Valerio, Luca, De centro gravitatis solidorum, 1604

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/267.jpg" pagenum="88"/>
              relato: huic autem proximus, & æqualis cylindrorum in­
                <lb/>
              ſcriptorum ſit NM baſim ipſi communem habens circu­
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              lum circa EFM: & conſequenti circumſcriptorum GQ
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              ſit. </s>
              <s>inſcriptorum æqualis PO baſim habens ipſi commu­
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              nem circulum circa GHO: ſint autem circulorum qui
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              ſunt baſes cylindrorum diametri in parabola per axim:
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              quæ quoniam ſunt communes ſectiones cum parabola per
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              axim planorum baſi conoidis, & inter ſe parallelorum,
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              erunt etiam ipſæ inter ſe, & parabolæ baſi AC parallelæ,
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              earumque dimidiæ vt EF, GH ad diametrum BD or­
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              dinatim applicatæ. </s>
              <s>Quoniam igitur in parabola ABC
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              eſt vt HB ad BF ita quadratum GH ad quadratum
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              EF, duplum erit
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              quadratum GH
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              quadrati EF: qua
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              re & circulus cir­
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              ca GO circuli
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              circa EM at que
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              adeo cylindrus
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              GQ cylindri E
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              L duplus, pro­
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              pter <17>qualitatem
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              altitudinum: ſed
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              & cylindrus NL
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                <figure id="id.043.01.267.1.jpg" xlink:href="043/01/267/1.jpg" number="195"/>
                <lb/>
              duplus eſt cylindri EL per conſtructionem; cylindrus igi­
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              tur GQ æqualis eſt cylindro NL: & ablato communi
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              NM cylindro, reliquus GQ deficiens cylindro NM
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              cylindro EL æqualis. </s>
              <s>Rurſus quia eſt vt KB ad BH,
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              ita quadratum IK ad quadratum GH, hoc eſt ita IR
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              cylindrus ad cylindrum GQ: ſed vt HB ad BF ita
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              erat cylindrus GQ ad cylindrum EL; tres igitur cy­
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              lindri IR, GQ, EL, tribus lineis BK, BH, BF, eodem
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              ordine proportionales erunt: ſed tres eædem lineæ ſeſe
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              æqualiter excedunt; tres igitur dicti cylindri ſeſe æqua-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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