Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <pb xlink:href="023/01/022.jpg"/>
              <s id="s.000199">Itaque quoniam duæ lineæ Kl, lm ſe ſe tangentes, duabus
                <lb/>
              lineis ſe ſe tangentibus ab, bc æquidiſtant; nec ſunt in e o­
                <lb/>
              dem plano: angulus klm æqualis eſt angulo abc: & ita an
                <lb/>
                <arrow.to.target n="marg26"/>
                <lb/>
              gulus lmk, angulo bca, & mkl ipſi cab æqualis probabi
                <lb/>
              tur. </s>
              <s id="s.000200">triangulum ergo klm eſt æquale, & ſimile triangulo
                <lb/>
              abc. quare & triangulo def. </s>
              <s id="s.000201">Ducatur linea cgo, & per ip
                <lb/>
              ſam, & per cf ducatur planum ſecans priſma; cuius & paral
                <lb/>
              lelogrammi ae communis ſectio ſit opq.</s>
              <s id="s.000202"> tranſibit linea
                <lb/>
              fq per h, & mp per n. </s>
              <s id="s.000203">nam cum plana æquidiſtantia ſecen
                <lb/>
              tur à plano cq, communes eorum ſectiones cgo, mp, fq
                <lb/>
              ſibi ipſis æquidiſtabunt. </s>
              <s id="s.000204">Sed & æquidiſtant ab, kl, de. </s>
              <s id="s.000205">an­
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                <arrow.to.target n="marg27"/>
                <lb/>
              guli ergo aoc, kpm, dqf inter ſe æquales ſunt: & ſunt
                <lb/>
              æquales qui ad puncta akd conſtituuntur. </s>
              <s id="s.000206">quare & reliqui
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              reliquis æquales; & triangula aco, Kmp, dfq inter ſe ſimi
                <lb/>
                <arrow.to.target n="marg28"/>
                <lb/>
              lia erunt. </s>
              <s id="s.000207">Vt igitur ca ad ao, ita fd ad dq: & permutando
                <lb/>
              ut ca ad fd, ita ao ad dq.</s>
              <s id="s.000208">eſt autem ca æqualis fd. </s>
              <s id="s.000209">ergo &
                <lb/>
              ao ipſi dq.</s>
              <s id="s.000210"> eadem quoque ratione & ao ipſi Kp æqualis
                <lb/>
              demonſtrabitur. </s>
              <s id="s.000211">Itaque ſi triangula, abc, def æqualia &
                <lb/>
                <figure id="id.023.01.022.1.jpg" xlink:href="023/01/022/1.jpg" number="15"/>
                <lb/>
              ſimilia inter ſe
                <expan abbr="aptẽtur">aptentur</expan>
              ,
                <lb/>
              cadet linea fq in lineam
                <lb/>
                <arrow.to.target n="marg29"/>
                <lb/>
              cgo. </s>
              <s id="s.000212">Sed &
                <expan abbr="centrũ">centrum</expan>
              gra
                <lb/>
              uitatis h in g
                <expan abbr="centrũ">centrum</expan>
              ca­
                <lb/>
              det. </s>
              <s id="s.000213">
                <expan abbr="trãſibit">tranſibit</expan>
              igitur linea
                <lb/>
              fq per h: & planum per
                <lb/>
              co & cf
                <expan abbr="ductũ">ductum</expan>
              per
                <expan abbr="axẽ">axem</expan>
                <lb/>
              gh ducetur:
                <expan abbr="idcircoq;">idcircoque</expan>
              li
                <lb/>
              neam mp
                <expan abbr="etiã">etiam</expan>
              per n
                <expan abbr="trã">tran</expan>
                <lb/>
              ſire neceſſe erit. </s>
              <s id="s.000214">Quo­
                <lb/>
              niam ergo fh, cg æqua­
                <lb/>
              les ſunt, &
                <expan abbr="æquidiſtãtes">æquidiſtantes</expan>
              :
                <lb/>
                <expan abbr="itemq;">itemque</expan>
              hq, go; rectæ li­
                <lb/>
              neæ, quæ ipſas
                <expan abbr="cõnectũt">connectunt</expan>
                <lb/>
              cmf, gnh, opq æqua­
                <lb/>
              les æquidiſtantes
                <expan abbr="erũt">erunt</expan>
              .</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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