Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/176.jpg" pagenum="89"/>
              conus
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              æqualis eſt conoidi IB
                <foreign lang="grc">γ</foreign>
              , vtpote inſcripti co­
                <lb/>
              ni IB
                <foreign lang="grc">γ</foreign>
              ſeſquialtero, cuius itidem ſeſquialter erat conus
                <lb/>
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              ; reliquum igitur coni <37>B
                <foreign lang="grc">θ</foreign>
              dempto cono
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              æqua­
                <lb/>
              le erit conoidis TBX fruſto TI
                <foreign lang="grc">γ</foreign>
              X. </s>
              <s>Rurſus quia eſt vt
                <lb/>
              cubus ex BD ad cubum ex BI ita conus SBV ad ſui ſi­
                <lb/>
              milem conum YBZ, in triplicata ſcilicet proportione la­
                <lb/>
              terum, ſiue axium DB, BF: ſed quia YF eſt æqualis BF,
                <lb/>
              propter ſimilitudinem triangulorum, eſt vt cubus ex BF ad
                <lb/>
              ſolidum ex BF & quadrato ex F
                <foreign lang="grc">δ</foreign>
              , ita quadratum ex FY
                <lb/>
              ad quadratum ex F
                <foreign lang="grc">δ</foreign>
              , hoc eſt circulus circa YZ ad
                <expan abbr="circulũ">circulum</expan>
                <lb/>
              circa
                <foreign lang="grc">δε</foreign>
              , hoc eſt conus YBZ ad conum
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              ex æquali
                <lb/>
              igitur erit vt cubus ex BD ad ſolidum ex BF, & quadra­
                <lb/>
              to F
                <foreign lang="grc">δ</foreign>
              , ita conus SBV ad conum
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              : ſed vt ſolidum
                <lb/>
              ex BF, & quadrato F
                <foreign lang="grc">δ</foreign>
              , ad ſolidum ex BF & quadrato
                <lb/>
              F<37>, ita eſt ſimiliter vt ante conus
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              ad conum <37>B
                <foreign lang="grc">θ</foreign>
              ; ex
                <lb/>
              æquali igitur erit vt cubus ex BD ad ſolidum ex BF, &
                <lb/>
              quadrato F<37>, ita conus SBV, ad conum <37>B
                <foreign lang="grc">θ</foreign>
              : ſed con­
                <lb/>
              uertendo, & per conuerſionem rationis, eſt vt ſolidum ex
                <lb/>
              BF, & quadrato F<37>, ad ſolidum ex BF, & quadrato,
                <lb/>
              quo plus poteſt F<37> quàm F
                <foreign lang="grc">δ</foreign>
              , ita conus <37>B
                <foreign lang="grc">θ</foreign>
              ad ſui reli­
                <lb/>
              quum dempto cono <35>B
                <foreign lang="grc">ε</foreign>
              ; ex æquali igitur, vt cubus ex
                <lb/>
              BD ad ſolidum ex BF & quadrato, quo plus poteſt F<37>,
                <lb/>
              quàm F
                <foreign lang="grc">δ</foreign>
              , hoc eſt, quo plus poteſt Q quàm P quadrato
                <lb/>
              ex R, ita erit conus SBV, ad reliquum coni <37>B
                <foreign lang="grc">θ</foreign>
              dem­
                <lb/>
              pto cono
                <foreign lang="grc">δ</foreign>
              B
                <foreign lang="grc">ε</foreign>
              , hoc eſt ad fruſtum TI
                <foreign lang="grc">γ</foreign>
              X. Rurſus, quo­
                <lb/>
              niam duo cubi ex BF, FD, & ſolidum ex BF, FD, &
                <lb/>
              tripla ipſius BD, ſunt æqualia cubo ex BD; erit id quo
                <lb/>
              plus poteſt cubice recta BD quàm BF, cubus ex
                <lb/>
              FD, & ſolidum ex BF, FD, & tripla ipſius BD: cum
                <lb/>
              igitur ſit vt cubus ex BD ad cubum ex BF, ita conus
                <lb/>
              SBV ad conum YBZ; erit per conuerſionem rationis, &
                <lb/>
              conuertendo, vt cubus ex FD vna cum ſolido ex BF,
                <lb/>
              FD, & tripla ipſius BD ad cubum ex BD, ita fruſtum
                <lb/>
              SYZV, ad conum SBV: ſed cubus ex BD, ad ſoli-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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