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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          <p>
            <s xml:id="echoid-s16108" xml:space="preserve">
              <pb o="636" file="0652" n="653" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            erit Cohærentia ſegmenti I H ad Cohærentiam ſegmenti B D, in
              <lb/>
            ratione compoſita ex
              <emph style="ol">A G</emph>
              <emph style="super">q</emph>
            ad A E X E C & </s>
            <s xml:id="echoid-s16109" xml:space="preserve">ex ratione
              <emph style="ol">I H</emph>
              <emph style="super">c</emph>
            ad
              <lb/>
              <emph style="ol">B D</emph>
              <emph style="super">c.</emph>
            </s>
            <s xml:id="echoid-s16110" xml:space="preserve">adeoque erunt Cohærentiæ ſegmentorum I H, B D:</s>
            <s xml:id="echoid-s16111" xml:space="preserve">:
              <emph style="ol">A G</emph>
              <emph style="super">q</emph>
              <lb/>
            X
              <emph style="ol">I H</emph>
              <emph style="super">c</emph>
            ad A E X E C X
              <emph style="ol">B D</emph>
              <emph style="super">c</emph>
            .</s>
            <s xml:id="echoid-s16112" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div615" type="section" level="1" n="615">
          <head xml:id="echoid-head734" xml:space="preserve">PROPOSITIO CXII.</head>
          <p style="it">
            <s xml:id="echoid-s16113" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s16114" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s16115" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s16116" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16117" xml:space="preserve">Sit parabolois A C E utrimque fulta in
              <lb/>
            A & </s>
            <s xml:id="echoid-s16118" xml:space="preserve">E, cujus axis borizontalis ſecetur ſegmentis L K, F H per-
              <lb/>
            pendicularibus ad axin A B. </s>
            <s xml:id="echoid-s16119" xml:space="preserve">erit Cohærentia ſegmenti L K ad Co-
              <lb/>
            bærentiam ſegmenti F H, in ratione compoſita ex A G X I L, ad
              <lb/>
            I B X F G.</s>
            <s xml:id="echoid-s16120" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16121" xml:space="preserve">Nam eſt Cohærentia ſegmenti L K ad eam ſegmenti F H, uti
              <lb/>
              <emph style="ol">A G</emph>
              <emph style="super">q</emph>
            X
              <emph style="ol">I L</emph>
              <emph style="super">c</emph>
            , ad A I X I B X
              <emph style="ol">F G</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s16122" xml:space="preserve">ſed eſt Cubus I L =
              <emph style="ol">I L</emph>
              <emph style="super">q</emph>
            X I L. </s>
            <s xml:id="echoid-s16123" xml:space="preserve">ita
              <lb/>
              <emph style="ol">F G</emph>
              <emph style="super">c</emph>
            = F G
              <emph style="super">q</emph>
            X F G. </s>
            <s xml:id="echoid-s16124" xml:space="preserve">eſt vero I L
              <emph style="super">q</emph>
            ,
              <emph style="ol">F G</emph>
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s16125" xml:space="preserve">: A I, A G adeoque A I X I L,
              <lb/>
            A G X F G:</s>
            <s xml:id="echoid-s16126" xml:space="preserve">:
              <emph style="ol">I L</emph>
              <emph style="super">c</emph>
            ,
              <emph style="ol">F G</emph>
              <emph style="super">c</emph>
            . </s>
            <s xml:id="echoid-s16127" xml:space="preserve">hinc erit Cohærentia ſegmenti L K, ad
              <lb/>
            eam ſegmenti F H:</s>
            <s xml:id="echoid-s16128" xml:space="preserve">: A G
              <emph style="super">q</emph>
            X A I X I L, A I, X I B X A G X F G.
              <lb/>
            </s>
            <s xml:id="echoid-s16129" xml:space="preserve">factaque utriuſque quantitatis diviſione per A G X A I, erit Cohæ-
              <lb/>
            rentia L K ad eam in F H:</s>
            <s xml:id="echoid-s16130" xml:space="preserve">: A G X I L ad I B X F G.</s>
            <s xml:id="echoid-s16131" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div616" type="section" level="1" n="616">
          <head xml:id="echoid-head735" xml:space="preserve">PROPOSITIO CXIII.</head>
          <p style="it">
            <s xml:id="echoid-s16132" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s16133" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s16134" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s16135" xml:space="preserve">5. </s>
            <s xml:id="echoid-s16136" xml:space="preserve">Solidum ſemicirculare A C E B F D, utrim-
              <lb/>
            que in A & </s>
            <s xml:id="echoid-s16137" xml:space="preserve">B ſuffultum, eſt ubivis æqualis reſiſtentiæ.</s>
            <s xml:id="echoid-s16138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16139" xml:space="preserve">Ducatur enim quælibet D C, E F perpendicularis in diametrum
              <lb/>
            A B, eritque Cohærentia C D ad E F in ratione duplicata altitudi-
              <lb/>
            nis D C ad E F, quatenus altitudinem ſolidi ſpectamus: </s>
            <s xml:id="echoid-s16140" xml:space="preserve">verum
              <lb/>
            eſt momentum ponderis maximi ſuſpenſi ex D, ad momentum
              <lb/>
            ſuſpenſi ex F, uti rectangulum A D X D B, ad rectangulum A F X F B.
              <lb/>
            </s>
            <s xml:id="echoid-s16141" xml:space="preserve">verum ex natura circuli, uti A D X D B ad A F X F B:</s>
            <s xml:id="echoid-s16142" xml:space="preserve">:
              <emph style="ol">D C</emph>
              <emph style="super">q</emph>
            , ad
              <lb/>
              <emph style="ol">F E</emph>
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s16143" xml:space="preserve">: Cohærentia in D C ad Cohærentiam in F E. </s>
            <s xml:id="echoid-s16144" xml:space="preserve">adeoque erit
              <lb/>
            momentum ponderis maximi idem in E F ac in C D, erit igitur hoc
              <lb/>
            ſolidum ubivis æqualis reſiſtentiæ.</s>
            <s xml:id="echoid-s16145" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16146" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s16147" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s16148" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s16149" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16150" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s16151" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16152" xml:space="preserve">Si A C E B D F ſit circulus, & </s>
            <s xml:id="echoid-s16153" xml:space="preserve">proinde
              <lb/>
            ſolidum fuerit diſcus circularis, qui utrimque ad extremum </s>
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