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-div551" type="section" level="1" n="551">
          <p style="it">
            <s xml:id="echoid-s14730" xml:space="preserve">
              <pb o="596" file="0612" n="613" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            Cohærentiam ſuam eandem rationem, quam D B E m?</s>
            <s xml:id="echoid-s14731" xml:space="preserve">mentum cum
              <lb/>
            ſuo pondere habet ſuam Cohærentiam.</s>
            <s xml:id="echoid-s14732" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14733" xml:space="preserve">Quantitatibus vocatis ut ante in Prop. </s>
            <s xml:id="echoid-s14734" xml:space="preserve">LXIX. </s>
            <s xml:id="echoid-s14735" xml:space="preserve">erit momentum
              <lb/>
            ex gravitate ſolidi D B E = {9/80} a a c r. </s>
            <s xml:id="echoid-s14736" xml:space="preserve">& </s>
            <s xml:id="echoid-s14737" xml:space="preserve">momentum ponderis = a p,
              <lb/>
            ratio Cohærentiæ = r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14738" xml:space="preserve">Ponatur ordinata quæſita in ſegmento
              <lb/>
            = y. </s>
            <s xml:id="echoid-s14739" xml:space="preserve">ea enim datâ invenitur abſciſia facile, quia ut
              <emph style="ol">C F</emph>
              <emph style="super">3</emph>
            ad
              <emph style="ol">G E</emph>
              <emph style="super">3</emph>
              <lb/>
            :</s>
            <s xml:id="echoid-s14740" xml:space="preserve">: F B, ad G B. </s>
            <s xml:id="echoid-s14741" xml:space="preserve">hinc etiam r
              <emph style="super">3</emph>
            , y
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14742" xml:space="preserve">: {a. </s>
            <s xml:id="echoid-s14743" xml:space="preserve">ay
              <emph style="super">3</emph>
            /r
              <emph style="super">3</emph>
            } = F B. </s>
            <s xml:id="echoid-s14744" xml:space="preserve">unde ſoliditas
              <lb/>
            A B C quæſitæ paraboloidis erit = {3 a c y
              <emph style="super">5</emph>
            /10 r
              <emph style="super">4</emph>
            .</s>
            <s xml:id="echoid-s14745" xml:space="preserve">} & </s>
            <s xml:id="echoid-s14746" xml:space="preserve">momentum = {9/80}
              <lb/>
            {a a c y
              <emph style="super">8</emph>
            /r
              <emph style="super">7</emph>
            .</s>
            <s xml:id="echoid-s14747" xml:space="preserve">} ordinentur nunc momenta & </s>
            <s xml:id="echoid-s14748" xml:space="preserve">Cohærentiæ in proportio-
              <lb/>
            nem, erit
              <lb/>
            {9/80} a a c r + a p. </s>
            <s xml:id="echoid-s14749" xml:space="preserve">r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14750" xml:space="preserve">: {9 a a c y
              <emph style="super">8</emph>
            . </s>
            <s xml:id="echoid-s14751" xml:space="preserve">y
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14752" xml:space="preserve">/80 r
              <emph style="super">7</emph>
            }
              <lb/>
            Ex quibus eruitur y = {5r
              <emph style="super">5</emph>
            +p r
              <emph style="super">4</emph>
            /a c.</s>
            <s xml:id="echoid-s14753" xml:space="preserve">}</s>
          </p>
        </div>
        <div xml:id="echoid-div552" type="section" level="1" n="552">
          <head xml:id="echoid-head666" xml:space="preserve">PROPOSITIO LXXIII.</head>
          <p style="it">
            <s xml:id="echoid-s14754" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14755" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14756" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14757" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14758" xml:space="preserve">In Conoide Parabolica quarti ordinis
              <lb/>
            A B C, ejusque ſegmento D B E, exponere quænam ſit Proportio
              <lb/>
            momentorum ex propria gravitate ad Cobærentias.</s>
            <s xml:id="echoid-s14759" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14760" xml:space="preserve">Vocetur C F, r. </s>
            <s xml:id="echoid-s14761" xml:space="preserve">F B, a. </s>
            <s xml:id="echoid-s14762" xml:space="preserve">Peripheria circuli baſeos = c. </s>
            <s xml:id="echoid-s14763" xml:space="preserve">& </s>
            <s xml:id="echoid-s14764" xml:space="preserve">ſit pa-
              <lb/>
            rabolæ natura 1 x
              <unsure/>
            = y
              <emph style="super">4</emph>
            . </s>
            <s xml:id="echoid-s14765" xml:space="preserve">ſit G E = b. </s>
            <s xml:id="echoid-s14766" xml:space="preserve">peripheria = {b c/r}. </s>
            <s xml:id="echoid-s14767" xml:space="preserve">G B
              <lb/>
            abſciſſa = {a b
              <emph style="super">4</emph>
            /r
              <emph style="super">4</emph>
            }</s>
          </p>
          <p>
            <s xml:id="echoid-s14768" xml:space="preserve">Erit ſoliditas Parabolæ A B C = {1/3}a c r. </s>
            <s xml:id="echoid-s14769" xml:space="preserve">quia in omni Parabola,
              <lb/>
            poſito y
              <emph style="super">m</emph>
            = x. </s>
            <s xml:id="echoid-s14770" xml:space="preserve">ſoliditas eſt = {m/2m+4} a c r. </s>
            <s xml:id="echoid-s14771" xml:space="preserve">Centrum gravitatis
              <lb/>
            deinde inveſtigetur, diſtat hoc etiam in omni Parabola a vertice B,
              <lb/>
            quantitate {m+2/2m+2} a. </s>
            <s xml:id="echoid-s14772" xml:space="preserve">adeoque in caſu propoſito diſtabit centrum
              <lb/>
            gravitatis a puncto G quantitate {2/8} a. </s>
            <s xml:id="echoid-s14773" xml:space="preserve">per quam multiplicata </s>
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