Valerio, Luca, De centro gravitatis solidorvm libri tres

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/109.jpg" pagenum="22"/>
              maior baſis, circulus maximus, cuius diameter AD, minor
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              autem, cuius diameter BC: & cylindrus AE, cuius baſis
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              circulus AD, axis FG; & vt FG ad FA, ita ſit FA, ad
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              MN, à qua abſcindatur NO, pars tertia ipſius FG. </s>
              <s>Dico
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              ABCD
                <expan abbr="portionẽ">portionem</expan>
              ad cylindrum AE eſſe vt OM ad MN.
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              </s>
              <s>Poſita enim G
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              H, æquali ipſi
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              FG, deſcriba­
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              tur circa axim
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              FG, cylindrus
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              L
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              , & conus
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              HFK. </s>
              <s>Quoniam
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              igitur duo cylin
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              dri AE, LK,
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              ſunt eiuſdem al­
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                <figure id="id.043.01.109.1.jpg" xlink:href="043/01/109/1.jpg" number="81"/>
                <lb/>
              titudinis, erunt inter ſe vt baſes, AD, KH. hoc eſt cy­
                <lb/>
              lindrus AE ad cylindrum LK, duplicatam habebit pro­
                <lb/>
              portionem diametri AD, ad diametrum KH, hoc eſt eius,
                <lb/>
              quæ eſt ſemidiametri AF ad ſemidiametrum GH. hoc eſt
                <lb/>
              eam, quæ eſt MN ad GH, ſiue FG. </s>
              <s>Sed vt FG ad tertiam
                <lb/>
              ſui partem NO, ita eſt cylindrus KL, ad conum KFH;
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              ex æquali igitur, erit vt MN ad NO, ita cylindrus AE
                <lb/>
              ad conum
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              FH, hoc eſt ad reliquum cylindri AE dem
                <lb/>
              pta ABCD portione: & per conuerſionem rationis, vt
                <lb/>
              NM, ad MO, ita cylindrus AE ad portionem ABCD:
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              & conuertendo, vt MO ad MN, ita portio ABCD ad
                <lb/>
              cylindrum AE. </s>
              <s>Quod eſt propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XV.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis portio ſphæræ abſciſſa duobus planis
                <lb/>
              parallelis neutro per centrum, nec centrum inter­
                <lb/>
              cipientibus ad cylindrum, cuius baſis æqualis eſt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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