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

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        <div xml:id="echoid-div294" type="section" level="1" n="210">
          <pb o="62" file="527.01.062" n="62" rhead="2 L*IBER* S*TATICÆ*"/>
          <p>
            <s xml:id="echoid-s1920" xml:space="preserve">Atquarti exempli demonſtratio pendet è proportione rectarum D G, H B
              <lb/>
            & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">triangulorum A C D, A C B; </s>
            <s xml:id="echoid-s1922" xml:space="preserve">Et enim ut D G ad H B ſic erit, ſumpta com-
              <lb/>
            muni altitudine A C, rectangulum ſub D G in A C ad rectangulum ſub H B
              <lb/>
            in A C, hoc eſt (quia iſtorum dimidia ſunt) triangulum A C D ad triangu-
              <lb/>
            lum A C B.</s>
            <s xml:id="echoid-s1923" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1924" xml:space="preserve">Pari ratione quinti exempli demonſtratio, pendet ab analogia rectæ EK
              <lb/>
            cum I C ad L M & </s>
            <s xml:id="echoid-s1925" xml:space="preserve">quadranguli A C D E ad triangulum A C B. </s>
            <s xml:id="echoid-s1926" xml:space="preserve">Enimverò
              <lb/>
            cum L M ſit quarta in analogia rectarum A D, A C, H B rectangulum extre.
              <lb/>
            </s>
            <s xml:id="echoid-s1927" xml:space="preserve">marum A D in L M æquatur mediarum rectangulo A C in H B. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">Hinc tres
              <lb/>
            rectæ E K, I C, L M pro baſibus parallelogrammorum nobis ſunto, quarum
              <lb/>
            altitudo ſit eadem A D, ideoque ut E K & </s>
            <s xml:id="echoid-s1929" xml:space="preserve">C I ad L M ſic rectangula duo
              <lb/>
            E K in A D & </s>
            <s xml:id="echoid-s1930" xml:space="preserve">CI in A D ad L M in A D ſed duo illa rectangula ſunt dupli-
              <lb/>
            cia ſuorum triangulorũ hoc eſt quadranguli A E D C; </s>
            <s xml:id="echoid-s1931" xml:space="preserve">& </s>
            <s xml:id="echoid-s1932" xml:space="preserve">rectangulum L M in
              <lb/>
            A D duplum eſt trianguli A B C quia æquale eſt rectangulo A C in H D ut
              <lb/>
            ſupra jam patuit; </s>
            <s xml:id="echoid-s1933" xml:space="preserve">quamobrem erit quadrangulum A E D C ad triangulum
              <lb/>
            A B C ſicut E K & </s>
            <s xml:id="echoid-s1934" xml:space="preserve">I C ad B H ſed ſic quoque eſt propter conſtructionem,
              <lb/>
            G N ad N F quare N eſt optatum gravitatis centrum.</s>
            <s xml:id="echoid-s1935" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1936" xml:space="preserve">Sexti exempli demonſtratio huic affinis eſt. </s>
            <s xml:id="echoid-s1937" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1938" xml:space="preserve">Itaque dati
              <lb/>
            rectilinei cujuſcunque gravitatis centrum invenimus. </s>
            <s xml:id="echoid-s1939" xml:space="preserve">Quod oportuit.</s>
            <s xml:id="echoid-s1940" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div295" type="section" level="1" n="211">
          <head xml:id="echoid-head224" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s1941" xml:space="preserve">Interim dum hæc pralo ſubjiciuntur nactus ſuns Federici Commandini Com-
              <lb/>
            mentarium in Archimedis quadraturam paraboles, ubi ad 6 propoſitionem recti-
              <lb/>
            lineorum gravitatis centrum invenire docet, modo ab horum utroque diverſo. </s>
            <s xml:id="echoid-s1942" xml:space="preserve">Siquis
              <lb/>
            cognoſcendi ſit cupidus ipſum conſulat.</s>
            <s xml:id="echoid-s1943" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div296" type="section" level="1" n="212">
          <head xml:id="echoid-head225" xml:space="preserve">5 THEOREMA. 7 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1944" xml:space="preserve">Securiculæ gravitatis centrum eſt in recta laterum paral-
              <lb/>
            lelorum biſectionem connectente.</s>
            <s xml:id="echoid-s1945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1946" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1947" xml:space="preserve">A B C D ſecuricula eſt qualem in Geometricis definivimus,
              <lb/>
            duobus lateribus A B, D C parallela, recta ab E biſegmento A B, connexa cum
              <lb/>
            F biſegmento ipſius D E. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Quadrilateri A B C D gravitatis
              <lb/>
            centrum in jungente E F conſiſtere demonſtretur.</s>
            <s xml:id="echoid-s1950" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1951" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1952" xml:space="preserve">Tres rectæ D A, E F, C B, propter homologiam ſeg-
              <lb/>
            mentorum A E, E B, D F, F C eodem coïbunt in G.</s>
            <s xml:id="echoid-s1953" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div297" type="section" level="1" n="213">
          <head xml:id="echoid-head226" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1954" xml:space="preserve">Triangulum G D C ſuſpenſum ex rectâ G F faciet ſegmen-
              <lb/>
              <figure xlink:label="fig-527.01.062-01" xlink:href="fig-527.01.062-01a" number="103">
                <image file="527.01.062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.062-01"/>
              </figure>
            ta GFC, G F D per 2 propoſ. </s>
            <s xml:id="echoid-s1955" xml:space="preserve">ſitu ęquilibria; </s>
            <s xml:id="echoid-s1956" xml:space="preserve">ideoq́ue triangu-
              <lb/>
            li G D C gravitatis centrum in recta G F conſiſtet. </s>
            <s xml:id="echoid-s1957" xml:space="preserve">Sed G E B
              <lb/>
            triangulum triangulo G E A itidem ſitu æquilibre eſt, æqualia
              <lb/>
            igitur & </s>
            <s xml:id="echoid-s1958" xml:space="preserve">ſitu ęquilibria utrimque deducta relinquent quadran-
              <lb/>
            gula A E F D, E F B C quoque ſitu æquilibria, & </s>
            <s xml:id="echoid-s1959" xml:space="preserve">gravitatis
              <lb/>
            centrum in ipſa G E, neque tamen in ſegmento exteriore
              <lb/>
            E G, quamobrem in ipſâ E F. </s>
            <s xml:id="echoid-s1960" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">Itaque ſecu-
              <lb/>
            riculæ gravitatis centrum eſtin rectâ parallelorum laterum bi-
              <lb/>
            ſectrice.</s>
            <s xml:id="echoid-s1962" xml:space="preserve"/>
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