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-div356" type="section" level="1" n="356">
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            <s xml:id="echoid-s11052" xml:space="preserve">
              <pb o="477" file="0491" n="491" rhead="CORPORUM FIRMORUM."/>
            erit in majori ratione, quam Cohærentia B F ad Soliditatem B K P F.
              <lb/>
            </s>
            <s xml:id="echoid-s11053" xml:space="preserve">ſed Coni ſunt tertiæ partes Cylindrorum, hoceſt ſoliditatum hacte-
              <lb/>
            nus conſideratarum, adeoque erit Cohærentia D G ad ſoliditatem
              <lb/>
            coni D A G, in majori ratione, quam Cohærentia in B F ad ſolidi-
              <lb/>
            tatem Coni B A F.</s>
            <s xml:id="echoid-s11054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11055" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s11056" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11057" xml:space="preserve">Quo igitur ſectio D G propior apici Coni A ponatur,
              <lb/>
            eo Cohærentia baſeos D G ad ſoliditatem abſciſſi coni majorem ra-
              <lb/>
            tionem habebit; </s>
            <s xml:id="echoid-s11058" xml:space="preserve">quare quo longior ſit Conus eo Cohærentia baſeos
              <lb/>
            ad ſuam Cohærentiam minorem rationem habebit.</s>
            <s xml:id="echoid-s11059" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11060" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s11061" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11062" xml:space="preserve">Eadem conveniunt Pyramidibus quibuſcunque rectis.</s>
            <s xml:id="echoid-s11063" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div357" type="section" level="1" n="357">
          <head xml:id="echoid-head467" xml:space="preserve">PROPOSITIO XIV.</head>
          <p style="it">
            <s xml:id="echoid-s11064" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s11065" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s11066" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s11067" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11068" xml:space="preserve">Si Coni recti A B F, baſis B F cobæreat cum
              <lb/>
            lacunari, ut axis C A ſit ad borizontem perpendicularis, atque ſe-
              <lb/>
            cetur plano borizontali D G, erit Cobærentia abſoluta baſeos Coni
              <lb/>
            A B F, ad Cobærentiam baſeos ſegmenti D E G, in ratione duplicata
              <lb/>
            altitudinis C A ad E A.</s>
            <s xml:id="echoid-s11069" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11070" xml:space="preserve">Sit enim axis Coni A E C; </s>
            <s xml:id="echoid-s11071" xml:space="preserve">ducantur ex punctis E & </s>
            <s xml:id="echoid-s11072" xml:space="preserve">C, quæ ſunt
              <lb/>
            centra circulorum, rectæ C B, E D: </s>
            <s xml:id="echoid-s11073" xml:space="preserve">erit A E, A C:</s>
            <s xml:id="echoid-s11074" xml:space="preserve">: E D, C B.
              <lb/>
            </s>
            <s xml:id="echoid-s11075" xml:space="preserve">per propoſ. </s>
            <s xml:id="echoid-s11076" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11077" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s11078" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11079" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s11080" xml:space="preserve">Eucli. </s>
            <s xml:id="echoid-s11081" xml:space="preserve">ſed eſt circulus radii E D ad cir-
              <lb/>
            culum radii C B, uti
              <emph style="ol">E D</emph>
              <emph style="super">q</emph>
            ad
              <emph style="ol">C B</emph>
              <emph style="super">q</emph>
            per prop. </s>
            <s xml:id="echoid-s11082" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s11084" xml:space="preserve">12. </s>
            <s xml:id="echoid-s11085" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s11086" xml:space="preserve">
              <lb/>
            Euclid. </s>
            <s xml:id="echoid-s11087" xml:space="preserve">adeoque eſt circulus D E G ad circulum B C F:</s>
            <s xml:id="echoid-s11088" xml:space="preserve">:
              <emph style="ol">A E</emph>
              <emph style="super">q</emph>
              <emph style="ol">A C</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s11089" xml:space="preserve">
              <lb/>
            verum Cohærentiæ abſolutæ baſium Conorum A D G, A B F, ſunt
              <lb/>
            inter ſe uti baſes D G E, B C F, adeoque ſunt Cohærentiæ ambo
              <lb/>
            rum Conorum in ratione duplicata altitudinum A E, A C.</s>
            <s xml:id="echoid-s11090" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div358" type="section" level="1" n="358">
          <head xml:id="echoid-head468" xml:space="preserve">PROPOSITIO XV.</head>
          <p style="it">
            <s xml:id="echoid-s11091" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s11092" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s11093" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s11094" xml:space="preserve">11. </s>
            <s xml:id="echoid-s11095" xml:space="preserve">Sit ſolidum parabolicum, ex circumacta Para-
              <lb/>
            bola circa axin natum, cujus baſis B F lacunari affixa ut axis C A
              <lb/>
            borizonti perpendicularis, ſecetur plano borizontali D E G, erit
              <lb/>
            Cobærentia baſeos B C F ad Cobærentiam ſegmenti D E G, in ratio-
              <lb/>
            ne altitudinis A C ad A E menſuratæ a vertice.</s>
            <s xml:id="echoid-s11096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11097" xml:space="preserve">Sit enim B D A G F Parabola Apolloniana, cujus axis eſt A </s>
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