Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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        <div xml:id="echoid-div285" type="section" level="1" n="203">
          <pb o="61" file="527.01.061" n="61" rhead="*DE* S*TATICÆ PRINCIPIIS*."/>
        </div>
        <div xml:id="echoid-div286" type="section" level="1" n="204">
          <head xml:id="echoid-head217" xml:space="preserve">4 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1866" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1867" xml:space="preserve">ABCD irregulare & </s>
            <s xml:id="echoid-s1868" xml:space="preserve">inordinatum quadran-
              <lb/>
            gulum eſto. </s>
            <s xml:id="echoid-s1869" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">Gravitatis centrum nobis l
              <unsure/>
            in-
              <lb/>
            veniendum eſt.</s>
            <s xml:id="echoid-s1871" xml:space="preserve"/>
          </p>
          <figure number="100">
            <image file="527.01.061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.061-01"/>
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        </div>
        <div xml:id="echoid-div287" type="section" level="1" n="205">
          <head xml:id="echoid-head218" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s1872" xml:space="preserve">Quadrangulum rectâ A C in duo triangulaſecto ipſorum
              <lb/>
            gravitatis centra, 3 propoſ. </s>
            <s xml:id="echoid-s1873" xml:space="preserve">adjumento, inveniuntor. </s>
            <s xml:id="echoid-s1874" xml:space="preserve">Trian-
              <lb/>
            guli A B C, eſto E; </s>
            <s xml:id="echoid-s1875" xml:space="preserve">A C D vero F; </s>
            <s xml:id="echoid-s1876" xml:space="preserve">recta denique E F jugum. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">quo facto D G,
              <lb/>
            B H perpendiculares ducuntor in A C. </s>
            <s xml:id="echoid-s1878" xml:space="preserve">jugo F E, ſecto in I, ut radius I E, ſit
              <lb/>
            ad radium I F, quemadmodum D G ad B H; </s>
            <s xml:id="echoid-s1879" xml:space="preserve">I gravitatis centrum eſſe dico.</s>
            <s xml:id="echoid-s1880" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div288" type="section" level="1" n="206">
          <head xml:id="echoid-head219" xml:space="preserve">5 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1881" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1882" xml:space="preserve">ABCDE quinquangulum inordinatum eſto.</s>
            <s xml:id="echoid-s1883" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1884" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1885" xml:space="preserve">Gravitatis centrum inveniendum eſt.</s>
            <s xml:id="echoid-s1886" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div289" type="section" level="1" n="207">
          <head xml:id="echoid-head220" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s1887" xml:space="preserve">Quinquangulo duabus diagoniis AC, AD in tria triangula reſoluto, qua-
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            dranguli A C D E gravitatis centrum F per 4 propoſ. </s>
            <s xml:id="echoid-s1888" xml:space="preserve">& </s>
            <s xml:id="echoid-s1889" xml:space="preserve">trian-
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                <image file="527.01.061-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.061-02"/>
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            guli A C B, G per 3 propoſ. </s>
            <s xml:id="echoid-s1890" xml:space="preserve">inveniuntor, quæ connectat ju-
              <lb/>
            gum F G; </s>
            <s xml:id="echoid-s1891" xml:space="preserve">tum B G in A C, CI & </s>
            <s xml:id="echoid-s1892" xml:space="preserve">E K in A D perpendicu-
              <lb/>
            lares ſunto, & </s>
            <s xml:id="echoid-s1893" xml:space="preserve">tribus rectis A D, A C, H B in eadem analogia
              <lb/>
            quarta inveniatur LM, deniqueſecato jugum F G in N ut
              <lb/>
            ratio ſegmentorum GN, NF eadem ſit quæ C I & </s>
            <s xml:id="echoid-s1894" xml:space="preserve">E K ad
              <lb/>
            ipſam L M. </s>
            <s xml:id="echoid-s1895" xml:space="preserve">N optatum gravitatis centrum eſſe dico.</s>
            <s xml:id="echoid-s1896" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div291" type="section" level="1" n="208">
          <head xml:id="echoid-head221" xml:space="preserve">6 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1897" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1898" xml:space="preserve">ABCDEF inordinatum ſexangulum eſto.</s>
            <s xml:id="echoid-s1899" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1900" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">Gravitatis centrum inveniendum eſt.</s>
            <s xml:id="echoid-s1902" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div292" type="section" level="1" n="209">
          <head xml:id="echoid-head222" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s1903" xml:space="preserve">Sexangulum tribus diagoniis in quatuor triangula dirimito, & </s>
            <s xml:id="echoid-s1904" xml:space="preserve">quadrangu-
              <lb/>
            lorum ADCB, ADEF gravitatis centra G, H per 4 propoſ. </s>
            <s xml:id="echoid-s1905" xml:space="preserve">invenito, quæ
              <lb/>
            connectat jugum GH. </s>
            <s xml:id="echoid-s1906" xml:space="preserve">deinde in AC perpendiculares
              <lb/>
            demittuntor BI, DK. </s>
            <s xml:id="echoid-s1907" xml:space="preserve">ſimiliter AL, EM in FD, jam
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            tribus rectis quarum prima F D ſecunda AC, tertia
              <lb/>
            compoſita ex BI & </s>
            <s xml:id="echoid-s1908" xml:space="preserve">K D, in eâdem analogiâ invenito
              <lb/>
            quartam N O, tumq́ue jugum H G ſecato in P ut ratio
              <lb/>
            ſegmentorũ G P, P H eadem ſit quæ compoſitæ ex A L
              <lb/>
            & </s>
            <s xml:id="echoid-s1909" xml:space="preserve">E M ad ipſam N O. </s>
            <s xml:id="echoid-s1910" xml:space="preserve">Ajo P quæſitum eſſe gravi-
              <lb/>
            tatis centrum. </s>
            <s xml:id="echoid-s1911" xml:space="preserve">Atque ita deinceps in cæteris multangulis.</s>
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        <div xml:id="echoid-div294" type="section" level="1" n="210">
          <head xml:id="echoid-head223" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1913" xml:space="preserve">In primo exemplo eſtradius N E ad radium N F, ſicut H I ad H L, at ſic
              <lb/>
            quoque eſt parallelogrammum ut G H I K ad parallelogrammum G H L M;
              <lb/>
            </s>
            <s xml:id="echoid-s1914" xml:space="preserve">& </s>
            <s xml:id="echoid-s1915" xml:space="preserve">æqueordinatè ut G H I K ad G H L M, hoc eſt per conſtructionem triangu-
              <lb/>
            lum A C D ad triangulum A C B ſicut N E ad N F. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">Punctum igitur N
              <lb/>
            (per primam 1 lib. </s>
            <s xml:id="echoid-s1917" xml:space="preserve">propoſitionem) eſt expoſiti quadranguli gravitatis cen-
              <lb/>
            trum. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">Simillima eritſecundi tertiiq́ue exempli demonſtratio.</s>
            <s xml:id="echoid-s1919" xml:space="preserve"/>
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