Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="25" xlink:href="023/01/057.jpg"/>
            <p type="main">
              <s id="s.000517">Sint duo priſmata ae, af, quorum eadem baſis quadri­
                <lb/>
              latera abcd:
                <expan abbr="ſitq;">ſitque</expan>
              priſmatis ae altitudo eg; & priſmatis
                <lb/>
              af altitudo fh. </s>
              <s id="s.000518">Dico priſma ae ad priſma af eam habere
                <lb/>
              proportionem, quam eg ad fh. </s>
              <s id="s.000519">iungatur enim ac: & in
                <lb/>
              unoquoque priſmate duo priſmata intelligantur, quorum
                <lb/>
                <figure id="id.023.01.057.1.jpg" xlink:href="023/01/057/1.jpg" number="49"/>
                <lb/>
              baſes ſint triangu
                <lb/>
              la abc, acd. </s>
              <s id="s.000520">habe
                <lb/>
              bunt duo priſma­
                <lb/>
              te in eadem baſi
                <lb/>
              abc conſtituta,
                <lb/>
              proportionem
                <expan abbr="eã">eam</expan>
                <lb/>
              dem, quam ipſo­
                <lb/>
              rum altitudines e
                <lb/>
              g, fh, ex iam de­
                <lb/>
              monſtratis. </s>
              <s id="s.000521">& ſi­
                <lb/>
              militer alia duo,
                <lb/>
              quæ ſunt in baſi a
                <lb/>
                <arrow.to.target n="marg62"/>
                <lb/>
              c d. </s>
              <s id="s.000522">quare totum priſma ae ad priſma af eandem propor
                <lb/>
              tionem habebit, quam altitudo eg ad fh altitudinem. </s>
              <lb/>
              <s id="s.000523">Quòd cum priſmata ſint pyramidum tripla, & ipſæ pyrami
                <lb/>
              des, quarum eadem eſt baſis quadrilatera, & altitudo priſ­
                <lb/>
              matum altitudini æqualis, eam inter ſe proportionem ha­
                <lb/>
              bebunt, quam altitudines.</s>
            </p>
            <p type="margin">
              <s id="s.000524">
                <margin.target id="marg62"/>
              12. quinti</s>
            </p>
            <p type="main">
              <s id="s.000525">Si uero priſmata baſes æquales habeant,
                <expan abbr="nõ">non</expan>
              eaſdem, ſint
                <lb/>
              duo eiuſmodi priſmata ae, fl: & ſit baſis priſmatis ae qua
                <lb/>
              drilaterum abcd; & priſmatis fl quadrilaterum fghk. </s>
              <lb/>
              <s id="s.000526">Dico priſma ae ad priſma fl ita eſſe, ut altitudo illius ad
                <lb/>
              huius altitudinem. </s>
              <s id="s.000527">nam ſi altitudo ſit eadem,
                <expan abbr="intelligãtur">intelligantur</expan>
                <lb/>
                <arrow.to.target n="marg63"/>
                <lb/>
              duæ pyramides abcde, fghkl. </s>
              <s id="s.000528">quæ
                <expan abbr="ĩtcrſe">interſe</expan>
              æquales
                <expan abbr="erũt">erunt</expan>
              ,
                <lb/>
              cum æquales baſes, & altitudinem eandem habeant. </s>
              <s id="s.000529">quare
                <lb/>
                <arrow.to.target n="marg64"/>
                <lb/>
              & priſmata ae, fl, quæ ſunt
                <expan abbr="harũ">harum</expan>
              pyramidum tripla, æqua­
                <lb/>
              lia ſint neceſſe eſt. </s>
              <s id="s.000530">ex quibus perſpicue conſtat
                <expan abbr="propoſitũ">propoſitum</expan>
              . </s>
              <lb/>
              <s id="s.000531">Si uero altitudo priſmatis fl ſit maior, à priſmate fl ab­
                <lb/>
              ſcindatur priſma fm, quod æque altum ſit,
                <expan abbr="atq;">atque</expan>
              ipſum ae. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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