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

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        <div xml:id="echoid-div297" type="section" level="1" n="213">
          <pb o="63" file="527.01.063" n="63" rhead="*DE* S*TATICÆ PRINCIPIIS*."/>
        </div>
        <div xml:id="echoid-div299" type="section" level="1" n="214">
          <head xml:id="echoid-head227" xml:space="preserve">6 THEOREMA. 8 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1963" xml:space="preserve">Securiculæ gravitatis centrum rectam parallelorum la-
              <lb/>
            terum biſectricen
              <unsure/>
            ita ſecat, ut ſegmentum biſectricis mi-
              <lb/>
            nori latericon terminum ad reliquum ſit, ut majoris pa-
              <lb/>
            ralleli lateris duplum minore auctum, ad duplum mino-
              <lb/>
            ris cum majore.</s>
            <s xml:id="echoid-s1964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1965" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1966" xml:space="preserve">Latera A B, D C, ſecuriculæ A B C D parallela ſunto, biſectrix
              <lb/>
            E F, & </s>
            <s xml:id="echoid-s1967" xml:space="preserve">gravitatis centrum G, Q*VAESITVM*. </s>
            <s xml:id="echoid-s1968" xml:space="preserve">Duplam D C auctam ipſa
              <lb/>
            A B, & </s>
            <s xml:id="echoid-s1969" xml:space="preserve">Duplam A B cum D C, ſegmentis G E, G F proportionales eſſe de-
              <lb/>
            monſtrandum eſto. </s>
            <s xml:id="echoid-s1970" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1971" xml:space="preserve">Diagonia D B tripartito dividatur
              <lb/>
            in punctis H, I, parallelæ ab his terminis K L, M N, contra latus D C inter-
              <lb/>
            ſecent E F in O & </s>
            <s xml:id="echoid-s1972" xml:space="preserve">P. </s>
            <s xml:id="echoid-s1973" xml:space="preserve">Deniqueacta E D interſecet M I in Q; </s>
            <s xml:id="echoid-s1974" xml:space="preserve">F B verò ipſam
              <lb/>
            K L in puncto R, atque harum interſectionum puncta connectat Q R.</s>
            <s xml:id="echoid-s1975" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div300" type="section" level="1" n="215">
          <head xml:id="echoid-head228" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1976" xml:space="preserve">Quandoquidem centrum gravitatis trianguli B D C per 2 propoſ. </s>
            <s xml:id="echoid-s1977" xml:space="preserve">eſt in
              <lb/>
            recta B F, & </s>
            <s xml:id="echoid-s1978" xml:space="preserve">per 5 propoſ. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">etiam in recta
              <lb/>
            K L, centrum erit in concurſu R, eâdem ra-
              <lb/>
            tione Q erit centrum gravitatis trianguli
              <lb/>
              <figure xlink:label="fig-527.01.063-01" xlink:href="fig-527.01.063-01a" number="104">
                <image file="527.01.063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.063-01"/>
              </figure>
            A B D. </s>
            <s xml:id="echoid-s1980" xml:space="preserve">Quamobrem Q R horum triangu-
              <lb/>
            lorum jugum crit, in quo utriuſq; </s>
            <s xml:id="echoid-s1981" xml:space="preserve">ſeu quod
              <lb/>
            idem eſt ſecuriculæ A B C D gravitatis cen-
              <lb/>
            trum conſiſtit, ſed idem per propoſ. </s>
            <s xml:id="echoid-s1982" xml:space="preserve">7 quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s1983" xml:space="preserve">eſtin F E; </s>
            <s xml:id="echoid-s1984" xml:space="preserve">Itaque G centrum gravitatis erit
              <lb/>
            quadranguli A B C D. </s>
            <s xml:id="echoid-s1985" xml:space="preserve">Triangula autem
              <lb/>
            C D B, A B D, intra eaſdem parallelas ex
              <lb/>
            hypotheſi cõſiſtentia, erunt ut baſes, hoc eſt, D C ad A B, ut C D B ad A B D,
              <lb/>
            ſed ſic per 1 propoſ. </s>
            <s xml:id="echoid-s1986" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">radius G Q ad G R, atque ita P G ad G O (quia
              <lb/>
            clauduntur parallelis M N, K L) omiſſis itaque mediis, ut D C ad A B ſic
              <lb/>
            G P ad G O. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">Ideoq́ue (per 15, 16 & </s>
            <s xml:id="echoid-s1989" xml:space="preserve">24 propoſ. </s>
            <s xml:id="echoid-s1990" xml:space="preserve">5. </s>
            <s xml:id="echoid-s1991" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1992" xml:space="preserve">Euclid.) </s>
            <s xml:id="echoid-s1993" xml:space="preserve">ut dupla D C
              <lb/>
            cum A B, ad duplam A B auctam ipſa D C, ſic dupla G O, aucta G P, ad du-
              <lb/>
            plam G P plus ipſa G O. </s>
            <s xml:id="echoid-s1994" xml:space="preserve">Verum G E æquatur duplici G P cum G O; </s>
            <s xml:id="echoid-s1995" xml:space="preserve">Et
              <lb/>
            G F item duplici G O plus G P. </s>
            <s xml:id="echoid-s1996" xml:space="preserve">Quamobrem ut D C bis plus A B, ad A B
              <lb/>
            bis plus D C, ſic G E ad G F. </s>
            <s xml:id="echoid-s1997" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1998" xml:space="preserve">Itaque ſecuriculæ gravi-
              <lb/>
            tatis centrum, &</s>
            <s xml:id="echoid-s1999" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2000" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div302" type="section" level="1" n="216">
          <head xml:id="echoid-head229" xml:space="preserve">3 PROBLEMA. 9 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2001" xml:space="preserve">Dato cum totius plani, tum ſegmenti cujus ad reliquum
              <lb/>
            ratio ſit nota, gravitatis centro; </s>
            <s xml:id="echoid-s2002" xml:space="preserve">ejuſdem reliqui centrum
              <lb/>
            invenire.</s>
            <s xml:id="echoid-s2003" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div303" type="section" level="1" n="217">
          <head xml:id="echoid-head230" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s2004" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2005" xml:space="preserve">Rectilinei plani A B C D gravitatis centrum E, ſegmenti verò
              <lb/>
            B D A, F centrum eſto. </s>
            <s xml:id="echoid-s2006" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2007" xml:space="preserve">Reliqui ſegmenti B D C gravita-
              <lb/>
            tis centrum invenire.</s>
            <s xml:id="echoid-s2008" xml:space="preserve"/>
          </p>
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