Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000823">
                <pb pagenum="39" xlink:href="023/01/085.jpg"/>
              dem, cuius baſis eſt quadratum abcd, & altitudo eg: &
                <lb/>
              in pyramidem, cuius
                <expan abbr="eadẽ">eadem</expan>
              baſis,
                <expan abbr="altitudoq;">altitudoque</expan>
              fg; ut ſint eg,
                <lb/>
              gf ſemidiametri ſphæræ, & linea una. </s>
              <s id="s.000824">
                <expan abbr="Cũ">Cum</expan>
              igitur g ſit ſphæ­
                <lb/>
              ræ centrum, erit etiam centrum circuli, qui circa
                <expan abbr="quadratũ">quadratum</expan>
                <lb/>
              abcd deſcribitur: & propterea eiuſdem quadrati grauita
                <lb/>
              tis centrum: quod in prima propoſitione huius demon­
                <lb/>
              ſtratum eſt. </s>
              <s id="s.000825">quare pyramidis abcde axis erit eg: & pyra
                <lb/>
              midis abcdf axis fg. </s>
              <s id="s.000826">Itaque ſit h centrum grauitatis py­
                <lb/>
              ramidis abcde, & pyramidis abcdf centrum ſit
                <emph type="italics"/>
              K:
                <emph.end type="italics"/>
              per­
                <lb/>
              ſpicuum eſt ex uigeſima ſecunda propoſitione huius,
                <expan abbr="lineã">lineam</expan>
                <lb/>
                <figure id="id.023.01.085.1.jpg" xlink:href="023/01/085/1.jpg" number="74"/>
                <lb/>
              ch triplam eſſe hg:
                <expan abbr="cõ">com</expan>
                <lb/>
                <expan abbr="ponendoq;">ponendoque</expan>
              eg ipſius g
                <lb/>
              h quadruplam. </s>
              <s id="s.000827">&
                <expan abbr="eadẽ">eadem</expan>
                <lb/>
              ratione fg
                <expan abbr="quadruplã">quadruplam</expan>
                <lb/>
              ipſius gk quod cum e
                <lb/>
              g, gf ſint æquales, & h
                <lb/>
              g, g
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              neceſſario æqua­
                <lb/>
              les erunt. </s>
              <s id="s.000828">ergo ex quar
                <lb/>
              ta propoſitione primi
                <lb/>
              libri Archimedis de
                <expan abbr="cẽ-tro">cen­
                  <lb/>
                tro</expan>
              grauitatis
                <expan abbr="planorũ">planorum</expan>
              ,
                <lb/>
              totius octahedri, quod
                <lb/>
              ex dictis pyramidibus
                <lb/>
              conſtat, centrum graui
                <lb/>
              tatis erit punctum g idem, quod ipſius ſphæræ centrum.</s>
            </p>
            <p type="main">
              <s id="s.000829">Sit icoſahedrum ad deſcriptum in ſphæra, cuius
                <expan abbr="centrũ">centrum</expan>
                <lb/>
              ſit g. </s>
              <s id="s.000830">Dico g ipſius icoſahedri grauitatis eſſe centrum. </s>
              <s id="s.000831">Si
                <lb/>
              enim ab angulo a per g ducatur recta linea uſque ad ſphæ
                <lb/>
              ræ ſuperficiem; conſtat ex ſexta decima propoſitione libri
                <lb/>
              tertii decimi elementorum, cadere eam in angulum ipſi a
                <lb/>
              oppoſitum. </s>
              <s id="s.000832">cadat in d:
                <expan abbr="ſitq;">ſitque</expan>
              una aliqua baſis icoſahedri tri­
                <lb/>
              angulum abc: & iunctæ bg, producantur, & cadant in
                <lb/>
              angulos ef, ipſis bc oppoſitos. </s>
              <s id="s.000833">Itaque per triangula
                <lb/>
              abc, def ducantur plana ſphæram ſecantia.</s>
              <s id="s.000834"> erunt hæ </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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