Valerio, Luca, De centro gravitatis solidorvm libri tres

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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/200.jpg" pagenum="21"/>
              tribus ſolidis communem, poſitas in eodem plano, quæ ſunt
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              AF parallelogrammum, triangulum EDF, & ſemicir­
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              culus, vel ſemi ellipſis ABC: & ſint ſectiones rectæ GO,
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              HN, KM: hæ igitnr erunt diametri eiuſdem rationis trium
                <lb/>
              ſectionum, ſcilicet circulorum, vel ellipſium ſirnilium, qui­
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              bus erit commune centrum L, in quo nimirum axis BD
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              tres dictas lineas GO, HN, KM, bifariam ſecat. </s>
              <s>Vt
                <lb/>
              igitur de ſolido AF diximus, ſint circa axem BL, & ſuper
                <lb/>
              baſes circulos, vel ellipſes circa HN, KM cylindri, vel
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              portiones cylindricæ HP, KQ, qui vnà cum portione
                <lb/>
              cylindrica, vel cylindro GF ipſa ſectione facto, erunt inter
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              eadem plana paral­
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              lela per EF, GO.
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              </s>
              <s>Dico trium cylin­
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              drorum, vel cylin­
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              dri portionum GF,
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              HP, KQ,
                <expan abbr="reliquũ">reliquum</expan>
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              ipſius GF dempto
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              HP, ipſi KQ eſse
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                <figure id="id.043.01.200.1.jpg" xlink:href="043/01/200/1.jpg" number="147"/>
                <lb/>
              æquale. </s>
              <s>Quoniam
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              enim cylindri, & cy­
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              lindri portiones eiuſdem altitudinis inter ſe ſunt vt ba­
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              ſes, circuli autem, & ſimiles ellipſes; inter ſe, vt quæ à
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              diametris eiuſdem rationis fiunt quadrata; ex Archime­
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              de, hoc eſt vt earum quartæ partes, quæ à ſemidiame­
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              tris quadrata deſcribuntur; erit vt quadratum LO ad
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              quadratum LN, ita cylindrus, vel portio cylindrica
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              GF ad cylindrum, vel portionem cylindricam PH: &
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              diuidendo, vt rectangulum LNO bis vnà cum quadra­
                <lb/>
              to NO, ad quadratum LN, ita reliquum cylindri, vel
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              portionis cylindricæ GF, dempto ipſo PH, ad ipſum
                <lb/>
              PH: ſed vt quadratum LN ad quadratum LM, ita eſt
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              vt ſupra, cylindrus, vel portio cylindrica HP ad cylin­
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              drum, vel portionem cylindricam KQ, ex æquali igitur, </s>
            </p>
          </chap>
        </body>
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