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-div516" type="section" level="1" n="516">
          <pb o="567" file="0583" n="584" rhead="CORPORUM FIRMORUM."/>
        </div>
        <div xml:id="echoid-div517" type="section" level="1" n="517">
          <head xml:id="echoid-head629" xml:space="preserve">PROPOSITIO XXXIX.</head>
          <p style="it">
            <s xml:id="echoid-s13619" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13620" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s13621" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13622" xml:space="preserve">37. </s>
            <s xml:id="echoid-s13623" xml:space="preserve">Sunt momenta gravitatis in Cylindris ejus-
              <lb/>
            dem materiæ A B C D, E F G H in ratione compoſitâ ex magnitudi-
              <lb/>
            ne Cylindri A B C D, ad E F G H, & </s>
            <s xml:id="echoid-s13624" xml:space="preserve">ex longitudine A D ad E H.</s>
            <s xml:id="echoid-s13625" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13626" xml:space="preserve">Sunt gravitates horum Cylindrorum, uti ſunt magnitudines:
              <lb/>
            </s>
            <s xml:id="echoid-s13627" xml:space="preserve">ſunt centra gravitatis in medio Cylindrorum x & </s>
            <s xml:id="echoid-s13628" xml:space="preserve">z, quamobrem
              <lb/>
            concipiendæ ſunt gravitates ſuſpenſæ ex x & </s>
            <s xml:id="echoid-s13629" xml:space="preserve">z, quarum momen-
              <lb/>
            ta habentur ductis diſtantiis S X, R Z in pondera; </s>
            <s xml:id="echoid-s13630" xml:space="preserve">ſed eſt S X ad
              <lb/>
            R Z:</s>
            <s xml:id="echoid-s13631" xml:space="preserve">: A D, E H. </s>
            <s xml:id="echoid-s13632" xml:space="preserve">igitur momenta cylindrorum ſunt in ratione
              <lb/>
            compoſita magnitudinum B D ad F H, & </s>
            <s xml:id="echoid-s13633" xml:space="preserve">longitudinum A D ad E H.</s>
            <s xml:id="echoid-s13634" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div518" type="section" level="1" n="518">
          <head xml:id="echoid-head630" xml:space="preserve">PROPOSITIO XL.</head>
          <p style="it">
            <s xml:id="echoid-s13635" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13636" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s13637" xml:space="preserve">fig 37. </s>
            <s xml:id="echoid-s13638" xml:space="preserve">Dato cylindro A B C D, & </s>
            <s xml:id="echoid-s13639" xml:space="preserve">pondere I ap-
              <lb/>
            penſo extremitati, minimo ſed frangente. </s>
            <s xml:id="echoid-s13640" xml:space="preserve">invenire longitudinem
              <lb/>
            minimam ejusdem cylindri, ut propria gravitate frangatur.</s>
            <s xml:id="echoid-s13641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13642" xml:space="preserve">Vocetur longitudo A D dati cylindri l. </s>
            <s xml:id="echoid-s13643" xml:space="preserve">pondus I datum p. </s>
            <s xml:id="echoid-s13644" xml:space="preserve">ra-
              <lb/>
            dius baſeos A B r. </s>
            <s xml:id="echoid-s13645" xml:space="preserve">circumferentia c. </s>
            <s xml:id="echoid-s13646" xml:space="preserve">erit baſis = {1/2} cr. </s>
            <s xml:id="echoid-s13647" xml:space="preserve">& </s>
            <s xml:id="echoid-s13648" xml:space="preserve">ſolidi-
              <lb/>
            tas cylindri ={1/2} c r l. </s>
            <s xml:id="echoid-s13649" xml:space="preserve">quia centrum gravitatis eſt in medio cylindri,
              <lb/>
            erit momentum gravitatis ={1/2} c r l X {1/2} l. </s>
            <s xml:id="echoid-s13650" xml:space="preserve">={1/4}c r l l ponderis momen-
              <lb/>
            tum erit =p l. </s>
            <s xml:id="echoid-s13651" xml:space="preserve">longitudo quæſita vocetur x. </s>
            <s xml:id="echoid-s13652" xml:space="preserve">erit ſoliditas quæſiti
              <lb/>
            cylindri ={1/2} c r x. </s>
            <s xml:id="echoid-s13653" xml:space="preserve">& </s>
            <s xml:id="echoid-s13654" xml:space="preserve">momentum gravitatis hujus cylindri ={1/4} c r x x.
              <lb/>
            </s>
            <s xml:id="echoid-s13655" xml:space="preserve">quod debet eſſe æquale momentoponderis I & </s>
            <s xml:id="echoid-s13656" xml:space="preserve">momento gravitatis
              <lb/>
            in dato cylindro, adeoque {1/4} c r x x =pl + {1/4} c r l l. </s>
            <s xml:id="echoid-s13657" xml:space="preserve">facta utrim-
              <lb/>
            que diviſione per {1/4}cr. </s>
            <s xml:id="echoid-s13658" xml:space="preserve">fit xx ={pl+{1/4}c r l l/{1/4}cr.</s>
            <s xml:id="echoid-s13659" xml:space="preserve">}: </s>
            <s xml:id="echoid-s13660" xml:space="preserve">unde x ={pl+{1/4} crll.</s>
            <s xml:id="echoid-s13661" xml:space="preserve">/{1/4}cr.</s>
            <s xml:id="echoid-s13662" xml:space="preserve">}</s>
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        </div>
        <div xml:id="echoid-div519" type="section" level="1" n="519">
          <head xml:id="echoid-head631" xml:space="preserve">PROPOSITIO XLI.</head>
          <p style="it">
            <s xml:id="echoid-s13663" xml:space="preserve">Dato cylindro horizontaliter parieti infigendo, multo longiori
              <lb/>
            quam ut ſuum pondus ferat, invenire quænam pars abſcindenda
              <lb/>
            ſit, ut absque metu rupturæ parieti immittatur, ſit tamen rupturæ
              <lb/>
            proximus.</s>
            <s xml:id="echoid-s13664" xml:space="preserve"/>
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