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-div509" type="section" level="1" n="509">
          <p>
            <s xml:id="echoid-s13387" xml:space="preserve">
              <pb o="561" file="0577" n="578" rhead="CORPORUM FIRMORUM."/>
            nis, alterum Gigantis triplo majoris, exhibuit, quæ quoque in
              <lb/>
            noſtra Tab. </s>
            <s xml:id="echoid-s13388" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s13389" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13390" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13391" xml:space="preserve">conſpiciuntur: </s>
            <s xml:id="echoid-s13392" xml:space="preserve">Si autem Gigantes tam
              <lb/>
            craſſa non habuerint oſſa, tum ex materia multo duriore magisque
              <lb/>
            reſiſtente quam noſtra ſunt, formata fuerunt. </s>
            <s xml:id="echoid-s13393" xml:space="preserve">Natura tamen ani-
              <lb/>
            malia maxima genuit longiſſimis inſtructa oſſibus, uti Balænas,
              <lb/>
            piſceſque alios, verum his conceſſit aquam, non Aërem, pro me-
              <lb/>
            dio, in quo ſeſe moveant; </s>
            <s xml:id="echoid-s13394" xml:space="preserve">quia aquæ gravitas ſpecifica eſt ad Aë-
              <lb/>
            rem circiter uti 800 ad 1, hinc animalis & </s>
            <s xml:id="echoid-s13395" xml:space="preserve">oſſium gravitas in Aqua
              <lb/>
            tantundem decreſcit, unde graciliora oſſa, quam quæ ope hujus
              <lb/>
            Propoſitionis determinarentur, ſufficiunt.</s>
            <s xml:id="echoid-s13396" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div510" type="section" level="1" n="510">
          <head xml:id="echoid-head622" xml:space="preserve">PROPOSITIO XXXII.</head>
          <p style="it">
            <s xml:id="echoid-s13397" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13398" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s13399" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13400" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13401" xml:space="preserve">Dato parallelopipedo E A F D, in quo momen-
              <lb/>
            tum gravitatis ad Cohærentiam ſit in quacunque ratione, con-
              <lb/>
            ſtruere aliud parallelopipedum o e a k, baſeos proportionalis ad E A F,
              <lb/>
            in quo momentum gravitatis ad Cohærentiam ſuam ſit in eadem
              <lb/>
            ratione.</s>
            <s xml:id="echoid-s13402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13403" xml:space="preserve">Vocetur A E a. </s>
            <s xml:id="echoid-s13404" xml:space="preserve">E F b. </s>
            <s xml:id="echoid-s13405" xml:space="preserve">A D, c. </s>
            <s xml:id="echoid-s13406" xml:space="preserve">erit parallelopipedum A E F D
              <lb/>
            = a b c. </s>
            <s xml:id="echoid-s13407" xml:space="preserve">momentum ex gravitate = {1/2} a b c c. </s>
            <s xml:id="echoid-s13408" xml:space="preserve">& </s>
            <s xml:id="echoid-s13409" xml:space="preserve">Cohærentia = a a b. </s>
            <s xml:id="echoid-s13410" xml:space="preserve">quia
              <lb/>
            baſes amborum parallelopipedorum ponuntur proportionales, erit E F,
              <lb/>
            E A:</s>
            <s xml:id="echoid-s13411" xml:space="preserve">: oe, ea. </s>
            <s xml:id="echoid-s13412" xml:space="preserve">ſi o e, = f. </s>
            <s xml:id="echoid-s13413" xml:space="preserve">& </s>
            <s xml:id="echoid-s13414" xml:space="preserve">ea = x. </s>
            <s xml:id="echoid-s13415" xml:space="preserve">erit b. </s>
            <s xml:id="echoid-s13416" xml:space="preserve">a:</s>
            <s xml:id="echoid-s13417" xml:space="preserve">; f. </s>
            <s xml:id="echoid-s13418" xml:space="preserve">x. </s>
            <s xml:id="echoid-s13419" xml:space="preserve">unde x = {a f.</s>
            <s xml:id="echoid-s13420" xml:space="preserve">/b}
              <lb/>
            ſit, a k = z. </s>
            <s xml:id="echoid-s13421" xml:space="preserve">erit parallelopipedum, o e a k = {a f f z:</s>
            <s xml:id="echoid-s13422" xml:space="preserve">/b} ejuſque momen-
              <lb/>
            tum ex gravitate = {1/2} {a f f z z.</s>
            <s xml:id="echoid-s13423" xml:space="preserve">/b} atque Cohærentia = {a a f
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s13424" xml:space="preserve">/b b} quia
              <lb/>
            amborum momenta ex gravitate ad ſuas Cohærentias ſupponuntur
              <lb/>
            in eadem ratione, erit {{1/2} a f f z z.</s>
            <s xml:id="echoid-s13425" xml:space="preserve">/b} {a a f
              <emph style="super">3</emph>
            /b b}:</s>
            <s xml:id="echoid-s13426" xml:space="preserve">: {1/2} a b c c. </s>
            <s xml:id="echoid-s13427" xml:space="preserve">a a b. </s>
            <s xml:id="echoid-s13428" xml:space="preserve">unde eli-
              <lb/>
            citur z = {c c f.</s>
            <s xml:id="echoid-s13429" xml:space="preserve">/b}</s>
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