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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          <pb o="575" file="0591" n="592" rhead="CORPORUM FIRMORUM."/>
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        <div xml:id="echoid-div530" type="section" level="1" n="530">
          <head xml:id="echoid-head642" xml:space="preserve">PROPOSITIO LII.</head>
          <p style="it">
            <s xml:id="echoid-s13979" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s13980" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s13981" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s13982" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13983" xml:space="preserve">& </s>
            <s xml:id="echoid-s13984" xml:space="preserve">6. </s>
            <s xml:id="echoid-s13985" xml:space="preserve">Sit priſma Triangulare A A B C D rectan-
              <lb/>
            gulum in B, & </s>
            <s xml:id="echoid-s13986" xml:space="preserve">horizontale, cujus latus planum A A B inferius & </s>
            <s xml:id="echoid-s13987" xml:space="preserve">
              <lb/>
            horizonti parallelum, angulus ſolidus C C ſuperior, erit Cohæren-
              <lb/>
            tia ejus reſpectiva ad eam parallelopipedi baſin A D B C duplo ma-
              <lb/>
            jorem habentis, uti ſumma omnium quadratorum linearum f f,
              <lb/>
            g g, h h, i i, B C perpendicularium in latus A B, ad ſummam
              <lb/>
            omnium quadratorum A D, f F, g G, h H, i i. </s>
            <s xml:id="echoid-s13988" xml:space="preserve">B C.</s>
            <s xml:id="echoid-s13989" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13990" xml:space="preserve">Sit latus A B diviſum in partes infinite parvas A f, f g, g h, h i,
              <lb/>
            i B: </s>
            <s xml:id="echoid-s13991" xml:space="preserve">concipiantur ductæ ex his omnibus punctis rectæ f f, g g, h h,
              <lb/>
            i i, B C, perpendiculares in A B; </s>
            <s xml:id="echoid-s13992" xml:space="preserve">completoque quadrato A D C B,
              <lb/>
            producantur rectæ uſque in F. </s>
            <s xml:id="echoid-s13993" xml:space="preserve">G, H, I, C; </s>
            <s xml:id="echoid-s13994" xml:space="preserve">erit Cohærentia rectæ
              <lb/>
            f f in Priſmate, ad Cohærentiam rectæ f F in parallelopipedo, in
              <lb/>
            ratione duplicata altitudinis f F ad altitudinem f F per Prop. </s>
            <s xml:id="echoid-s13995" xml:space="preserve">XXII.
              <lb/>
            </s>
            <s xml:id="echoid-s13996" xml:space="preserve">eodem modo erit Cohærentia g g ad g G in ratione duplicata g g ad
              <lb/>
            g G, atque ita porro comparata erit Cohærentia aliarum rectarum
              <lb/>
            h h, i i, B C in Priſmate, ad Cohærentiam g G, h H, i I, B C in
              <lb/>
            parallelopipedo A D B C. </s>
            <s xml:id="echoid-s13997" xml:space="preserve">Quare uti ſumma quadratorum omnium
              <lb/>
            rectarum f f, g g, h h, i i, B C, ad ſummam omnium quadratorum
              <lb/>
            A D, f F, G g, H h, I i, C B, ita eſt Cohærentia reſpectiva Priſma-
              <lb/>
            tis Trigoni, ad Cohærentiam parallelopipedi, baſin planam A D B C
              <lb/>
            habentis duplo majorem.</s>
            <s xml:id="echoid-s13998" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13999" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14000" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14001" xml:space="preserve">Sed omnes rectæ f f, g g, h h, i i, B C infinite parvo in-
              <lb/>
            tervallo remotæ complent integrum Triangulum A B C, veluti eæ-
              <lb/>
            dem productæ uſque ad D, F, G, H I, C complent Quadratum A D
              <lb/>
            C B, quare erit Cohærentia Triangularis baſeos A B C, ad eam Qua-
              <lb/>
            dratæ baſeos A D B C, uti quadratum Trianguli A B C, ad quadra-
              <lb/>
            tum quadrati A D B C. </s>
            <s xml:id="echoid-s14002" xml:space="preserve">eſt vero Triangulum A B C dimidium qua-
              <lb/>
            drati A D B C, ſive uti 1 ad 2. </s>
            <s xml:id="echoid-s14003" xml:space="preserve">quorum quadrata ſunt uti 1 ad 4.
              <lb/>
            </s>
            <s xml:id="echoid-s14004" xml:space="preserve">quare Cohærentia baſeos triangularis A B C erit ad Cohærentiam
              <lb/>
            baſeos A D B C, uti 1 ad 4.</s>
            <s xml:id="echoid-s14005" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14006" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14007" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14008" xml:space="preserve">Si in fig. </s>
            <s xml:id="echoid-s14009" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14010" xml:space="preserve">Angulus Priſmatis Triangularis D A C in-
              <lb/>
            ferne ponatur, & </s>
            <s xml:id="echoid-s14011" xml:space="preserve">latus planum D C ſuperius, erit Cohærentia re-
              <lb/>
            ſpectiva eadem Priſmatis A B C.</s>
            <s xml:id="echoid-s14012" xml:space="preserve"/>
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