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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      <text xml:lang="la" type="free">
        <div xml:id="echoid-div546" type="section" level="1" n="546">
          <p>
            <s xml:id="echoid-s14628" xml:space="preserve">
              <pb o="593" file="0609" n="610" rhead="CORPORUM FIRMORUM."/>
            unde eruitur x = {cddrr/aacr + 12ap}</s>
          </p>
        </div>
        <div xml:id="echoid-div547" type="section" level="1" n="547">
          <head xml:id="echoid-head661" xml:space="preserve">PROPOSITIO LXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s14629" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14630" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14631" xml:space="preserve">fig I. </s>
            <s xml:id="echoid-s14632" xml:space="preserve">Data Conoide Parabolica D B E, datoque
              <lb/>
            pondere appenſo P, cujus momentum ſimul cum momento Conoidis
              <lb/>
            ex gravitate, ad momentum Cobærentiæ ejuſdem ſolidi quamlibet
              <lb/>
            babeat rationem; </s>
            <s xml:id="echoid-s14633" xml:space="preserve">Conoidem datam ita producere in F, ut ejus pon-
              <lb/>
            deris momentum ad ſuam Cobærentiam ſit in eadem ratione.</s>
            <s xml:id="echoid-s14634" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14635" xml:space="preserve">Ponatur G D radius = r. </s>
            <s xml:id="echoid-s14636" xml:space="preserve">peripheria circuli baſeos = c. </s>
            <s xml:id="echoid-s14637" xml:space="preserve">G B = a.
              <lb/>
            </s>
            <s xml:id="echoid-s14638" xml:space="preserve">pondus P = p. </s>
            <s xml:id="echoid-s14639" xml:space="preserve">B F quæſita = x. </s>
            <s xml:id="echoid-s14640" xml:space="preserve">erit C F radius baſeos = {rrx/a}. </s>
            <s xml:id="echoid-s14641" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s14642" xml:space="preserve">peripheria circuli baſeos = c {x/a}.</s>
            <s xml:id="echoid-s14643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14644" xml:space="preserve">Eſt ſolidum DBE = {acr/4}. </s>
            <s xml:id="echoid-s14645" xml:space="preserve">ejus momentum ex gravitate = {aacr/12}.
              <lb/>
            </s>
            <s xml:id="echoid-s14646" xml:space="preserve">& </s>
            <s xml:id="echoid-s14647" xml:space="preserve">momentum ponderis P = ap. </s>
            <s xml:id="echoid-s14648" xml:space="preserve">Cohærentia = 8r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14649" xml:space="preserve">Eſt autem
              <lb/>
            ſolidum A B C = {1/4} crx{x/a}, ejusque momentum {crxx/12}{x/a}. </s>
            <s xml:id="echoid-s14650" xml:space="preserve">& </s>
            <s xml:id="echoid-s14651" xml:space="preserve">Cohæ-
              <lb/>
            rentia = 8 {r
              <emph style="super">6</emph>
            x
              <emph style="super">3</emph>
            /a
              <emph style="super">3</emph>
            }. </s>
            <s xml:id="echoid-s14652" xml:space="preserve">Quia igitur ambo momenta Conoidum ad ſuas
              <lb/>
            Cohærentias ſupponuntur eſſe in eadem ratione, erit {aacr/12} + ap. </s>
            <s xml:id="echoid-s14653" xml:space="preserve">
              <lb/>
            8r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14654" xml:space="preserve">: {crxx/12} {x.</s>
            <s xml:id="echoid-s14655" xml:space="preserve">/a}. </s>
            <s xml:id="echoid-s14656" xml:space="preserve">{8r
              <emph style="super">3</emph>
            x/a} {x/a}.</s>
            <s xml:id="echoid-s14657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14658" xml:space="preserve">Quorum extremis mediisque terminis per ſe multiplicatis, at-
              <lb/>
            que diviſione facta per 8 {x/a}. </s>
            <s xml:id="echoid-s14659" xml:space="preserve">fit {cr
              <emph style="super">4</emph>
            xx/12} = {aacr
              <emph style="super">4</emph>
            x/12a} + {apr
              <emph style="super">3</emph>
            x/a}.
              <lb/>
            </s>
            <s xml:id="echoid-s14660" xml:space="preserve">& </s>
            <s xml:id="echoid-s14661" xml:space="preserve">inſtituta diviſione per {cr
              <emph style="super">4</emph>
            /12}. </s>
            <s xml:id="echoid-s14662" xml:space="preserve">fit
              <lb/>
            x x = ax + 12{px/cr}. </s>
            <s xml:id="echoid-s14663" xml:space="preserve">unde per tranſpoſitionem.</s>
            <s xml:id="echoid-s14664" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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