Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000469">
                <pb pagenum="23" xlink:href="023/01/053.jpg"/>
              eſt ſolidi gm altitudo ad oe altitudinem ſolidi mc, uel
                <expan abbr="quã">quam</expan>
                <lb/>
              axis kq ad ql axem. </s>
              <s id="s.000470">Si uero axis kl non ſit perpendicularis
                <lb/>
              ad planum baſis; ducatur a puncto k ad idem planum per
                <lb/>
              pendicularis kr,
                <expan abbr="occurrẽs">occurrens</expan>
              plano mnop in s. </s>
              <s id="s.000471">ſimiliter
                <expan abbr="de-mõſtrabimus">de­
                  <lb/>
                monſtrabimus</expan>
              ſolidum gm ad
                <expan abbr="ſolidũ">ſolidum</expan>
              mc ita eſſe, ut axis kq
                <lb/>
              ad axem ql. </s>
              <s id="s.000472">Sed ut Kq ad ql, ita ks altitudo ad altitudi­
                <lb/>
                <arrow.to.target n="marg52"/>
                <lb/>
              nem sr; nam lineæ Kl, Kr à planis æquidiſtantibus in eaſ­
                <lb/>
              dem proportiones ſecantur. </s>
              <s id="s.000473">ergo ſolidum gm ad ſolidum
                <lb/>
              mc
                <expan abbr="eandẽ">eandem</expan>
              proportionem habet, quam altitudo ad
                <expan abbr="altitudinẽ">altitu
                  <lb/>
                dinem</expan>
              , uel quam axis ad axem. </s>
              <s id="s.000474">quod
                <expan abbr="demõſtrare">demonſtrare</expan>
              oportebat.</s>
            </p>
            <p type="margin">
              <s id="s.000475">
                <margin.target id="marg50"/>
              25 undeci
                <lb/>
              mi.</s>
            </p>
            <p type="margin">
              <s id="s.000476">
                <margin.target id="marg51"/>
                <expan abbr="ſextĩ">ſextim</expan>
              .</s>
            </p>
            <p type="margin">
              <s id="s.000477">
                <margin.target id="marg52"/>
              17. unde­
                <lb/>
              cimi</s>
            </p>
            <p type="head">
              <s id="s.000478">THEOREMA XV. PROPOSITIO XIX.</s>
            </p>
            <p type="main">
              <s id="s.000479">Solida parallelepipeda in eadem baſi, uel in
                <lb/>
              æqualibus baſibus conſtituta eam inter ſe propor
                <lb/>
              tionem habent, quam altitudines: & ſi axes ipſo­
                <lb/>
              rum cum baſibus æquales angulos contineant,
                <lb/>
              eam quoque, quam axes proportionem
                <expan abbr="habebũt">habebunt</expan>
              .</s>
            </p>
            <p type="main">
              <s id="s.000480">Sint ſolida parallelepipeda in
                <expan abbr="eadẽ">eadem</expan>
              baſi
                <expan abbr="cõſtituta">conſtituta</expan>
              abcd,
                <lb/>
              abef: & ſit ſolidi abcd altitudo minor: producatur au­
                <lb/>
              tem planum cd adeo, ut ſolidum abef ſecet; cuius ſectio
                <lb/>
                <figure id="id.023.01.053.1.jpg" xlink:href="023/01/053/1.jpg" number="44"/>
                <lb/>
                <arrow.to.target n="marg53"/>
                <lb/>
              ſit gh. </s>
              <s id="s.000481">
                <expan abbr="erũt">erunt</expan>
              ſoli
                <lb/>
              da abcd, abgh
                <lb/>
              in eadem baſi,
                <lb/>
              & æquali altitu
                <lb/>
              dine inter ſe æ­
                <lb/>
              qualia. </s>
              <s id="s.000482">
                <expan abbr="Quoniã">Quoniam</expan>
                <lb/>
              igitur ſolidum
                <lb/>
              abef ſecatur
                <lb/>
              plano baſibus
                <lb/>
                <expan abbr="æquidiſtãte">æquidiſtante</expan>
              , erit
                <lb/>
                <arrow.to.target n="marg54"/>
                <lb/>
              ſolidum ghef
                <lb/>
              adipſum abgh </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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