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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          <pb o="631" file="0647" n="648" rhead="CORPORUM FIRMORUM."/>
        </div>
        <div xml:id="echoid-div608" type="section" level="1" n="608">
          <head xml:id="echoid-head727" xml:space="preserve">PROPOSITIO CV.</head>
          <p style="it">
            <s xml:id="echoid-s15913" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15914" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s15915" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15916" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15917" xml:space="preserve">Dato ſolido A B, utrimque fulcro innixo,
              <lb/>
            ac datæ altitudinis & </s>
            <s xml:id="echoid-s15918" xml:space="preserve">latitudinis, atque dato pondere maximo ſu-
              <lb/>
            ſpenſo ex E loco non medio, invenire latitudinem alterius ſolidi
              <lb/>
            D F æque longi, duobus fulcris impoſiti, quod in ſui medio G idem pon-
              <lb/>
            dus geſtare poſſit.</s>
            <s xml:id="echoid-s15919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15920" xml:space="preserve">Quia pondera ex locis E & </s>
            <s xml:id="echoid-s15921" xml:space="preserve">C ſuſpenſa ponuntur maxima, quæ
              <lb/>
            geſtari â ſolidis poſſunt, erunt æqualia Cohærentiis eorum loco-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s15922" xml:space="preserve">Eſt autem Cohærentia in loco E ad eam in loco medio C, uti
              <lb/>
              <emph style="ol">D C</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15923" xml:space="preserve">ad rectangulum ex A E X E B. </s>
            <s xml:id="echoid-s15924" xml:space="preserve">fiat nunc latitudo ſolidi A B,
              <lb/>
            ad D F uti eſt rectangulum A E X E B ad D C
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15925" xml:space="preserve">eritque Cohærentia
              <lb/>
            in puncto medio C, ſolidi D F æqualis Cohærentiæ in puncto E ſo-
              <lb/>
            lidi A B. </s>
            <s xml:id="echoid-s15926" xml:space="preserve">Vocetur proinde latitudo ſolidi A B = l. </s>
            <s xml:id="echoid-s15927" xml:space="preserve">& </s>
            <s xml:id="echoid-s15928" xml:space="preserve">ſolidi D F
              <lb/>
            = x. </s>
            <s xml:id="echoid-s15929" xml:space="preserve">erit x = {lX A C
              <emph style="super">q</emph>
            /A E X E B}.</s>
            <s xml:id="echoid-s15930" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div609" type="section" level="1" n="609">
          <head xml:id="echoid-head728" xml:space="preserve">PROPOSITIO CVI.</head>
          <p style="it">
            <s xml:id="echoid-s15931" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15932" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s15933" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15934" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15935" xml:space="preserve">Dato ſoldio A B longiſſimo & </s>
            <s xml:id="echoid-s15936" xml:space="preserve">craſſiſſimo,
              <lb/>
            impoſitoque duobus fulcris, ex cujus medio C pendeat pondus maxi-
              <lb/>
            mum, invenire longitudinem ſolidi ſimilis D E imponendi ſuis ful-
              <lb/>
            cris, multo minoris craſſitiei, quod gerat idem pondus ex ſui me-
              <lb/>
            dio.</s>
            <s xml:id="echoid-s15937" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15938" xml:space="preserve">Vocetur longitudo dimidia A C ſolidi longioris & </s>
            <s xml:id="echoid-s15939" xml:space="preserve">craſſioris A B
              <lb/>
            l. </s>
            <s xml:id="echoid-s15940" xml:space="preserve">altitudo a. </s>
            <s xml:id="echoid-s15941" xml:space="preserve">latitudo b. </s>
            <s xml:id="echoid-s15942" xml:space="preserve">Tum longitudo dimidia ſo-
              <lb/>
            lidi tenuioris D E, ſit D G & </s>
            <s xml:id="echoid-s15943" xml:space="preserve">vocetur x. </s>
            <s xml:id="echoid-s15944" xml:space="preserve">cujus altitudo c. </s>
            <s xml:id="echoid-s15945" xml:space="preserve">latitu-
              <lb/>
            do d. </s>
            <s xml:id="echoid-s15946" xml:space="preserve">Eſt Cohærentia ſolidi A C B ad eam ſolidi D G E. </s>
            <s xml:id="echoid-s15947" xml:space="preserve">æque
              <lb/>
            longi ſuppoſiti, in ratione duplicata altitudinis a a ad eam altitu-
              <lb/>
            dinis c c & </s>
            <s xml:id="echoid-s15948" xml:space="preserve">latitudinis b ad d. </s>
            <s xml:id="echoid-s15949" xml:space="preserve">poſitis his ſolidis non æque longis, erit
              <lb/>
            momentum ponderis pendentis ex C ad illud ex G, in ratione D G
              <lb/>
            ad A C. </s>
            <s xml:id="echoid-s15950" xml:space="preserve">quamobrem in requiſitis Cohærentiis æqualibus utriuſque
              <lb/>
            ſolidi A C B, D G E, erit a a b x = c c d l. </s>
            <s xml:id="echoid-s15951" xml:space="preserve">unde x = {c c d l.</s>
            <s xml:id="echoid-s15952" xml:space="preserve">/a a b} </s>
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