Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/081.jpg" pagenum="73"/>
            <p type="main">
              <s>Sit pyramidis quadrilateram baſim habentis fruſtum
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              ABCDEFGH, cuius axis KL, atque in ipſo centrum
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              grauitatis O. </s>
              <s>Dico axim KL, ſectum eſse in puncto O,
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              vt propoſuimus. </s>
              <s>Ductis enim AC, EG, quæ ſimilium
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              ſectionum angulos æquales ſubtendant B, F, qui late­
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              ribus homologis continentur, fruſta erunt pyramidum
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              triangulas baſes habentium AFG, AGH: ſit autem fru­
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              ſti AFG, axis
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              TP, & in eo eiuſ
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              dem fruſti cen­
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              trum grauitatis
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              M, & fruſti AG
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              H, axis VQ, &
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              in eo centrum
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              grauitatis N, &
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              iungantur TV,
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              MN,
                <expan abbr="Pq.">Pque</expan>
              Quo
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              niam igitur eſt
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              pyramidis fru­
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              ſtum, quod pro­
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              ponitur; omnia
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                <figure id="id.043.01.081.1.jpg" xlink:href="043/01/081/1.jpg" number="52"/>
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              cius producta latera concurrent in vno puncto, qui eſt pyra­
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              midis vertex: fruſta igitur, in quæ diuiſum eſt fruſtum pro­
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              poſitum earum ſunt pyramidum, quæ verticem habent
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              communem cum pyramide, cuius eſt fruſtum propoſitum:
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              tres igitur talium fruſtorum axes, vt pote ſegmenta axium
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              trium prædictarum pyramidum in communi illo vertice
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              concurrent: quilibet igitur duo trium prædictorum axium
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              KL, TP, VQ, erunt in eodem plano: TP, igitur, &
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              VQ, ſunt in eodem plano. </s>
              <s>Eadem autem ratione, qua
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              vtebamur de priſmate K, centrum grauitatis K, baſis
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              EH, eſt in linea TV, & L, baſis BD, centrum grauita­
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              tis eſt in linea
                <expan abbr="Pq;">Pque</expan>
              reliquæ igitur KL, MN, erunt in eo­
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              dem plano trapezij PTVQ, ſeque mutuo ſecabunt: cum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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