Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000300">
                <pb pagenum="13" xlink:href="023/01/033.jpg"/>
              trianguli ghK, & ipſius
                <foreign lang="grc">ρτ</foreign>
              axis medium.</s>
            </p>
            <p type="margin">
              <s id="s.000301">
                <margin.target id="marg35"/>
              5.huius</s>
            </p>
            <p type="margin">
              <s id="s.000302">
                <margin.target id="marg36"/>
              2. ſexti.
                <lb/>
              12 quinti.</s>
            </p>
            <p type="margin">
              <s id="s.000303">
                <margin.target id="marg37"/>
              2. ſexti.</s>
            </p>
            <p type="margin">
              <s id="s.000304">
                <margin.target id="marg38"/>
              19. ſexti</s>
            </p>
            <p type="margin">
              <s id="s.000305">
                <margin.target id="marg39"/>
              2. uel 12.
                <lb/>
              quinti.</s>
            </p>
            <p type="margin">
              <s id="s.000306">
                <margin.target id="marg40"/>
              8. quinti.</s>
            </p>
            <p type="margin">
              <s id="s.000307">
                <margin.target id="marg41"/>
              28. unde
                <lb/>
              cimi</s>
            </p>
            <p type="margin">
              <s id="s.000308">
                <margin.target id="marg42"/>
              15. quinti</s>
            </p>
            <p type="margin">
              <s id="s.000309">
                <margin.target id="marg43"/>
              19. quinti
                <lb/>
              apud
                <expan abbr="Cãpanum">Cam
                  <lb/>
                panum</expan>
              </s>
            </p>
            <p type="main">
              <s id="s.000310">Sit priſma ag, cuius oppoſita plana ſint quadrilatera
                <lb/>
              abcd, efgh:
                <expan abbr="ſecenturq;">ſecenturque</expan>
              ac, bf, cg, dh bifariam: & per di­
                <lb/>
              uiſiones planum ducatur; quod ſectionem faciat quadrila­
                <lb/>
              terum Klmn. </s>
              <s id="s.000311">Deinde iuncta ac per lineas ac, ae ducatur
                <lb/>
              planum
                <expan abbr="ſecãs">ſecans</expan>
              priſma, quod ipſum diuidet in duo priſmata
                <lb/>
              triangulares baſes habentia abcefg, adcehg. </s>
              <s id="s.000312">Sint
                <expan abbr="autẽ">autem</expan>
                <lb/>
                <figure id="id.023.01.033.1.jpg" xlink:href="023/01/033/1.jpg" number="24"/>
                <lb/>
              triangulorum abc, efg gra­
                <lb/>
              uitatis centra op: & triangu­
                <lb/>
              lorum adc, ehg centra qr:
                <lb/>
                <expan abbr="iunganturq;">iunganturque</expan>
              op, qr; quæ pla­
                <lb/>
              no klmn occurrant in pun­
                <lb/>
              ctis st. </s>
              <s id="s.000313">erit ex iis, quæ demon
                <lb/>
              ſtrauimus, punctum s grauita
                <lb/>
              tis centrum trianguli klm; &
                <lb/>
              ipſius priſmatis abcefg: pun
                <lb/>
              ctum uero t centrum grauita
                <lb/>
              tis trianguli Knm, & priſma­
                <lb/>
              tis adc, ehg. </s>
              <s id="s.000314">iunctis igitur
                <lb/>
              oq, pr, st, erit in linea oq
                <expan abbr="cẽ">cen</expan>
                <lb/>
              trum grauitatis quadrilateri
                <lb/>
              abcd, quod ſit u: & in linea
                <lb/>
              pr
                <expan abbr="cẽtrum">centrum</expan>
              quadrilateri efgh
                <lb/>
              ſit autem x. </s>
              <s id="s.000315">denique iungatur
                <lb/>
              u x, quæ ſecet lineam ſ t in y. </s>
              <s id="s.000316">ſe
                <lb/>
              cabit enim cum ſint in eodem
                <lb/>
                <arrow.to.target n="marg44"/>
                <lb/>
              plano:
                <expan abbr="atq;">atque</expan>
              erit y grauitatis centrum quadrilateri Klmn. </s>
              <lb/>
              <s id="s.000317">Dico idem punctum y centrum quoque gra uitatis eſſe to­
                <lb/>
              tius priſmatis. </s>
              <s id="s.000318">Quoniam enim quadrilateri klmn graui­
                <lb/>
              tatis centrum eſt y: linea sy ad yt ean dem proportionem
                <lb/>
              habebit, quam triangulum knm ad triangulum klm, ex 8
                <lb/>
              Archimedis de centro grauitatis planorum. </s>
              <s id="s.000319">Vt autem
                <expan abbr="triã">trian</expan>
                <lb/>
              gulum knm ad ipſum klm, hoc eſt ut triangulum adc ad
                <lb/>
              triangulum abc, æqualia enim ſunt, ita priſma adcehg </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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