Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000279">
                <pb xlink:href="023/01/030.jpg"/>
              tu, xy ipſi gh æquidiſtare. </s>
              <s id="s.000280">Et quoniam triangula, quæ
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              fiunt à lineis Ky, yu, us, sh æqualia ſunt inter ſe, & ſimilia
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                <arrow.to.target n="marg38"/>
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              triangulo Kmh: habebit triangulum Kmh ad
                <expan abbr="triangulũ">triangulum</expan>
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              K
                <foreign lang="grc">δ</foreign>
              y duplam proportionem eius, quæ eſt lineæ kh ad Ky. </s>
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              <s id="s.000281">ſed Kh poſita eſt quadrupla ipſius ky. </s>
              <s id="s.000282">ergo triangulum
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              kmh ad triangulum K
                <foreign lang="grc">δ</foreign>
              y
                <expan abbr="eãdem">eandem</expan>
              proportionem habebit,
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              quam ſexdecim ad
                <expan abbr="unũ">unum</expan>
              : & ad quatuor triangula k
                <foreign lang="grc">δ</foreign>
              y, yu,
                <lb/>
              us, s
                <foreign lang="grc">α</foreign>
              h habebit eandem, quam ſexdecim ad quatuor, hoc
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              eſt quam hK ad ky: & ſimiliter eandem habere demonſtra
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                <figure id="id.023.01.030.1.jpg" xlink:href="023/01/030/1.jpg" number="22"/>
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              bitur trian­
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              gulum kmg
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              ad quatuor
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                <expan abbr="triãgula">triangula</expan>
              K
                <foreign lang="grc">δ</foreign>
                <lb/>
              x, x
                <foreign lang="grc">γ</foreign>
              t, t
                <foreign lang="grc">β</foreign>
              r,
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                <arrow.to.target n="marg39"/>
                <lb/>
              rzg. </s>
              <s id="s.000283">quare
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              totum trian
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              gulum Kgh
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              ad omnia tri
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              angula gzr,
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              r
                <foreign lang="grc">β</foreign>
              t, t
                <foreign lang="grc">γ</foreign>
              x, x
                <foreign lang="grc">δ</foreign>
                <lb/>
              K, K
                <foreign lang="grc">δ</foreign>
              y, yu,
                <lb/>
              us, s
                <foreign lang="grc">α</foreign>
              h ita
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              erit, ut hk ad
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              ky, hoc eſt
                <lb/>
              ut hm ad m
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              q. </s>
              <s id="s.000284">Si igitur in
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              triangulis abc, def deſcribantur figuræ ſimiles ei, quæ de­
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              ſcripta eſt in ghK triangulo: & per lineas ſibi reſponden­
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              tes plana ducantur: totum priſma af diuiſum erit in tria
                <lb/>
              ſolida parallelepipeda y
                <foreign lang="grc">γ,</foreign>
              u
                <foreign lang="grc">β,</foreign>
              sz, quorum baſes ſunt æqua
                <lb/>
              les & ſimiles ipſis parallelogrammis y
                <foreign lang="grc">γ,</foreign>
              u
                <foreign lang="grc">β,</foreign>
              sz: & in octo
                <lb/>
              priſmata gzr, r
                <foreign lang="grc">β</foreign>
              t, t
                <foreign lang="grc">γ</foreign>
              x, x
                <foreign lang="grc">δ</foreign>
                <lb/>
              K, k
                <foreign lang="grc">δ</foreign>
              y, yu, us, s
                <foreign lang="grc">α</foreign>
              h: quorum
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              item baſes æquales, & ſimiles ſunt dictis triangulis; altitu­
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              do autem in omnibus, totius priſmatis altitudini </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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