Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/188.jpg" pagenum="9"/>
              GH, MN. </s>
              <s>Dico ſolidi ABC ſectionum, minorem eſſe
                <lb/>
              proportionem, ipſius IK ad GH, quàm GH ad MN.
                <lb/>
              </s>
              <s>Iunctis enim MRS, KSN; quoniam tres rectæ IK,
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              RS, MN, ſeſe æqualiter excedunt in trapezio KM; mi­
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              nor erit proportio IK ad RS, quàm RS ad MN: ſed cir
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              culi, & ſimiles ellipſes duplicatam habent inter ſe propor­
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              tionem diametrorum eiuſdem rationis; trium igitur præ­
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              dictarum ſolidi ABC ſectionum minor erit proportio IK
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              ad RS quàm RS ad MN: ſed maior eſt proportio circu­
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              li, vel ellipſis GH ad circulum, vel ellipſim MN, quàm
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              circuli, vel ellipſis RS, ad circulum, vel ellipſim MN;
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              multo ergo minor proportio erit circuli, vel ellipſis IK ad
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              circulum, vel ellipſim RS, quàm circuli, vel ellipſis GH ad
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              circulum, vel ellipſim MN: ſed minor eſt proportio cir­
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              culi vel ellipſis I
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              ad circulum, vel ellipſim GH, quàm
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              eiuſdem circuli, vel ellipſis IK ad circulum, vel ellipſim
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              RS; multo ergo minor proportio erit circuli, vel ellipſis
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              IK ad circulum, vel ellipſim GH quàm circuli, vel ellip­
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              ſis GH ad circulum, vel ellipſim MN. </s>
              <s>Quod demon­
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              ſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO VI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si ſphæroides ſecetur plano vtcumque præter
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              quàm ad axem, circa quem ſphæroides deſcribi­
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              tur erecto nam tunc circulus fit. </s>
              <s>ſectio ellipſis erit:
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              ſimilis autem ipſi alia quæcumque ſectio ſphæ­
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              roidis eidem parallela: earumque omnes diame­
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              tri quæ eiuſdem ſunt rationis erunt in eodem pla­
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              no per axem. </s>
            </p>
            <p type="main">
              <s>Extant hæc demonſtrata ab Archimede in ſuo de ſphæ­
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              roidibus, & conoidibus. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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