4} d d f f o o.</s>
            <s xml:id="echoid-s13496" xml:space="preserve">}.</s>
            <s xml:id="echoid-s13497" xml:space="preserve"/>
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        <div xml:id="echoid-div513" type="section" level="1" n="513">
          <head xml:id="echoid-head625" xml:space="preserve">PROPOSITIO XXXV.</head>
          <p style="it">
            <s xml:id="echoid-s13498" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13499" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s13500" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13501" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13502" xml:space="preserve">Dato parallelopipedo A B C D, in quo gravita-
              <lb/>
            tis momentum, una cum momento ponderis dati H pendentis ex D,
              <lb/>
            ad Cohærentiam ſuam habeat quamlibet rationem; </s>
            <s xml:id="echoid-s13503" xml:space="preserve">ad rectam da-
              <lb/>
            tam I K, applicare aliud parallelopipedum, æquale A B C D, </s>
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