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

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        <div xml:id="echoid-div335" type="section" level="1" n="239">
          <pb o="71" file="527.01.071" n="71" rhead="*DE* S*TATICÆ PRINCIPIIS*."/>
        </div>
        <div xml:id="echoid-div336" type="section" level="1" n="240">
          <head xml:id="echoid-head254" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2309" xml:space="preserve">Triangula NOP, RST, FG, KLM, ſimilia ſunt triangulo BCD, & </s>
            <s xml:id="echoid-s2310" xml:space="preserve">
              <lb/>
            puncta Q, I, E, in iſtis ſimili ſitu reſpondent puncto E in triangulo BCD,
              <lb/>
            quod ejuſdem gravitatis eſt centrum, ideo Q, I, E, ſuorum triangulorum
              <lb/>
              <figure xlink:label="fig-527.01.071-01" xlink:href="fig-527.01.071-01a" number="114">
                <image file="527.01.071-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.071-01"/>
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            gravitatis ſunt centra, & </s>
            <s xml:id="echoid-s2311" xml:space="preserve">I E axis priſmatis
              <lb/>
            FGHKLM quem medium, per 15 pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s2312" xml:space="preserve">gravitatis centrum incîdit; </s>
            <s xml:id="echoid-s2313" xml:space="preserve">ſic item
              <lb/>
            Q I axis priſmatis NOPRST medius à
              <lb/>
            centro ſuo dividetur, quamobrem ſolidum
              <lb/>
            ex utroque priſmate compoſitum centrum
              <lb/>
            habet in Q E hoc eſt in A E, verumenim-
              <lb/>
            vero hujuſmodi priſmatum frequentiſſima
              <lb/>
            inſcriptio, componet ſolidum quod ad py-
              <lb/>
            ramidis ſoliditatem proximè accedat, cujus
              <lb/>
            tamen gravitatis centrum in axe A E ſem-
              <lb/>
            per hæreat. </s>
            <s xml:id="echoid-s2314" xml:space="preserve">Sed ſolidum tale poteſt intra py-
              <lb/>
            ramidem inſcribi ut ejus à pyramide diffe-
              <lb/>
            rentia quocunque dato corpore minor ſit,
              <lb/>
            unde efficitur, poſita diametro A E gravita-
              <lb/>
            tis ſitum unius partis à reliqua minori etiam
              <lb/>
            quam dari poſlit differentiâ abeſſe; </s>
            <s xml:id="echoid-s2315" xml:space="preserve">Quod
              <lb/>
            eodem quo ſupra ſyllogiſmo evincam.</s>
            <s xml:id="echoid-s2316" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2317" xml:space="preserve">Ineæqualium ſitu gravium ponderum differentiâ minus pondus dari poteſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2318" xml:space="preserve">Sed borum ponderum differentiâ pondus minus exhiberi nullum poteſt. </s>
            <s xml:id="echoid-s2319" xml:space="preserve">
              <lb/>
            Itaque horum ponderum differentia nulla eſt.</s>
            <s xml:id="echoid-s2320" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2321" xml:space="preserve">Simillima demonſtratio erit in cæteris quorum baſes erunt quadrangulæ,
              <lb/>
            aut quomodocunque multangulæ, vel rotundæ denique.</s>
            <s xml:id="echoid-s2322" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2323" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2324" xml:space="preserve">Itaque, centrum gravitatis pyramidis eſt in axe.</s>
            <s xml:id="echoid-s2325" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div338" type="section" level="1" n="241">
          <head xml:id="echoid-head255" xml:space="preserve">6 PROBLEMA. 17 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2326" xml:space="preserve">Pyramidís triangulæ baſis gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2327" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2328" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2329" xml:space="preserve">Pyramidis ABC baſis ſit BCD.</s>
            <s xml:id="echoid-s2330" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2331" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2332" xml:space="preserve">Gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2333" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div339" type="section" level="1" n="242">
          <head xml:id="echoid-head256" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2334" xml:space="preserve">Duarum hedrarum BCD, ABC gravitatis
              <lb/>
              <figure xlink:label="fig-527.01.071-02" xlink:href="fig-527.01.071-02a" number="115">
                <image file="527.01.071-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.071-02"/>
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            centra EF, oppoſitis verticibus connexa rectis AE,
              <lb/>
            BF ſeſe incîdent in G & </s>
            <s xml:id="echoid-s2335" xml:space="preserve">cum utraque ſit diameter,
              <lb/>
            Ajo G eſſe centrum optatum.</s>
            <s xml:id="echoid-s2336" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div341" type="section" level="1" n="243">
          <head xml:id="echoid-head257" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2337" xml:space="preserve">Etenim pyramidis gravitatis centrum eſt in AE,
              <lb/>
            itemq́ue in B F per 16 propoſ. </s>
            <s xml:id="echoid-s2338" xml:space="preserve">eſt itaque in G ipſa-
              <lb/>
            rum mutua interſectione.</s>
            <s xml:id="echoid-s2339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2340" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2341" xml:space="preserve">Pyramidis igitur à triangula baſi aſſurgentis, centrum gra-
              <lb/>
            vitatis, ut petebatur, invenimus.</s>
            <s xml:id="echoid-s2342" xml:space="preserve"/>
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