Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000392">
                <pb xlink:href="023/01/042.jpg"/>
              partes d. </s>
              <s id="s.000393">in pyramide igitur inſcripta erit quædam figura,
                <lb/>
              ex priſmatibus æqualem altitudinem habentibus
                <expan abbr="cõſtans">conſtans</expan>
              ,
                <lb/>
              ad partes e: & altera circumſcripta ad partes d. </s>
              <s id="s.000394">Sed unum­
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              quodque eorum priſmatum, quæ in figura inſcripta conti­
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              nentur, æquale eſt priſmati, quod ab eodem fit triangulo in
                <lb/>
              figura circumſcripta: nam priſma pq priſmati po eſt æ­
                <lb/>
              quale; priſma st æquale priſmati sr; priſma xy priſmati
                <lb/>
              xu; priſma
                <foreign lang="grc">ηθ</foreign>
              priſmati
                <foreign lang="grc">η</foreign>
              z; priſma
                <foreign lang="grc">μν</foreign>
              priſmati
                <foreign lang="grc">μλ;</foreign>
              priſ­
                <lb/>
              ma
                <foreign lang="grc">ρσ</foreign>
              priſmati
                <foreign lang="grc">ρπ;</foreign>
              & priſma
                <foreign lang="grc">φχ</foreign>
              priſmati
                <foreign lang="grc">φτ</foreign>
              æquale. </s>
              <s id="s.000395">re­
                <lb/>
              linquitur ergo, ut circumſcripta figura exuperet
                <expan abbr="inſcriptã">inſcriptam</expan>
                <lb/>
              priſmate, quod baſim habet abc triangulum, & axem ef. </s>
              <lb/>
              <s id="s.000396">Illud uero minus eſt ſolida magnitudine propoſita. </s>
              <s id="s.000397">
                <expan abbr="Eadẽ">Eadem</expan>
                <lb/>
              ratione inſcribetur, & circumſcribetur ſolida figura in py­
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              ramide, quæ quadrilateram, uel
                <expan abbr="plurilaterã">plurilateram</expan>
              baſim habeat.</s>
            </p>
            <p type="head">
              <s id="s.000398">PROBLEMA II. PROPOSITIO XI.</s>
            </p>
            <p type="main">
              <s id="s.000399">DATO cono, fieri poteſt, ut figura ſolida in­
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              ſcribatur, & altera circumſcribatur ex cylindris
                <lb/>
              æqualem habentibus altitudinem, ita ut circum­
                <lb/>
              ſcripta ſuperet inſcriptam, magnitudine, quæ ſo­
                <lb/>
              lida magnitudine propoſita ſit minor.</s>
            </p>
            <p type="main">
              <s id="s.000400">SIT conus, cuius axis bd: & ſecetur plano per axem
                <lb/>
              ducto, 'ut ſectio ſit triangulum abc:
                <expan abbr="intelligaturq;">intelligaturque</expan>
              cylin­
                <lb/>
              drus, qui baſim eandem, & eundem axem habeat. </s>
              <s id="s.000401">Hoc igi­
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              tur cylindro continenter bifariam ſecto, relinquetur cylin
                <lb/>
              drus minor ſolida magnitudine propoſita. </s>
              <s id="s.000402">Sit autem is cy
                <lb/>
              lindrus, qui baſim habet circulum circa diametrum ac, &
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              axem de. </s>
              <s id="s.000403">Itaque diuidatur bd in partes æquales ipſi de
                <lb/>
              in punctis fghKlm: & per ea ducantur plana conum ſe­
                <lb/>
              cantia; quæ baſi æquidiſtent. </s>
              <s id="s.000404">erunt ſectiones circuli, cen­
                <lb/>
              tra in axi habentes, ut in primo libro conicorum, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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