Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000572">
                <pb pagenum="28" xlink:href="023/01/063.jpg"/>
              uel coni portionis axis à centro grauitatis ita diui
                <lb/>
              ditur, ut pars, quæ terminatur ad uerticem reli­
                <lb/>
              quæ partis, quæ ad baſim, ſit tripla.</s>
            </p>
            <p type="main">
              <s id="s.000573">Sit pyramis, cuius baſis triangulum abc; axis de; & gra
                <lb/>
              uitatis centrum K. </s>
              <s id="s.000574">Dico lineam dk ipſius Ke triplam eſſe. </s>
              <lb/>
              <s id="s.000575">trianguli enim bdc centrum grauitatis ſit punctum f;
                <expan abbr="triã">trian</expan>
                <lb/>
              guli adc
                <expan abbr="centrũ">centrum</expan>
              g; & trianguli adb ſit h: & iungantur af,
                <lb/>
              b g, ch. </s>
              <s id="s.000576">Quoniam igitur
                <expan abbr="centrũ">centrum</expan>
              grauitatis pyramidis in axe
                <lb/>
                <arrow.to.target n="marg66"/>
                <lb/>
                <expan abbr="cõſiſtit">conſiſtit</expan>
              :
                <expan abbr="ſuntq;">ſuntque</expan>
              de, af, bg, ch
                <expan abbr="eiuſdẽ">eiuſdem</expan>
              pyramidis axes: conue
                <lb/>
              nient omnes in
                <expan abbr="idẽ">idem</expan>
                <expan abbr="punctũ">punctum</expan>
              k, quod eſt grauitatis centrum. </s>
              <lb/>
              <s id="s.000577">Itaque animo concipiamus hanc pyramidem diuiſam in
                <lb/>
              quatuor pyramides, quarum baſes ſint ipſa pyramidis
                <lb/>
                <arrow.to.target n="marg67"/>
                <lb/>
                <figure id="id.023.01.063.1.jpg" xlink:href="023/01/063/1.jpg" number="57"/>
                <lb/>
              triangula; &
                <emph type="ul"/>
              axis
                <emph.end type="ul"/>
              pun­
                <lb/>
              ctum k quæ quidem py­
                <lb/>
              ramides inter ſe æquales
                <lb/>
              ſunt, ut
                <expan abbr="demõſtrabitur">demonſtrabitur</expan>
              . </s>
              <lb/>
              <s id="s.000578">Ducatur
                <expan abbr="enĩ">enim</expan>
              per lineas
                <lb/>
              dc, de planum
                <expan abbr="ſecãs">ſecans</expan>
              , ut
                <lb/>
              ſit ipſius, & baſis abc
                <expan abbr="cõ">com</expan>
                <lb/>
              munis ſectio recta linea
                <lb/>
              cel:
                <expan abbr="eiuſdẽ">eiuſdem</expan>
              uero &
                <expan abbr="triã-guli">trian­
                  <lb/>
                guli</expan>
              adb ſit linea dhl. erit linea al æqualis ipſi
                <lb/>
              lb: nam centrum graui­
                <lb/>
              tatis trianguli conſiſtit
                <lb/>
              in linea, quæ ab angulo
                <lb/>
              ad dimidiam baſim per­
                <lb/>
              ducitur, ex tertia deci­
                <lb/>
              ma Archimedis. </s>
              <lb/>
              <s id="s.000579">quare
                <lb/>
                <arrow.to.target n="marg68"/>
                <lb/>
              triangulum acl æquale
                <lb/>
              eſt triangulo bcl: & propterea pyramis, cuius baſis trian­
                <lb/>
              gulum acl, uertex d, eſt æqualis pyramidi, cuius baſis bcl
                <lb/>
                <arrow.to.target n="marg69"/>
                <lb/>
              triangulum, & idem uertex. </s>
              <s id="s.000580">pyramides enim, quæ ab
                <expan abbr="eodẽ">eodem</expan>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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