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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            <s xml:id="echoid-s15952" xml:space="preserve">
              <pb o="632" file="0648" n="649" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            igitur a a b. </s>
            <s xml:id="echoid-s15953" xml:space="preserve">ſit major quam c c d l erit Problema impoſſibile.</s>
            <s xml:id="echoid-s15954" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div610" type="section" level="1" n="610">
          <head xml:id="echoid-head729" xml:space="preserve">PROPOSITIO CVII.</head>
          <p style="it">
            <s xml:id="echoid-s15955" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15956" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s15957" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15958" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15959" xml:space="preserve">Ad datam longitudinem A L infinita ſolida
              <lb/>
            priſmatica aut Cylindrica applicare, quæ utrimque in A & </s>
            <s xml:id="echoid-s15960" xml:space="preserve">L ſuf-
              <lb/>
            fulta in medio gerant pondus, babeantque Cohærentiam æqualem
              <lb/>
            Cohærentiæ dati priſmatis vel Cylindri, cujus longitudo eſt A E,
              <lb/>
            altitudo A F, latitudo F G.</s>
            <s xml:id="echoid-s15961" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15962" xml:space="preserve">Fiat ut A E ad A L, ita F G ad F D, & </s>
            <s xml:id="echoid-s15963" xml:space="preserve">per D, inter aſympto-
              <lb/>
            tos E A, A F deſcripta intelligatur Hyperbola C D C quadratica,
              <lb/>
            cujus ordinatæ F D, B C ſint reciproce ut abſciſſarum B A, A F
              <lb/>
            quadrata; </s>
            <s xml:id="echoid-s15964" xml:space="preserve">ita ut productum ex quadrato B A in B C ſemper ſit æqua-
              <lb/>
            le producto quadrati A F in F D. </s>
            <s xml:id="echoid-s15965" xml:space="preserve">Quodlibet priſma arbitrariæ al-
              <lb/>
            titudinis A B, latitudinis correſpondentis ordinatæ B C, & </s>
            <s xml:id="echoid-s15966" xml:space="preserve">datæ
              <lb/>
            longitudinis A L ſatisfaciet quæſito. </s>
            <s xml:id="echoid-s15967" xml:space="preserve">Nam poſitis priſmatibus æque
              <lb/>
            longis, ut A L, erit Cohærentia eorum in ratione duplicata altitu-
              <lb/>
            dinis A B, A F, & </s>
            <s xml:id="echoid-s15968" xml:space="preserve">ſimplici latitudinis B C, F D. </s>
            <s xml:id="echoid-s15969" xml:space="preserve">ſive
              <emph style="ol">A B</emph>
              <emph style="super">q</emph>
            X B C & </s>
            <s xml:id="echoid-s15970" xml:space="preserve">
              <lb/>
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
            X F D. </s>
            <s xml:id="echoid-s15971" xml:space="preserve">ſed ex natura Hyperbolæ eſt
              <emph style="ol">A B</emph>
              <emph style="super">q</emph>
            X B C =
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
              <lb/>
            XX F D. </s>
            <s xml:id="echoid-s15972" xml:space="preserve">quare hæc priſmata, aut cylindri æqualem Cohæren-
              <lb/>
            tiam habent; </s>
            <s xml:id="echoid-s15973" xml:space="preserve">quæ nunc demonſtranda eſt æqualis illi priſmatis dati
              <lb/>
            A F G E. </s>
            <s xml:id="echoid-s15974" xml:space="preserve">Eſt momentum pondéris ſuſpenſi ex medio A L. </s>
            <s xml:id="echoid-s15975" xml:space="preserve">ad mo-
              <lb/>
            mentum ponderis ſuſpenſi ex medio A E, uti A L ad A E: </s>
            <s xml:id="echoid-s15976" xml:space="preserve">quare ſi
              <lb/>
            Cohærentiæ priſmatum ſint inter ſe uti hæc momenta, erunt priſ-
              <lb/>
            mata æqualis Cohærentiæ: </s>
            <s xml:id="echoid-s15977" xml:space="preserve">Cohærentia dati priſmatis eſt =
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
              <lb/>
            X F G. </s>
            <s xml:id="echoid-s15978" xml:space="preserve">Cohærentia alterius eſt
              <emph style="ol">A B</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15979" xml:space="preserve">X B C. </s>
            <s xml:id="echoid-s15980" xml:space="preserve">adeoque debent eſſe
              <lb/>
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
            X F G. </s>
            <s xml:id="echoid-s15981" xml:space="preserve">A E:</s>
            <s xml:id="echoid-s15982" xml:space="preserve">:
              <emph style="ol">A B</emph>
            X B C, A L. </s>
            <s xml:id="echoid-s15983" xml:space="preserve">eſt
              <emph style="ol">A B</emph>
              <emph style="super">q</emph>
            X B C. </s>
            <s xml:id="echoid-s15984" xml:space="preserve">=
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
              <lb/>
            X F D. </s>
            <s xml:id="echoid-s15985" xml:space="preserve">adeoque hac quantitate loco prioris poſita, erit
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
            X F G:
              <lb/>
            </s>
            <s xml:id="echoid-s15986" xml:space="preserve">A E:</s>
            <s xml:id="echoid-s15987" xml:space="preserve">:
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
            X F D, A L. </s>
            <s xml:id="echoid-s15988" xml:space="preserve">antecedentibus terminis proportionis di-
              <lb/>
            viſis per
              <emph style="ol">A F</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15989" xml:space="preserve">erit F G. </s>
            <s xml:id="echoid-s15990" xml:space="preserve">A E:</s>
            <s xml:id="echoid-s15991" xml:space="preserve">: F D: </s>
            <s xml:id="echoid-s15992" xml:space="preserve">A L. </s>
            <s xml:id="echoid-s15993" xml:space="preserve">quæ quantitates ſunt
              <lb/>
            proportionales per conſtructionem, adeoque erunt Cohærentiæ
              <lb/>
            quemadmodum momenta ponderum. </s>
            <s xml:id="echoid-s15994" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s15995" xml:space="preserve">E. </s>
            <s xml:id="echoid-s15996" xml:space="preserve">D.</s>
            <s xml:id="echoid-s15997" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15998" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15999" xml:space="preserve">Extendi poteſt hæc Propoſitio etiam ad Priſmata, Paralle-
              <lb/>
            lopipeda, & </s>
            <s xml:id="echoid-s16000" xml:space="preserve">Cylindros, quæ uno extremo ſui parietibus inſiguntur,
              <lb/>
            ex altero extremo pondus gerunt.</s>
            <s xml:id="echoid-s16001" xml:space="preserve"/>
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