Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/139.jpg" pagenum="52"/>
              ram ex cylindris vel cylindri portionibus, vel
                <expan abbr="parallelogrã-mis">parallelogram­
                  <lb/>
                mis</expan>
              æqualium
                <expan abbr="altitudinũ">altitudinum</expan>
              circumſcribi poſſe, cuius centrum
                <lb/>
              grauitatis ſit propinquius puncto F, quàm punctum G: figu­
                <lb/>
              ræ enim ABC figura, qualem diximus circumſcribatur, cu­
                <lb/>
              ius reſiduum dempta figura ABC, ad figuram ABC mi­
                <lb/>
              norem habeat proportionem, quàm FG, ad GB, ſit autem
                <lb/>
              figuræ circumſcriptæ centrum grauitatis K, nempe in axe,
                <lb/>
              vel diametro BD. </s>
              <s>Dico
                <lb/>
              lineam FK minorem eſſe
                <lb/>
              quàm FG, atque adeo lon
                <lb/>
              gitudine propoſita. </s>
              <s>Quo­
                <lb/>
              niam enim F eſt centrum
                <lb/>
              grauitatis figuræ ABC,
                <lb/>
              erit centrum grauitatis
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              ,
                <lb/>
              figuræ circumſcriptæ ipſi
                <lb/>
              ABC propinquius termi­
                <lb/>
              no B, quàm punctum F,
                <lb/>
              ſed centrum grauitatis fi­
                <lb/>
              guræ ABC quòd eſt F, &
                <lb/>
              figuræ circumſcriptæ, quod
                <lb/>
              eſt K & eius reſidui dem­
                <lb/>
                <figure id="id.043.01.139.1.jpg" xlink:href="043/01/139/1.jpg" number="108"/>
                <lb/>
              pta figura ABC ſunt in communi axe, vel diametro BD;
                <lb/>
              erit igitur dicti reſidui in linea BK, centrum grauitatis,
                <lb/>
              quod ſit H. </s>
              <s>Minor autem proportio eſt prædicti reſidui
                <lb/>
              ad figuram ABC, hoc eſt ipſius FK ad KH, quàm FG
                <lb/>
              ad GB, & multo minor, quàm FG ad GH; & compo­
                <lb/>
              nendo minor proportio FH ad HK, quàm FH ad HG;
                <lb/>
              ergo KH maior erit, quàm GH; reliqua igitur F
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              mi­
                <lb/>
              nor, quàm FG atque adeo longitudine propoſita. </s>
              <s>Fieri
                <lb/>
              ergo poteſt, quod proponebatur. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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