Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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        <body>
          <chap>
            <p type="main">
              <s id="s.000844">
                <pb pagenum="40" xlink:href="023/01/087.jpg"/>
              eſſe punctum g. </s>
              <s id="s.000845">Sequitur ergo ut icoſahedri centrum gra
                <lb/>
              uitatis ſit idem, quod ipſius ſphæræ centrum.</s>
            </p>
            <p type="margin">
              <s id="s.000846">
                <margin.target id="marg97"/>
              13. primi</s>
            </p>
            <p type="margin">
              <s id="s.000847">
                <margin.target id="marg98"/>
              14. primi</s>
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            <p type="main">
              <s id="s.000848">Sit dodecahedrum af in ſphæra deſignatum, ſitque ſphæ
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              ræ centrum m. </s>
              <s id="s.000849">Dico m centrum eſſe grauitatis ipſius do­
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              decahedri. </s>
              <s id="s.000850">Sit enim pentagonum abcde una ex duode­
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              cim baſibus ſolidi af: & iuncta am producatur ad ſphæræ
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              ſuperficiem. </s>
              <s id="s.000851">cadet in angulum ipſi a oppoſitum; quod col­
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              ligitur ex decima ſeptima propoſitione tertiidecimi libri
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              elementorum. </s>
              <s id="s.000852">cadat in f. </s>
              <s id="s.000853">at ſi ab aliis angulis bcde per
                <expan abbr="cẽ">cen</expan>
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              trum itidem lineæ ducantur ad ſuperficiem ſphæræ in pun
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              cta ghkl; cadent hæ in alios angulos baſis, quæ ipſi abcd
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              baſi opponitur. </s>
              <s id="s.000854">tranſeant ergo per pentagona abcde,
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              fghKl plana ſphæram ſecantia, quæ facient ſectiones cir­
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              culos æquales inter ſe ſe: poſtea ducantur ex centro ſphæræ
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                <figure id="id.023.01.087.1.jpg" xlink:href="023/01/087/1.jpg" number="76"/>
                <lb/>
              m perpendiculares ad pla­
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              na dictorum
                <expan abbr="circulorũ">circulorum</expan>
              ; ad
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              circulum quidem abcde
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              perpendicularis mn: & ad
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              circulum fghKl ipſa mo,
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                <arrow.to.target n="marg99"/>
                <lb/>
              erunt puncta no
                <expan abbr="circulorũ">circulorum</expan>
                <lb/>
              centra: & lineæ mn, mo in
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              ter ſe æquales: quòd circu­
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                <arrow.to.target n="marg100"/>
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              li æquales ſint. </s>
              <s id="s.000855">Eodem mo
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              do, quo ſupra, demonſtrabi
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              mus lineas mn, mo in
                <expan abbr="unã">unam</expan>
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              atque eandem lineam con­
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              uenire. </s>
              <s id="s.000856">ergo cum puncta no ſint centra circulorum, con­
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              ſtat ex prima huius &
                <expan abbr="pentagonorũ">pentagonorum</expan>
              grauitatis eſſe centra:
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                <expan abbr="idcircoq;">idcircoque</expan>
              mn, mo pyramidum abcdem, fghklm axes. </s>
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              <s id="s.000857">ponatur abcdem pyramidis grauitatis centrum p: & py
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              ramidis fghklm ipſum q centrum. </s>
              <s id="s.000858">erunt pm, mq æqua­
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              les, & punctum m grauitatis centrum magnitudinis, quæ
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              ex ipſis pyramidibus conſtat. </s>
              <s id="s.000859">
                <expan abbr="eodẽ">eodem</expan>
              modo probabitur qua­
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              rumlibet pyramidum, quæ è regione opponuntur,
                <expan abbr="centrũ">centrum</expan>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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