Valerio, Luca, De centro gravitatis solidorum, 1604

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/028.jpg" pagenum="20"/>
              liter igitur vt ante oſtenderemus, vnamquamque qua­
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              tuor pyramidum, quarum communis vertex S, baſes au­
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              tem triangula, quæ ſunt circa pyramidem ABCD, eſse
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              quartam partem pyramidis ABCD. </s>
              <s>Siue igitur pun­
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              ctum S, cadat intra vnam priorum quatuor pyrami­
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              dum, ſiue in earum aliquo latere, ſeu triangulo; neceſ­
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              ſario erit pars æquali toti; tam enim tota vna pyramis
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              quatuor priorum, quarum communis vertex F, quàm eius
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              pars, vna quatuor pyramidum poſteriorum, quarum com­
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              munis vertex S, erit eiuſdem ABCD, pyramidis pars
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              quarta. </s>
              <s>Ex abſurdo igitur non in alio puncto à puncto F
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              ſecabunt ſe in eaſdem rationes quatuor rectæ, quæ ab angu
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              lis ad oppoſita triangula pyramidis ABCD, ducantur.
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              </s>
              <s>Manifeſtum eſt igitur propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO IX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis pyramis baſim habens triangulam di­
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              uiditur in quatuor pyra mides æquales, & ſimiles
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              inter ſe, & toti, & vnum octaedrum totius pyrami­
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              dis dimidium, ip ſi que concentricum. </s>
            </p>
            <p type="main">
              <s>Sit pyramis ABCD, cuius baſis triangulum ABC,
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              ſectisque omnibus lateribus bifariam, iungantur rectæ FG,
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              GH, HF, FK, KL, LM, M
                <emph type="italics"/>
              K
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              , KH, HM, GL, LF.
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              </s>
              <s>Dico quatuor pyramides DKLM, LFBG, KHFA,
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              MHGC, æquales eſse, & ſimiles inter ſe, & toti pyrami­
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              di ABCD: octaedrum autem eſse LFGM
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              H, & di­
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              midium pyramidis ABCD, ipſique concentricum. </s>
              <s>Du­
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              cantur enim rectæ DNH, BQH, LN: & poſita BE, du
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              pla ipſius BH, iungatur DOC, in triangulo DBH, &
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              ponatur DP, ipſius PE, tripla, & connectantur rectæ LP,
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              PH. </s>
              <s>Quoniam igitur E, eſt centrum trianguli ABC, </s>
            </p>
          </chap>
        </body>
      </text>
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