Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/052.jpg" pagenum="44"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis polygoni æquilateri, & æquianguli
                <lb/>
              idem eſt centrum grauitatis, & figuræ. </s>
            </p>
            <p type="main">
              <s>Sit polygonum æquilaterum, & æquiangulum ABC
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              DEFG, cuius ſit primo laterum numerus impar, centrum
                <lb/>
              autem ſit L. </s>
              <s>Dico punctum L, eſse centrum grauitatis
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              polygoni ABCDEFG; ſectis enim duobus lateribus
                <lb/>
              DE, FG, bifariam in punctis K, H, ducantur ab angulis
                <lb/>
              oppoſitis rectæ AH, CK. & rectæ BMG, CNF, CM,
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              MF, iungantur. </s>
              <s>Quoniam igitur ex decima tertia quar
                <lb/>
              ti Elem. quemadmodum in pentagono, ita in omni præ­
                <lb/>
              dicto polygono imparium multitudine laterum plane col­
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              ligitur centrum po­
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              lygoni eſse in qua­
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              libet recta, quæ ab
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              angulo ad medium
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              lateris oppoſiti du­
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              citur, quoniam ab
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              omnibus angulis ſic
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              ductæ ſecant ſe ſe
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              in eadem proportio­
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              ne æqualitatis, ita
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              vt eadem ſit propor
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              tio ſegmentorum,
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              quæ ad angulos, ad
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              ea, quæ ad latera
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                <figure id="id.043.01.052.1.jpg" xlink:href="043/01/052/1.jpg" number="30"/>
                <lb/>
              illis angulis oppoſita; rectæ AH, CK, ſecabunt ſe ſe in
                <lb/>
              puncto L. </s>
              <s>Rurfus quoniam ex eadem Euclidis angulus
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              BAL, æqualis eſt angulo GAL, ſed AB, eſt æqualis
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              AG, & AM, communis, erit baſis BM, æqualis baſi </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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