Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/025.jpg" pagenum="17"/>
              ad centrum circuli tranſeuntis per tria puncta K, L, M, quod
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              ſit R, ducatur recta AR, & ER iungatur. </s>
              <s>Quoniam igi­
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              tur æquales rectæ ſunt AK, AL, AM, quæ ex puncto
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              A, in ſublimi pertinent ad ſubiectum planum: & punctum
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              R, eſt centrum circuli tranſeuntis per puncta N, O, P; cadet
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              recta AR ad ſubiectum planum perpendicularis. </s>
              <s>Eadem
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              ratione recta ER ducta à vertice E, pyramidis ENOP,
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              ad centrum R, circuli tranſeuntis per puncta N, O, P, hoc
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              eſt, per puncta K, L, M, illis congruentia, cadet ad idem
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              planum, ad quod linea AR, perpendicularis; itaque ab
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              eodem puncto R, ad idem planum, & ad eaſdem partes duæ
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              perpendiculares erunt excitatæ, quod fieri non poteſt:
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              punctum igitur E non cadet extra punctum A: quare la­
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              tus EN, congruet lateri AK, quorum EF, eſt æqualis
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              AK; igitur & EF, ipſi AB, congruet. </s>
              <s>eadem ratione la­
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              tus AG, congruet lateri AC, & latus EH, lateri AD, &
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              triangula triangulis, & pyramis EFGH, pyramidi ABC
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              D, & ipſi æqualis erit. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              COROLLARIVM.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Hinc facile colligitur omnia ſolida, quæ in py
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              ramides æqualibus, & ſimilibus triangulis com­
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              prehenſas multitudine æquales diuidi poſſunt, eſ
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              ſe inter ſe æqualia. </s>
              <s>Quocirca omnia priſmata, &
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              pyramides, & octahedra, omnia denique corpora
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              regularia æqualibus, & ſimilibus planis compre­
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              henſa inter ſe æqualia erunt. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO VIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis pyramidis triangulam baſim habentis
                <lb/>
              quatuor axes ſecant ſe in vno puncto in eaſdem ra­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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