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-div549" type="section" level="1" n="549">
          <pb o="595" file="0611" n="612" rhead="CORPORUM FIRMORUM."/>
          <p>
            <s xml:id="echoid-s14699" xml:space="preserve">Nam in Parabola Cubica eſt B G. </s>
            <s xml:id="echoid-s14700" xml:space="preserve">B F:</s>
            <s xml:id="echoid-s14701" xml:space="preserve">: D E
              <emph style="super">3</emph>
            ,
              <emph style="ol">AC</emph>
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14702" xml:space="preserve">ſed ut
              <lb/>
              <emph style="ol">DE</emph>
              <emph style="super">3</emph>
            ad
              <emph style="ol">AC</emph>
              <emph style="super">3</emph>
            , ita Cohærentia baſeos D G E ad Cohærentiam ba-
              <lb/>
            ſeos A F C. </s>
            <s xml:id="echoid-s14703" xml:space="preserve">adeoque ſunt hæ Cohærentiæ uti B G ad B F; </s>
            <s xml:id="echoid-s14704" xml:space="preserve">eſt au-
              <lb/>
            tem momentum ponderis P pendentis ex longitudine B G, ad mo-
              <lb/>
            mentum ponderis P pendentis ex longitudine B F, uti B G ad B F,
              <lb/>
            quare Cohærentiæ baſium, ſunt inter ſe uti momenta ponderis P,
              <lb/>
            adeoque erit hoc ſolidum Parabolicum ubivis æqualis Cohærentiæ.</s>
            <s xml:id="echoid-s14705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14706" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14707" xml:space="preserve">Idem verum erit de dimidio ſolido parabolico Cubico
              <lb/>
            C F B E: </s>
            <s xml:id="echoid-s14708" xml:space="preserve">ſi ideo in ſuperficie ſuperiori F G B oneretur æquabiliter
              <lb/>
            pondere, erit id pondus ſupra F B ad pondus ſupra G B, uti eſt F B
              <lb/>
            ad G B, hoc eſt uti Cohærentia baſeos C F ad eam baſeos G E.</s>
            <s xml:id="echoid-s14709" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div550" type="section" level="1" n="550">
          <head xml:id="echoid-head664" xml:space="preserve">PROPOSITIO LXXI.</head>
          <p style="it">
            <s xml:id="echoid-s14710" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14711" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14712" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14713" xml:space="preserve">I. </s>
            <s xml:id="echoid-s14714" xml:space="preserve">Data Conoide Cubica parabolica A B C,
              <lb/>
            ejuſque dato ſegmento D B E, una cum appenſo pondere P maximo,
              <lb/>
            quod geri poteſt ex D B E, invenire pondus ex vertice E Conoidis
              <lb/>
            A B C ſuſpendendum, quod ad ſuam Cobærentiam eandem bæbeat
              <lb/>
            rationem ac pondus P cum gravitate D B E ad ſuam.</s>
            <s xml:id="echoid-s14715" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14716" xml:space="preserve">Quantitatibus deſignatis ut in Propoſitione LXIX, erit momen-
              <lb/>
            tum ex gravitate Parabolæ D B E una cum momento ponderis P
              <lb/>
            = {9aacd
              <emph style="super">8</emph>
            /80r
              <emph style="super">7</emph>
            } + {ad
              <emph style="super">3</emph>
            p/r
              <emph style="super">3</emph>
            }. </s>
            <s xml:id="echoid-s14717" xml:space="preserve">Cohærentia vero = d
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14718" xml:space="preserve">& </s>
            <s xml:id="echoid-s14719" xml:space="preserve">momentum ex
              <lb/>
            gravitate parabolæ A B C = {9/80} aacr & </s>
            <s xml:id="echoid-s14720" xml:space="preserve">momentum ponderis quæ-
              <lb/>
            ſiti = a x. </s>
            <s xml:id="echoid-s14721" xml:space="preserve">Cohærentia = r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14722" xml:space="preserve">adeoque ordinanda erit hæc propor-
              <lb/>
            tio, {9aacd
              <emph style="super">8</emph>
            /80r
              <emph style="super">7</emph>
            } + {ad
              <emph style="super">3</emph>
            p/r
              <emph style="super">3</emph>
            }, d
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14723" xml:space="preserve">: {9/80} aacr + ax, r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14724" xml:space="preserve">ex quibus eruitur
              <lb/>
            pondus quæſitum x = {9/80} {acd
              <emph style="super">7</emph>
            /r
              <emph style="super">4</emph>
            } + P - {9/80} acr.</s>
            <s xml:id="echoid-s14725" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div551" type="section" level="1" n="551">
          <head xml:id="echoid-head665" xml:space="preserve">PROPOSITIO LXXII.</head>
          <p style="it">
            <s xml:id="echoid-s14726" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14727" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14728" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14729" xml:space="preserve">I. </s>
            <s xml:id="echoid-s14730" xml:space="preserve">Data Conoide Parabolica Cubica D B E una
              <lb/>
            cum pondere P appenſo, ſummo quod geſtari poteſt, producere Co-
              <lb/>
            noidem, ita ut producta A B C momento ſuæ gravitatis babeat </s>
          </p>
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