Valerio, Luca, De centro gravitatis solidorum, 1604

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/077.jpg" pagenum="69"/>
              punctum S, priſmatis BCDFGH. </s>
              <s>Quoniam igitur
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              quadrilateri EG, eſt centrum grauitatis K, cuius duorum
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              triangulorum centra grauitatis ſunt P, N; erit vt triangu­
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              lum FGH, ad triangulum EFH, hoc eſt vt priſma BC­
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              DFGH, ad priſma ABDEFH, ita NK, ad KP, hoc
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              eſt RM, ad MS; cum igitur ſit R, centrum grauitatis
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              priſmatis ABDEFH: ſicut & S, priſmatis BCDFGH;
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              totius priſmatis ABCDEFGH, centrum grauitatis erit
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              M. </s>
              <s>Quod ſi priſma baſim habeat quinquelateram; ab­
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              ſciſso rurſus priſmate vno triangulam baſim habente,
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              ſumptiſque axibus priſinatum, quorum alterum habebit
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              baſim quadrilateram, eadem demonſtratione propoſitum
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              concluderemus, & ſic deinceps in aliis. </s>
              <s>Manifeſtum eſt
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              igitur propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXV.
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              </s>
            </p>
            <p type="main">
              <s>Omnis fruſti pyramidis triangulam baſim
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              ha bentis centrum grauitatis eſt in axe, primum
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              ita diuiſo, vt ſegmentum attingens minorem
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              baſim ſit ad reliquum, vt duplum vnius laterum
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              maioris baſis vna cum latere homologo mino­
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              ris, ad duplum prædicti lateris minoris baſis,
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              vna cum latere homologo maioris. </s>
              <s>Deinde
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              à puncto ſectionis abſciſsa quarta parte ſeg­
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              menti, quod maiorem baſim attingit, & à pun­
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              cto, in quo ad minorem baſim axis termina­
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              tur ſumpta item quarta parte totius axis; in
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              eo puncto, in quo ſegmentum axis duabus po­
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              ſterioribus ſectionibus finitum ſic diuiditur, vt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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