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-div355" type="section" level="1" n="355">
          <pb o="476" file="0490" n="490" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
          <p>
            <s xml:id="echoid-s11020" xml:space="preserve">Primum inter Experimenta, inferius deſcribenda in hoc Capitevel
              <lb/>
            in ſequenti, quæratur quanta ſit Cohærentia abſoluta ejusdem cor-
              <lb/>
            poris ſub determinata craſſitie, hæc Cohærentia vocetur a. </s>
            <s xml:id="echoid-s11021" xml:space="preserve">& </s>
            <s xml:id="echoid-s11022" xml:space="preserve">
              <lb/>
            craſſities ſit b c. </s>
            <s xml:id="echoid-s11023" xml:space="preserve">Deinde quæratur quanta ſit gravitas corporis dati
              <lb/>
            in data longitudine, quæ ſit = g, & </s>
            <s xml:id="echoid-s11024" xml:space="preserve">pondus datum geſtandum ſit = p.
              <lb/>
            </s>
            <s xml:id="echoid-s11025" xml:space="preserve">erit igitur Cohærentia abſoluta a ad ſuam craſſitiem b c. </s>
            <s xml:id="echoid-s11026" xml:space="preserve">velutigravitas
              <lb/>
            corporis cum pondere annexo = g + p ad craſſitiem quæſitam: </s>
            <s xml:id="echoid-s11027" xml:space="preserve">
              <lb/>
            quæ tum erit = {b c g + b c p.</s>
            <s xml:id="echoid-s11028" xml:space="preserve">/a}?</s>
            <s xml:id="echoid-s11029" xml:space="preserve">? nam pondus geſtandum g + p eſt æqua-
              <lb/>
            le Cohærentiæ abſolutæ corporis dati ſub determinata craſſitie.</s>
            <s xml:id="echoid-s11030" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11031" xml:space="preserve">Scholion. </s>
            <s xml:id="echoid-s11032" xml:space="preserve">Hinc dato pondere ſuſpendendo ex catenis ferreis, filis
              <lb/>
            metallicis, funibuſve aut Lignis, aut datâ vi hæc corpora tenden-
              <lb/>
            te, â priori determinari ſemper poterit, quantæ craſſitiei deſide-
              <lb/>
            rantur, ne rumpantur: </s>
            <s xml:id="echoid-s11033" xml:space="preserve">Eſt hoc Problema magnæ utilitatis in praxi,
              <lb/>
            ne corpora ex quibus pondera ſunt ſuſpendenda, capiantur nimis
              <lb/>
            tenuia, atque ita olei & </s>
            <s xml:id="echoid-s11034" xml:space="preserve">operæ jactura fiat; </s>
            <s xml:id="echoid-s11035" xml:space="preserve">tum ne corpora craſ-
              <lb/>
            ſiora componantur, quam debent, inanesque fiant impenſæ.</s>
            <s xml:id="echoid-s11036" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div356" type="section" level="1" n="356">
          <head xml:id="echoid-head466" xml:space="preserve">PROPOSITIO XIII.</head>
          <p style="it">
            <s xml:id="echoid-s11037" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s11038" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s11039" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s11040" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11041" xml:space="preserve">Sidetur Conusrectus B A F, cujus baſis B C la-
              <lb/>
            cunari affixa, ita ut axis C A ſit perpendicularis ad borizontem,
              <lb/>
            qui ſecetur plano borizontali D G, erit Cobærentia abſoluta baſeos
              <lb/>
            B F ad ſoliditatem coni A B F in minori ratione, quam Cobærentia
              <lb/>
            abſoluta baſeos D G in ſegmento ad ſuam ſoliditatem.</s>
            <s xml:id="echoid-s11042" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11043" xml:space="preserve">Concipiatur ſuper baſi B F factus cylindrus altitudinis C A, qui
              <lb/>
            fit B K P F, tum ſuper baſi ſegmenti D G cylindrus ſit æque altus
              <lb/>
            O I L M. </s>
            <s xml:id="echoid-s11044" xml:space="preserve">erit Cohærentia abſoluta cylindri B K P F ad Cohærentiam
              <lb/>
            cylindri O I L M abſolutam, uti baſis B F ad baſin O I per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s11045" xml:space="preserve">8. </s>
            <s xml:id="echoid-s11046" xml:space="preserve">& </s>
            <s xml:id="echoid-s11047" xml:space="preserve">eſt ſoliditas cylindri B K F P, ad ſoliditatem cylindri O I L M,
              <lb/>
            uti baſis B F ad O I baſin: </s>
            <s xml:id="echoid-s11048" xml:space="preserve">ergo Cohærentiæ & </s>
            <s xml:id="echoid-s11049" xml:space="preserve">Soliditates ſunt inter
              <lb/>
            ſe uti baſes: </s>
            <s xml:id="echoid-s11050" xml:space="preserve">ſed eſt baſis O I ad ſoliditatem O I L M in minori ra-
              <lb/>
            tione, quam eadem baſis O I ad ſoliditatis prioris portionem, ſive ad
              <lb/>
            D L M G. </s>
            <s xml:id="echoid-s11051" xml:space="preserve">Ergo erit Cohærentia, in O I, ſive in æquali D G, ad ſolidita-
              <lb/>
            tem D L M G in majori ratione, quam cohærentia O I ad ſoliditatem
              <lb/>
            O I L M: </s>
            <s xml:id="echoid-s11052" xml:space="preserve">unde quoque cohærentia in D G ad ſoliditatem D G L </s>
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