Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/071.jpg" pagenum="63"/>
              monſtrauimus trium octaedrorum, quæ ſunt in pyrami­
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              dibus AFHK, FBGL, GHOM ſimul, centrum gra­
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              uitatis erit in axe D
                <emph type="italics"/>
              K
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              : ſed & octaedri in pyramide DK­
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              LM, & octaedri FGHKLM centra grauitatis ſunt
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              in axe DN; omnium igitur quinque octaedrorum, quæ
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              ſunt in tota pyramide ABCD ſimul centrum grauitatis
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              eſt in axe DN. </s>
              <s>Quod ſi rurſus in ſingulis quatuor præ­
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              dictarum pyramidum modo dicta ratione quina octaedra
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              deſcripta intelligantur, ſimiliter oſtenſum erit quina octa­
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              edra in ſingulis quatuor abſciſſarum pyramidum, velut
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              quatuor magnitudines, centra grauitatis habere in axibus
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              quatuor prædictarum pyramidum: ſunt autem hæc qua­
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              tuor compoſita ex quinis octaedris inter ſe æqualia, pro­
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              pter æqualitatem octaedrorum multitudine æqualium,
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              quæ æqualibus ſunt pyramidibus ipſorum duplis ord ine
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              diuiſionis inter ſe reſpondentibus inſcripta; igitur vt ante,
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              quater quinorum octaedrorum ſimul in axe DN erit
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              centrum grauitatis: ſed & octaedri FGHKLM centrum
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              grauitatis eſt in axe DN; vnius igitur & viginti octae­
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              drorum in pyramide ABCD exiſtentium ex hac ſecun­
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              da diuiſione, tanquàm vnius magnitudinis in axe DN erit
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              centrum grauitatis. </s>
              <s>Ab hoc igitur numero vnius & vi­
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              ginti octaedrorum in pyramide ABCD exiſtentium, ſi­
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              mili diuiſione illius reliquarum quatuor pyramidum primo
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              abſciſſarum procedentes, & eundem ſemper gyrum, quem
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              fecimus à quinario repetentes, poterunt eſse in tota AB­
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              CD pyramide tot, quemadmodum diximus, deſcripta,
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              octaedra, vt eorum numerus ſuperet quemcumque propo­
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              ſitum numerum, & omnium tanquàm vnius magnitudinis
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              in axe DN, ſit centrum grauitatis. </s>
              <s>Sic autem facienti, &
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              reliquarum pyramidum demptis præcedentibus octaedris,
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              dimidia octaedra ſemper auferenti, tandem relinquen­
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              tur pyramides minores ſimul ſumptæ quantacumque
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              magnitudine propoſita. </s>
              <s>Totius igitur pyramidis ABCD </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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