Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/149.jpg" pagenum="62"/>
              quæ interſecundam, & vltimam ſectionem inter­
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              ijcitur, vt exceſſus, quo maior extrema ad ſphæræ
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              ſemidiametrum, & axim portionis ſuperat ter­
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              tiam partem axis portionis; ad maiorem extre­
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              mam antedictam. </s>
            </p>
            <p type="main">
              <s>Sit portio ABCD ſphæræ, cuius centrum F: axis au­
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              tem portionis ſit EF abſciſsæ duobus planis parallelis,
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              quorum alterum tranſiens per punctum F faciat ſectio­
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              num circulum maximum, cuius diameter AD, reliquam
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              autem ſectionem minorem circulum, quæ minor baſis di­
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              citur, cuius di­
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              ameter BC:
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              & vt eſt EF
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              ad AD, ita
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              fiat AD ad
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              OP, cuius P
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              R, ſit æqua­
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              lis tertiæ parti
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              axis EF. </s>
              <s>Et
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              ſecta EF bi­
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                <figure id="id.043.01.149.1.jpg" xlink:href="043/01/149/1.jpg" number="114"/>
                <lb/>
              fariam in puncto M, & poſita EN ipſius EF quarta
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              parte, fiat vt RO ad OP, ita MN ad NL. </s>
              <s>Dico L eſſe
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              centrum grauitatis portionis ABCD. </s>
              <s>Nam circa axim
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              EF ſuper circulum maximum AD deſcribatur cylindrus
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              AG, cuius centrum grauitatis erit M: reliqui autem ex
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              cylindro AG dempta ABCD portione centrum graui­
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              tatis N. </s>
              <s>Quoniam igitur eſt vt RO ad OP, hoc eſt vt
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              MN ad NL, ita portio ABCD ad reliquum cylindri
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              AG, & diuidendo vt NM ad ML, ita portio ABCD ad
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              reliquum cylindri AG: & cylindri AG eſt N, prædicti au­
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              tem reſidui centrum grauitatis M; erit reliquæ portionis
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              ABCD centrum grauitatis L. </s>
              <s>Quod
                <expan abbr="demonſtrandũ">demonſtrandum</expan>
              erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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