Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000600">
                <pb pagenum="29" xlink:href="023/01/065.jpg"/>
              lh eandem habet proportionem, quam em ad mk, uideli­
                <lb/>
              cet triplam. </s>
              <s id="s.000601">quare linea lm ipſam ef ſecabit in puncto g:
                <lb/>
              etenim eg ad gf eſt, ut el ad lh. </s>
              <s id="s.000602">præterea quoniam hk, lm
                <lb/>
              æquidiſtant, erunt triangula hef, leg ſimilia:
                <expan abbr="itemq;">itemque</expan>
              inter
                <lb/>
              ſe ſimilia fek gem: & ut ef ad eg, ita hf ad lg: & ita fK ad
                <lb/>
              gm. </s>
              <s id="s.000603">ergo ut hf ad lg, ita fk ad gm: & permutando ut hf
                <lb/>
              ad fK, ita lg ad gm. </s>
              <s id="s.000604">ſed cum h ſit centrum trianguli abd;
                <lb/>
              & k
                <expan abbr="triãguli">trianguli</expan>
              bcd
                <expan abbr="punctũ">punctum</expan>
              uero f totius quadrilateri abcd
                <lb/>
              centrum: erit ex 8. Archimedis de centro grauitatis plano
                <lb/>
              rum hf ad fk ut triangulum bcd ad triangulum abd: ut,
                <lb/>
              autem bcd triangulum ad triangulum abd, ita pyramis
                <lb/>
                <figure id="id.023.01.065.1.jpg" xlink:href="023/01/065/1.jpg" number="58"/>
                <lb/>
              bcde ad pyramidem abde. </s>
              <s id="s.000605">ergo
                <lb/>
              linea lg ad gm erit, ut pyramis
                <lb/>
              bcde ad
                <expan abbr="pyramidẽ">pyramidem</expan>
              abde. </s>
              <s id="s.000606">ex quo
                <lb/>
              ſequitur, ut totius pyramidis
                <lb/>
              abcde punctum g ſit grauitatis
                <lb/>
              centrum. </s>
              <s id="s.000607">Rurſus ſit pyramis ba­
                <lb/>
              ſim habens pentagonum abcde:
                <lb/>
              & axem fg:
                <expan abbr="diuidaturq;">diuidaturque</expan>
              axis in
                <expan abbr="pũ">pun</expan>
                <lb/>
              cto h, ita ut fh ad hg triplam habe
                <lb/>
              at proportionem. </s>
              <s id="s.000608">Dico h grauita­
                <lb/>
              tis
                <expan abbr="centrũ">centrum</expan>
              eſſe pyramidis abcdef. </s>
              <lb/>
              <s id="s.000609">iungatur enim eb:
                <expan abbr="intelligaturq;">intelligaturque</expan>
                <lb/>
              pyramis, cuius uertex f, & baſis
                <lb/>
              triangulum abe: & alia pyramis
                <lb/>
              intelligatur eundem uerticem ha­
                <lb/>
              bens, & baſim bcde
                <expan abbr="quadrilaterũ">quadrilaterum</expan>
              :
                <lb/>
              ſit autem pyramidis abef axis fk
                <lb/>
              & grauitatis centrum l: & pyrami
                <lb/>
              dis bcdef axis fm, & centrum gra
                <lb/>
              uitatis n:
                <expan abbr="iunganturq;">iunganturque</expan>
              km, ln;
                <lb/>
              quæ per puncta gh tranſibunt. </s>
              <lb/>
              <s id="s.000610">Rurſus eodem modo, quo ſup ra,
                <lb/>
              demonſtrabimus lineas Kgm, lhn ſibi ipſis æquidiſtare: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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