Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/138.jpg" pagenum="51"/>
              lelogrammis circumſcribatur figuræ ABC, altera tertia fi­
                <lb/>
              gura, quemadmodum diximus in præcedenti, cuius cen­
                <lb/>
              trum grauitatis H, in linea GD cadat & ſit minor pro­
                <lb/>
              portio reſidui huius tertiæ figuræ circumſcriptæ ipſi ABC,
                <lb/>
              ad figuram ABC, quàm FG ad GD. </s>
              <s>Multo ergo mi­
                <lb/>
              nor proportio erit dicti reſidui ad figuram ABC quam F
                <lb/>
              H ad HD, fiat igitur vt prædictum reſiduum ad figuram
                <lb/>
              ABC, ita ex contraria parte FH ad HDK; prædicti igi­
                <lb/>
              tur reſidui centrum grauitatis erit K, extra ipſius terminos,
                <lb/>
              quod fieri non poteſt: Non igitur F centrum grauitatis fi­
                <lb/>
              guræ ABC cadit in puncto E, nec ſupra; ergo infra pun
                <lb/>
              ctum E: & ponitur E centrum grauitatis cuiuslibet figuræ
                <lb/>
              ex cylindris, vel cylindri portionibus, vel parallelogrammis
                <lb/>
              æqualium altitudinum quo modo diximus ipſi ABC cir­
                <lb/>
              cumſcriptæ. </s>
              <s>Manifeſtum eſt igitur propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omni prædictæ figuræ figura quædam ex cylin
                <lb/>
              dris, vel cylindri portionibus, vel parallelogram­
                <lb/>
              mis æqualium altitudi
                <lb/>
              num circumſcribi po­
                <lb/>
              teſt, cuius centri graui
                <lb/>
              tatis diſtantia à prædi­
                <lb/>
              ctæ figuræ centro gra­
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              uitatis ſit minor quan­
                <lb/>
              tacunque longitudine
                <lb/>
              propoſita. </s>
            </p>
            <figure id="id.043.01.138.1.jpg" xlink:href="043/01/138/1.jpg" number="107"/>
            <p type="main">
              <s>Sit figura ABC in
                <expan abbr="alterã">alteram</expan>
                <lb/>
              partem
                <expan abbr="deficiẽs">deficiens</expan>
              ſupradicta,
                <lb/>
              cuius centrum grauitatis F, propoſita autem
                <expan abbr="quantacũque">quantacumque</expan>
                <lb/>
                <expan abbr="lõgitudine">longitudine</expan>
              minor ſit FG ipſius BF. </s>
              <s>Dico figuræ ABC figu-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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