Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/112.jpg" pagenum="25"/>
              ſlum KLMN. </s>
              <s>Sed vt ZY ad X, ita erat cylindrus SO
                <lb/>
              ad PN cylindrum; ex æquali igitur erit vt ZY ad Z
                <foreign lang="grc">ω</foreign>
              ,
                <lb/>
              ita cylindrus SO ad fruſtum KLMN: hoc eſt, ad reli­
                <lb/>
              quum cylindri SO dempta ABCD portione, & per con­
                <lb/>
              uerſionem rationis, vt ZY, ad Y
                <foreign lang="grc">ω</foreign>
              , ita cylindrus SO ad
                <lb/>
                <expan abbr="portionẽ">portionem</expan>
              ABCD: & conuertendo vt
                <foreign lang="grc">ω</foreign>
              Y ad YZ, ita por­
                <lb/>
              tio ABCD ad SO cylindrum. </s>
              <s>Quod
                <expan abbr="demonſtrandũ">demonſtrandum</expan>
              erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XVI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis maior ſphæræ portio ad cylindrum, cu­
                <lb/>
              ius baſis æqualis eſt circulo maximo, altitudo au­
                <lb/>
              tem eadem portioni eam habet proportionem,
                <lb/>
              quam ad axim portionis habet exceſſus, quo ſeg­
                <lb/>
              mentum axis portionis inter ſphæræ centrum, &
                <lb/>
              baſim portionis interiectum ſuperat tertiam par­
                <lb/>
              tem minoris extremæ maiori poſita prædicto axis
                <lb/>
              ſegmento in proportione ſemidiametri ſphæræ
                <lb/>
              ad prædictum
                <lb/>
                <expan abbr="ſegmentũ">ſegmentum</expan>
              , vna
                <lb/>
              cum ſubſeſqui
                <lb/>
              altera reliqui
                <lb/>
              axis ſegmenti. </s>
            </p>
            <figure id="id.043.01.112.1.jpg" xlink:href="043/01/112/1.jpg" number="84"/>
            <p type="main">
              <s>Sit ſphæræ, cu
                <lb/>
              ius
                <expan abbr="centrũ">centrum</expan>
              G, dia
                <lb/>
              meter DGE ma
                <lb/>
              ior portio ABC,
                <lb/>
              axis autem por­
                <lb/>
              tionis BGF, com
                <lb/>
              munis cylindro
                <lb/>
              KH, cuius baſis æqualis ſit circulo maximo; baſis autem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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