Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/075.jpg" pagenum="67"/>
              FG, GH, homologa ſunt lateribus GO, ON. nam
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              dupla eſt FG, ipſius GO, & GH, ipſius ON; angulus
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              igitur OGN, æqualis erit angulo GFH; parallela igi­
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              tur GN, ipſi FH, & propterſimilitudinem triangulorum
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              dupla erit FH, ipſius GN. Rurſus, quoniam recta
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              OP, ſecat latera oppoſita parallelogrammi BD, bifa­
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              riam in punctis O, P, ſecta, & ipſa bifariam in puncto N,
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              erit punctum N, parallelogrammi BD, centrum graui­
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              tatis, atque ideo axis FN, pyramidis ABDEF. qua
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              ratione erit quoque axis FH, pyramidis ABCF: ſed
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              FL, eſt tripla ipſius LH; pyramidis igitur ABCF, cen­
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              trum grauitatis erit L. </s>
              <s>Rurſus quia eſt vt GK, ad KH,
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              ita GR, ad LH, propter ſimilitudinem triangulorum,
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              erit æqualis GR, ipſi LH: ſed eſt FH, quadrupla ip-,
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              ſius LH, quadrupla igitur FH, ipſius GR: ſed FH
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              erat dupla ipſius GN; quadrupla igitur FH, reliquæ
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              NR, ac proinde GR, RN, æquales erunt: recta igitur
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              FL, tripla erit vtriuſque ipſarum GR, RN, ſed vt FL,
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              ad NR, ita eſt FM, ad MN, propter ſimilitudinem trian
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              gulorum; recta igitur FM, erit ipſius MN, tripla, ſicut
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              & LM, ipſius MR: ſed quia KH, eſt æqualis GK,
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              erit & LK, æqualis RK; propter ſimilitudinem trian­
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              gulorum; cum igitur LK, ſit tripla ipſius MR, erit LK,
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              ipſius KM, dupla; vt igitur eſt pyramis ABEDF, ad
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              pyramidem ABCF, ita erit LK, ad KM; eſt autem M,
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              centrum grauitatis pyramidis ABED, ſicut & L, pyrami­
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              dis ABCF; totius igitur priſmatis ABCDEF, centrum
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              grauitatis erit K. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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