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-div545" type="section" level="1" n="545">
          <p>
            <s xml:id="echoid-s14586" xml:space="preserve">
              <pb o="592" file="0608" n="609" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            vitate = {aacr/12}. </s>
            <s xml:id="echoid-s14587" xml:space="preserve">momentum ponderis = ap. </s>
            <s xml:id="echoid-s14588" xml:space="preserve">Cohærentia = 8r
              <emph style="super">3</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s14589" xml:space="preserve">ſed Conoidis quæſitæ ſoliditas erit = {bbcx/4r}. </s>
            <s xml:id="echoid-s14590" xml:space="preserve">ejuſque momentum
              <lb/>
            = {bbcxx/12r}. </s>
            <s xml:id="echoid-s14591" xml:space="preserve">& </s>
            <s xml:id="echoid-s14592" xml:space="preserve">Cohærentia = 8b
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14593" xml:space="preserve">ponitur in Propoſitione
              <lb/>
            {aacr/12} + ap, 8r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14594" xml:space="preserve">: {bbcxx/12r}. </s>
            <s xml:id="echoid-s14595" xml:space="preserve">8b
              <emph style="super">3</emph>
              <lb/>
            unde eruitur x = 8aab
              <emph style="super">3</emph>
            cr + 96b
              <emph style="super">3</emph>
            ap - 8bbcrr.</s>
            <s xml:id="echoid-s14596" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14597" xml:space="preserve">Cognita longitudine parabolæ x, dataque ejus ordinata = b. </s>
            <s xml:id="echoid-s14598" xml:space="preserve">fa-
              <lb/>
            cile invenitur parameter = {bb/x}. </s>
            <s xml:id="echoid-s14599" xml:space="preserve">quâ erutâ deſcribetur parabola per
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s14600" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s14601" xml:space="preserve">vel VIII. </s>
            <s xml:id="echoid-s14602" xml:space="preserve">Hoſpitalii Lib. </s>
            <s xml:id="echoid-s14603" xml:space="preserve">I. </s>
            <s xml:id="echoid-s14604" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s14605" xml:space="preserve">Coniq. </s>
            <s xml:id="echoid-s14606" xml:space="preserve">deſcriptâ Para-
              <lb/>
            bolâ circa axin circumvolutâ, generabitur Conois parabolica quæ-
              <lb/>
            ſita.</s>
            <s xml:id="echoid-s14607" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div546" type="section" level="1" n="546">
          <head xml:id="echoid-head660" xml:space="preserve">PROPOSITIO LXVII.</head>
          <p style="it">
            <s xml:id="echoid-s14608" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14609" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14610" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14611" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14612" xml:space="preserve">Data Conoide parabolica gravi A B C dato-
              <lb/>
            que pondere P, cujus momentum ſimul cum momento ponderis dati
              <lb/>
            ſolidi ſit in quacunque ratione data, invenire aliam Conoidem pa-
              <lb/>
            rabolicam, quæ datam quamlibet babeat longitudinem, & </s>
            <s xml:id="echoid-s14613" xml:space="preserve">cujus
              <lb/>
            momentum ex gravitate ad Cohærentiam ſuam ſit in eadem ratione.</s>
            <s xml:id="echoid-s14614" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14615" xml:space="preserve">Quantitatibus Conoidis A B C vocatis ut in præcedenti Propoſi-
              <lb/>
            tione, erit Conoidis momentum = {aacr/12}. </s>
            <s xml:id="echoid-s14616" xml:space="preserve">momentum ponderis
              <lb/>
            = ap. </s>
            <s xml:id="echoid-s14617" xml:space="preserve">Cohærentia = 8r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14618" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14619" xml:space="preserve">Sit longitudo Conoidis quæſitæ data G F = d. </s>
            <s xml:id="echoid-s14620" xml:space="preserve">radius baſeos quæ-
              <lb/>
            ſitus G D = x. </s>
            <s xml:id="echoid-s14621" xml:space="preserve">erit ejus peri pheria = {cx/r}, ſolidum = {cdxx/4r}. </s>
            <s xml:id="echoid-s14622" xml:space="preserve">cujus mo-
              <lb/>
            mentum = {cddxx/12r}. </s>
            <s xml:id="echoid-s14623" xml:space="preserve">Cohærentia = 8x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14624" xml:space="preserve">quare ordinanda hæcpro-
              <lb/>
            portio, cum momenta gravitatis ad Cohærentias ſuas debent habe-
              <lb/>
            re eandem rationem, {cddxx/12r}. </s>
            <s xml:id="echoid-s14625" xml:space="preserve">8x
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14626" xml:space="preserve">: {aacr/12} + ap. </s>
            <s xml:id="echoid-s14627" xml:space="preserve">8r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14628" xml:space="preserve"/>
          </p>
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