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

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        <div xml:id="echoid-div343" type="section" level="1" n="245">
          <pb o="73" file="527.01.073" n="73" rhead="*DE* S*TATICÆ PRINCIPIIS.*"/>
        </div>
        <div xml:id="echoid-div346" type="section" level="1" n="246">
          <head xml:id="echoid-head260" xml:space="preserve">7 PROBLEMA. 19 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2381" xml:space="preserve">Solidi gravitatis centro & </s>
            <s xml:id="echoid-s2382" xml:space="preserve">ſegmenti ſui cujus ad reli-
              <lb/>
            quum ratio ſit data cognitis, ejuſdem reliqui ſegmenti gra-
              <lb/>
            vitatis centrum quoque invenire.</s>
            <s xml:id="echoid-s2383" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2384" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2385" xml:space="preserve">Corporis ABCD centrum gravitatis ſit E, ſegmenti verò BDA
              <lb/>
            centrum F. </s>
            <s xml:id="echoid-s2386" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2387" xml:space="preserve">Reliqui ſegmenti BCD gravitatis centrum in-
              <lb/>
            venire.</s>
            <s xml:id="echoid-s2388" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div347" type="section" level="1" n="247">
          <head xml:id="echoid-head261" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2389" xml:space="preserve">Fiat FE ad continuationem EG ut ſolidum BDC ad BDA; </s>
            <s xml:id="echoid-s2390" xml:space="preserve">ajo G eſſe
              <lb/>
            optatum gravitatis centrum reliqui ſegmenti BDC, cujus demonſtratio ſimil-
              <lb/>
            lima erit 9 propoſ. </s>
            <s xml:id="echoid-s2391" xml:space="preserve">Sed ſphæræ ſegmenti cujus ad re-
              <lb/>
              <figure xlink:label="fig-527.01.073-01" xlink:href="fig-527.01.073-01a" number="118">
                <image file="527.01.073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.073-01"/>
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            liquam ratio ſit data cum è ſecundo 9 propoſ. </s>
            <s xml:id="echoid-s2392" xml:space="preserve">exem-
              <lb/>
            plo ſatis plana ſit nullum paradigma proponam.</s>
            <s xml:id="echoid-s2393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2394" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2395" xml:space="preserve">Quamobrem datis gravitatis
              <lb/>
            centris totius ſolidi & </s>
            <s xml:id="echoid-s2396" xml:space="preserve">ſui ſegmĕti cujus ad reliquum
              <lb/>
            ratio inveniri poſſit, ejuſdem reliqui gravitatis cen-
              <lb/>
            trum, invenimus. </s>
            <s xml:id="echoid-s2397" xml:space="preserve">Quod feciſſe oportebat.</s>
            <s xml:id="echoid-s2398" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div349" type="section" level="1" n="248">
          <head xml:id="echoid-head262" xml:space="preserve">8 PROBLEMA. 20 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2399" xml:space="preserve">Pyramidis curtæ gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2401" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2402" xml:space="preserve">Eſto ABCDEF pyramis curta, cujus ſumma baſis ABC,
              <lb/>
            ima DEF. </s>
            <s xml:id="echoid-s2403" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2404" xml:space="preserve">Ejus gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2405" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div350" type="section" level="1" n="249">
          <head xml:id="echoid-head263" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2406" xml:space="preserve">Abſolvito curtam pyramidem, expleto defectu ABCG, & </s>
            <s xml:id="echoid-s2407" xml:space="preserve">axis ductus à
              <lb/>
            vertice G ad H centrum baſis D E F ſecet planum ABC in I, ſegmen verò
              <lb/>
            GL ita ſecetur in K ut GK ipſius KL ſit tripla,
              <lb/>
              <figure xlink:label="fig-527.01.073-02" xlink:href="fig-527.01.073-02a" number="119">
                <image file="527.01.073-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.073-02"/>
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            & </s>
            <s xml:id="echoid-s2408" xml:space="preserve">L totum axem ita incîdat ut pars ſumma GL
              <lb/>
            imæ LH ſit item tripla, denique eadem ſit ratio
              <lb/>
            jugi KL ad LM quæ curtæ pyramidis ABCDEF
              <lb/>
            ad complementum ABCG; </s>
            <s xml:id="echoid-s2409" xml:space="preserve">ajo M eſſa gravita-
              <lb/>
            tis optatum centrum.</s>
            <s xml:id="echoid-s2410" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div352" type="section" level="1" n="250">
          <head xml:id="echoid-head264" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2411" xml:space="preserve">L centrum eſt totius, K verò ſegmenti, ut au-
              <lb/>
            tem imum ſegmentum ad ſummum, ſic KL ad
              <lb/>
            LM. </s>
            <s xml:id="echoid-s2412" xml:space="preserve">Quare per 1 propoſ. </s>
            <s xml:id="echoid-s2413" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2414" xml:space="preserve">M fuerit optatum
              <lb/>
            gravitatis centrum. </s>
            <s xml:id="echoid-s2415" xml:space="preserve">Demonſtratio in cæteris cur-
              <lb/>
            tis pyramidibus multangulæ vel circularis baſis huic affinis eſt.</s>
            <s xml:id="echoid-s2416" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2417" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2418" xml:space="preserve">Quamobrem datæ curta pyramidis gravitatis centrum, ut
              <lb/>
            decuit, invenimus.</s>
            <s xml:id="echoid-s2419" xml:space="preserve"/>
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