Valerio, Luca, De centro gravitatis solidorum, 1604

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/242.jpg" pagenum="63"/>
              ellipſim NO. minor autem proportio eſt PQ ad RS,
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              quàm RS ad TV circuli igitur, vel ellipſis KH ad
                <expan abbr="circulũ">circulum</expan>
              ,
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              vel ellipſim LM, minor erit proportio <34> circuli, vel ellipſis
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              LM ad circulum, vel ellipſim NO: & duæ figuræ hemi­
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              ſphærium, vel hemiſphæroides ABC, & plana ARBSC,
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              ſunt circa axim, vel diametrum BD in alteram parte m
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              deficientes, quales definiuimus; vtriuſque igitur dictæ fi­
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              guræ vnum erit commune centrum grauitatis. </s>
              <s>Rurſus
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              poſito puncto F in medio axis BD, & FG ipſius GE
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              tripla, quoniam ponitur BG ad GD vt quinque ad tria;
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              qualium partium æqualium ipſi EG eſt FG trium, ta­
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              lium erit BG quindecim, & GD nouem, & talis EG
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              vna: dempta igitur GE ab ipſa DG, & addita ipſi BG,
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              qualium partium eſt BE ſexdecim, talium erit ED octo;
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              dupla igitur BE ipſius ED, & trianguli ABC centrum
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              grauitatis E. </s>
              <s>Rurſus quoniam ex quadratura parabolæ,
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              duarum portionum ARB, BSC triangulum ABC eſt
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              triplum; hoe eſt vt FG ad GE, ita ex contraria parte
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              triangulum ABC ad duas portiones ARB, BSC: Sed
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              trianguli ABC eſt centrum grauitatis E, & duarum por
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              tionum ARB, BSC ſimul per XXIII huius, centrum
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              grauitatis F, totius igitur figuræ ARBSC centrum gra
                <lb/>
              uitatis erit G, commune autem hoc centrum grauitatis
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              eſt hemiſphærio, vel hemiſphæroidi ABC. </s>
              <s>Manifeſtum
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              eſt igitur propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis minoris portionis ſphæræ, vel ſphæroi­
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              dis centrum grauitatis eſt in axe primum bifa­
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              riam ſecto: deinde ſecundum centrum grauitatis
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              reliqui ſolidi dempta portione ex cylindro, vel </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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