Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000701">
                <pb pagenum="34" xlink:href="023/01/075.jpg"/>
              culi, uel ellipſes cd, ef ab ad circulum, uel ellipſim ab. </s>
              <s id="s.000702">In­
                <lb/>
              telligatur pyramis q baſim habens æqualem tribus rectan
                <lb/>
              gulis ab, ef, cd; & altitudinem
                <expan abbr="eãdem">eandem</expan>
              , quam fruſtum ad. </s>
              <lb/>
              <s id="s.000703">intelligatur etiam conus, uel coni portio q, eadem altitudi
                <lb/>
              ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus ab,
                <lb/>
              ef, cd æqualis. </s>
              <s id="s.000704">poſtremo intelligatur pyramis alb, cuius. </s>
              <lb/>
              <s id="s.000705">baſis ſit rectangulum mnop, & altitudo eadem, quæ fru­
                <lb/>
              ſti:
                <expan abbr="itemq,">itemque</expan>
              intelligatur conus, uel coni portio alb, cuius
                <lb/>
              baſis circulus, uel ellipſis circa diametrum ab, & eadem al
                <lb/>
                <arrow.to.target n="marg86"/>
                <lb/>
              titudo. </s>
              <s id="s.000706">ut igitur rectangula ab, ef, cd ad rectangulum ab,
                <lb/>
              ita pyramis q ad pyramidem alb; & ut circuli, uel ellip­
                <lb/>
              ſes ab, ef, cd ad ab circulum, uel ellipſim, ita conus, uel co
                <lb/>
              ni portio q ad conum, uel coni portionem alb. </s>
              <s id="s.000707">conus
                <lb/>
              igitur, uel coni portio q ad conum, uel coni portionem
                <lb/>
              alb eſt, ut pyramis q ad pyramidem alb. </s>
              <s id="s.000708">ſed pyramis
                <lb/>
              alb ad pyramidem agb eſt, ut altitudo ad altitudinem, ex
                <lb/>
              20. huius: & ita eſt conus, uel coni portio alb ad conum,
                <lb/>
              uel coni portionem agb ex 14. duodecimi elementorum,
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              & ex iis, quæ nos demonſtrauimus in commentariis in un­
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              decimam de conoidibus, & ſphæroidibus, propoſitione
                <lb/>
              quarta. </s>
              <s id="s.000709">pyramis autem agb ad pyramidem cgd propor­
                <lb/>
              tionem habet compoſitam ex proportione baſium & pro
                <lb/>
              portione altitudinum, ex uigeſima prima huius: & ſimili­
                <lb/>
              ter conus, uel coni portio agb ad conum, uel coni portio­
                <lb/>
              nem cgd proportionem habet
                <expan abbr="compoſitã">compoſitam</expan>
              ex eiſdem pro­
                <lb/>
              portionibus, per ea, quæ in dictis commentariis demon­
                <lb/>
              ſtrauimus, propoſitione quinta, & ſexta: altitudo enim in
                <lb/>
              utriſque eadem eſt, & baſes inter ſe ſe eandem habent pro­
                <lb/>
              portionem. </s>
              <s id="s.000710">ergo ut pyramis agb ad pyramidem cgd, ita
                <lb/>
              eſt conus, uel coni portio agb ad agd conum, uel coni
                <lb/>
              portionem: & per
                <expan abbr="conuerſionẽ">conuerſionem</expan>
              rationis, ut pyramis agb
                <lb/>
              ad
                <expan abbr="ſruſtũ">fruſtum</expan>
              à pyramide abſciſſum, ita conus uel coni portio
                <lb/>
              agb ad fruſtum ad. </s>
              <s id="s.000711">ex æquali igitur, ut pyramis q ad fru­
                <lb/>
              ſtum à pyramide abſciſſum, ita conus uel coni portio q ad </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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