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

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        <div xml:id="echoid-div324" type="section" level="1" n="232">
          <pb o="69" file="527.01.069" n="69" rhead="*DE* S*TATICÆ PRINCIPITS.*"/>
        </div>
        <div xml:id="echoid-div326" type="section" level="1" n="233">
          <head xml:id="echoid-head246" xml:space="preserve">CENTROBARICA SOLIDORVM
            <lb/>
          DEINCEPS SVCCEDVNT.</head>
          <head xml:id="echoid-head247" xml:space="preserve">9 THE OREMA. 14 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2215" xml:space="preserve">Solidi cujuſlibet, & </s>
            <s xml:id="echoid-s2216" xml:space="preserve">figuræ & </s>
            <s xml:id="echoid-s2217" xml:space="preserve">gravitatis idem eſt cen-
              <lb/>
            trum.</s>
            <s xml:id="echoid-s2218" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2219" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2220" xml:space="preserve">Tetraë dri A B C D centrum ſit E, axis autem ab A per E cen-
              <lb/>
            trum occurrens baſi B C D in F, ſit A F.</s>
            <s xml:id="echoid-s2221" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2222" xml:space="preserve">Q*VALSITVM*. </s>
            <s xml:id="echoid-s2223" xml:space="preserve">Ipſum E gravitatis quoque centrum eſſe oſtenditor.</s>
            <s xml:id="echoid-s2224" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div327" type="section" level="1" n="234">
          <head xml:id="echoid-head248" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2225" xml:space="preserve">Solidum hoc ſuſpendito ex A E; </s>
            <s xml:id="echoid-s2226" xml:space="preserve">cum igitur tetraëdrum componatur è qua-
              <lb/>
            tuor pyramidibus ſimilibus & </s>
            <s xml:id="echoid-s2227" xml:space="preserve">inter ſe æqualibus quorum vertex communis ſit
              <lb/>
            E, ipſa A F erit ejus gravitatis diameter; </s>
            <s xml:id="echoid-s2228" xml:space="preserve">eadem ratio erit rectæ
              <lb/>
              <figure xlink:label="fig-527.01.069-01" xlink:href="fig-527.01.069-01a" number="111">
                <image file="527.01.069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.069-01"/>
              </figure>
            C E; </s>
            <s xml:id="echoid-s2229" xml:space="preserve">quare E centrum erit in concurſu diametrorum. </s>
            <s xml:id="echoid-s2230" xml:space="preserve">Similis
              <lb/>
            demonſtratio erit in reliquis corporibus cum auctis & </s>
            <s xml:id="echoid-s2231" xml:space="preserve">immi-
              <lb/>
            nutis tum etiam abſolutè ordinatis quæ centrum ſoliditatis
              <lb/>
            habebunt, nam ipſa ex diametris vel per angulum ſolidum, vel
              <lb/>
            per hedrarũ centra eductis ſuſpenſa, ratio ſitus componentum
              <lb/>
            pyramidum (quarum quidem vertices eodem coëunt, & </s>
            <s xml:id="echoid-s2232" xml:space="preserve">baſes
              <lb/>
            ſolidi ipſius ſint hedræ) ad latera omnia par erit, quamobrem
              <lb/>
            ex communi notitia, & </s>
            <s xml:id="echoid-s2233" xml:space="preserve">1 poſtulatum 1 lib. </s>
            <s xml:id="echoid-s2234" xml:space="preserve">univerſa ab hac recta
              <lb/>
            æquilibria dependebunt; </s>
            <s xml:id="echoid-s2235" xml:space="preserve">& </s>
            <s xml:id="echoid-s2236" xml:space="preserve">conſequenter mutua in centro
              <lb/>
            figuræ iſtiuſmodi diametrorum interſectio, ceutrum quoque gravitatis erit.</s>
            <s xml:id="echoid-s2237" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2238" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2239" xml:space="preserve">Itaque in ſolido & </s>
            <s xml:id="echoid-s2240" xml:space="preserve">figuræ & </s>
            <s xml:id="echoid-s2241" xml:space="preserve">gravitatis idem eſt centrum.</s>
            <s xml:id="echoid-s2242" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div329" type="section" level="1" n="235">
          <head xml:id="echoid-head249" xml:space="preserve">10 THE OREMA. 15 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2243" xml:space="preserve">Priſmatis gravitatis centrum eſt in axis medio.</s>
            <s xml:id="echoid-s2244" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div330" type="section" level="1" n="236">
          <head xml:id="echoid-head250" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s2245" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2246" xml:space="preserve">Eſto A B priſma baſis triangulæ A C D.</s>
            <s xml:id="echoid-s2247" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2248" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2249" xml:space="preserve">Axem à gravitatis ſuæ centro biſecari demonſtrator.</s>
            <s xml:id="echoid-s2250" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2251" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s2252" xml:space="preserve">D E biſecet latus A C, parallelæ autem H I, F G, ipſam
              <lb/>
            biſectricem interſecent in punctis K, L, & </s>
            <s xml:id="echoid-s2253" xml:space="preserve">parallelæ ſint F M, H N, I O, G P
              <lb/>
            ad ipſam D E; </s>
            <s xml:id="echoid-s2254" xml:space="preserve">dein de A Q oppoſitam D C bifariam ſecet in Q Ac denique
              <lb/>
            reliquæ he@ræ parallelogrammæ biſecentur plano R S baſi A D C parallelo,
              <lb/>
            à quò C B bifariam dividatur in puncto S.</s>
            <s xml:id="echoid-s2255" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div331" type="section" level="1" n="237">
          <head xml:id="echoid-head251" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2256" xml:space="preserve">Planum actum per D E & </s>
            <s xml:id="echoid-s2257" xml:space="preserve">rectam ſibi parallelam in plano R S reliquas he-
              <lb/>
            dras biſecante, tribuit priſma H N F M P G I in duo priſmata æqualia & </s>
            <s xml:id="echoid-s2258" xml:space="preserve">ſimi-
              <lb/>
            lia; </s>
            <s xml:id="echoid-s2259" xml:space="preserve">tranſit igitur per hujus inſcriptæ priſmatis gravitatis centrum, quo </s>
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