Valerio, Luca, De centro gravitatis solidorvm libri tres

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/156.jpg" pagenum="69"/>
              verticem habentibus communem centrum ſphæ­
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              ræ, baſes autem minores baſibus oppoſitis cylin­
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              dri circumſcripti: æqualibus circulo maximo, ſu­
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              mentes pro vertice minorem baſim, pro baſi, ma­
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              iorem baſim portionis immotis reliquis propoſi­
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              tum demonſtraremus. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXVIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis maioris portionis ſphæræ centrum gra
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              uitatis eſt in axe primum bifariam ſecto: Deinde
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              ſumpta ad verticem quarta parte ſegmenti axis,
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              quod centro ſphæræ, & portionis vertice finitur:
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              itemque ad baſim quarta parte reliqui ſegmenti
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              inter centrum ſphæræ, & baſim portionis interie­
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              cti. </s>
              <s>Deinde ſegmento axis, inter eas quartas par­
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              tes interiecto, ita diuiſo, vt pats propinquior baſi
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              ſit ad reliquam vt cubus ſegmenti axis, quod
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                <expan abbr="cẽtro">centro</expan>
              ſphæræ, & vertice portionis, ad cubum eius
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              quod centris ſphæræ, & baſis portionis termina­
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              tur; in eo puncto, in quo ſegmentum axis centro
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              ſphæræ, & ſectione penultima finitum ſic diuidi­
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              tur, vt pars prima & penultima ſectione termina­
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              ta ſit ad totam vltima & penultima ſectione termi
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              natam, vt exceſſus, quo ſegmentum axis portionis
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              inter centrum, & baſim portionis interiectum ſu­
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              perat tertiam partem minoris extremæ maiori po
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              ſita dicto axis ſegmento in proportione ſemidia-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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