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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        <div xml:id="echoid-div569" type="section" level="1" n="569">
          <p>
            <s xml:id="echoid-s15185" xml:space="preserve">
              <pb o="608" file="0624" n="625" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            ſoliditas hemisphærii A B C erit = {crr:</s>
            <s xml:id="echoid-s15186" xml:space="preserve">/3}. </s>
            <s xml:id="echoid-s15187" xml:space="preserve">abeſt quoque in hemisphæ-
              <lb/>
            rio centrum gravitatis {3/8} r ab A C. </s>
            <s xml:id="echoid-s15188" xml:space="preserve">adeoque erit hemisphærii
              <lb/>
            momentum = {cr
              <emph style="super">3</emph>
            /8}. </s>
            <s xml:id="echoid-s15189" xml:space="preserve">quod eſt duplo minus quam momentum Cy-
              <lb/>
            lindri.</s>
            <s xml:id="echoid-s15190" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div570" type="section" level="1" n="570">
          <head xml:id="echoid-head686" xml:space="preserve">PROPOSITIO XCI.</head>
          <p style="it">
            <s xml:id="echoid-s15191" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15192" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15193" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15194" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15195" xml:space="preserve">Determinare Cohærentiam hemisphærii
              <lb/>
            A B C & </s>
            <s xml:id="echoid-s15196" xml:space="preserve">ſegmenti ejus F B E, cujus baſis parallela baſi A D C. </s>
            <s xml:id="echoid-s15197" xml:space="preserve">po-
              <lb/>
            ſitis his baſibus parieti affixis.</s>
            <s xml:id="echoid-s15198" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15199" xml:space="preserve">Sunt hæ Cohærentiæ inter ſe, uti Cubi diametrorum in baſibus
              <lb/>
            A C, F E. </s>
            <s xml:id="echoid-s15200" xml:space="preserve">ut autem magnitudines horum cuborum noſcantur, vo-
              <lb/>
            cetur A D aut D B, r. </s>
            <s xml:id="echoid-s15201" xml:space="preserve">B G ſit = x. </s>
            <s xml:id="echoid-s15202" xml:space="preserve">eritque F G
              <emph style="super">q</emph>
            = 2rx-xx, unde
              <lb/>
            Cubus F G = 2rx-xx X 2rx - xx. </s>
            <s xml:id="echoid-s15203" xml:space="preserve">& </s>
            <s xml:id="echoid-s15204" xml:space="preserve">Cubus A D = r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s15205" xml:space="preserve">qua-
              <lb/>
            re Cohærentia baſeos A D C eſt ad eam baſeos F G E uti r
              <emph style="super">3</emph>
            ad
              <lb/>
            2rx - xx X 2rx - xx.</s>
            <s xml:id="echoid-s15206" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div571" type="section" level="1" n="571">
          <head xml:id="echoid-head687" xml:space="preserve">PROPOSITIO XCII.</head>
          <p style="it">
            <s xml:id="echoid-s15207" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15208" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15209" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15210" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15211" xml:space="preserve">Dati Hemispbærii ABC, & </s>
            <s xml:id="echoid-s15212" xml:space="preserve">ſegmenti
              <lb/>
            FBE invenire momenta ex gravitate oriunda, poſitis baſibus
              <lb/>
            A C, F E parieti ad horizontem perpendiculari affixis.</s>
            <s xml:id="echoid-s15213" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15214" xml:space="preserve">Vocetur radius circuli A D, r. </s>
            <s xml:id="echoid-s15215" xml:space="preserve">circumferentia circuli c. </s>
            <s xml:id="echoid-s15216" xml:space="preserve">erit mo.
              <lb/>
            </s>
            <s xml:id="echoid-s15217" xml:space="preserve">mentum Hemisphærii = {cr
              <emph style="super">3</emph>
            /8} per Propoſitionem XC: </s>
            <s xml:id="echoid-s15218" xml:space="preserve">Ponatur
              <lb/>
            B G = x. </s>
            <s xml:id="echoid-s15219" xml:space="preserve">& </s>
            <s xml:id="echoid-s15220" xml:space="preserve">G F = y. </s>
            <s xml:id="echoid-s15221" xml:space="preserve">ſumatur Gg pars infinite parva, erit
              <lb/>
            hæc = dx, ut proinde habeatur peripheria circuli deſcripti â
              <lb/>
            puncto F. </s>
            <s xml:id="echoid-s15222" xml:space="preserve">fiat ut r, c:</s>
            <s xml:id="echoid-s15223" xml:space="preserve">: y. </s>
            <s xml:id="echoid-s15224" xml:space="preserve">{cy/r} = peripheriæ, quæ ductain {1/2}y, dabit
              <lb/>
            {cyy/2r} = circulo; </s>
            <s xml:id="echoid-s15225" xml:space="preserve">hic multiplicatus per d x, dabit {cyvdx/2r} differentiale
              <lb/>
            ſolidum; </s>
            <s xml:id="echoid-s15226" xml:space="preserve">verum ex natura ſphæræ eſt yy = 2rx - xx unde pro yy
              <lb/>
            ſubſtituendo hunc valorem, fit{cyydx/2r} = cxdx - {cxxdx/2r}, </s>
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