Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000580">
                <pb xlink:href="023/01/064.jpg"/>
              ſunt uertice, eandem proportionem habent, quam
                <expan abbr="ipſarũ">ipſarum</expan>
                <lb/>
              baſes. </s>
              <s id="s.000581">eadem ratione pyramis aclk pyramidi bclk & py
                <lb/>
              ramis adlk ipſi bdlk pyramidi æqualis erit. </s>
              <s id="s.000582">Itaque ſi a py
                <lb/>
              ramide acld auferantur pyramides aclk, adlk: & à pyra
                <lb/>
              mide bcld
                <expan abbr="auferãtur">auferantur</expan>
              pyramides bclk dblK: quæ relin­
                <lb/>
              quuntur erunt æqualia. </s>
              <s id="s.000583">æqualis igitur eſt pyramis acdk
                <lb/>
              pyramidi bcdK. </s>
              <s id="s.000584">Rurſus ſi per lineas ad, de ducatur pla­
                <lb/>
              num quod pyramidem ſccet:
                <expan abbr="ſitq;">ſitque</expan>
              eius & baſis communis
                <lb/>
              ſectio aem: ſimiliter oſtendetur pyramis abdK æqualis
                <lb/>
              pyramidi acdk. </s>
              <s id="s.000585">ducto denique alio plano per lineas ca,
                <lb/>
              af: ut eius, & trianguli cdb communis ſectio ſit cfn, py­
                <lb/>
              ramis abck pyramidi acdk æqualis demonſtrabitur. </s>
              <s id="s.000586">
                <expan abbr="cũ">cum</expan>
                <lb/>
              ergo tres pyramides bcdk, abdk, abck uni, & eidem py
                <lb/>
              ramidi acdk ſint æquales, omnes inter ſe ſe æquales
                <expan abbr="erũt">erunt</expan>
              . </s>
              <lb/>
              <s id="s.000587">Sed ut pyramis abcd ad pyramidem abck ita de axis ad
                <lb/>
              axem ke, ex uigeſima propoſitione huius: ſunt enim hæ
                <lb/>
              pyramides in eadem baſi, & axes cum baſibus æquales con
                <lb/>
              tinent angulos, quòd in eadem recta linea conſtituantur. </s>
              <lb/>
              <s id="s.000588">quare diuidendo, ut tres pyramides acdk, bcdK, abdK
                <lb/>
              ad pyramidem abcK, ita dk ad Ke. </s>
              <s id="s.000589">conſtat igitur lineam
                <lb/>
              dK ipſius Ke triplam eſſe. </s>
              <s id="s.000590">ſed & ak tripla eſt Kf: itemque
                <lb/>
              bK ipſius kg: & ck ipſius kl tripla. </s>
              <s id="s.000591">quod eodem modo
                <lb/>
              demonſtrabimus.</s>
            </p>
            <p type="margin">
              <s id="s.000592">
                <margin.target id="marg66"/>
              17 huius</s>
            </p>
            <p type="margin">
              <s id="s.000593">
                <margin.target id="marg67"/>
                <emph type="italics"/>
              ucrfex
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000594">
                <margin.target id="marg68"/>
              1. sexti.</s>
            </p>
            <p type="margin">
              <s id="s.000595">
                <margin.target id="marg69"/>
              5. duode­
                <lb/>
              cimi.</s>
            </p>
            <p type="main">
              <s id="s.000596">Sit pyramis, cuius baſis quadrilaterum abcd; axis ef:
                <lb/>
              & diuidatur ef in g, ita ut eg ipſius gf ſit tripla. </s>
              <s id="s.000597">Dico cen­
                <lb/>
              trum grauitatis pyramidis eſſe punctum g. ducatur enim
                <lb/>
              linea bd diuidens baſim in duo triangula abd, bcd: ex
                <lb/>
              quibus
                <expan abbr="intelligãtur">intelligantur</expan>
                <expan abbr="cõſtitui">conſtitui</expan>
              duæ pyramides abde, bcde:
                <lb/>
              ſitque pyramidis abde axis eh; & pyramidis bcde axis
                <lb/>
              eK: & iungatur hK, quæ per f tranſibit: eſt enim in ipſa hK
                <lb/>
              centrum grauitatis magnitudinis compoſitæ ex triangulis
                <lb/>
              abd, bcd, hoc eſt ipſius quadrilateri. </s>
              <s id="s.000598">Itaque centrum gra
                <lb/>
              uitatis pyramidis abde ſit punctum l: & pyramidis bcde
                <lb/>
                <arrow.to.target n="marg70"/>
                <lb/>
              ſit m. </s>
              <s id="s.000599">ducta igitur lm ipſi hm lineæ æquidiſtabit. </s>
              <s id="s.000600">nam el ad </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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