Valerio, Luca, De centro gravitatis solidorvm libri tres

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                <pb xlink:href="043/01/026.jpg" pagenum="18"/>
              tiones, ita vt ſegmenta, quæ ad angulos, eo­
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              rum, quæ ad oppoſita triangula, ſint tripla; ex quo
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              puncto tota pyramis diuiditur in quatuor pyrami
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              des æquales. </s>
              <s>Et in nullo alio puncto quatuor re­
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              ctæ lineæ ductæ ab angulis ad triangula oppoſita
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              pyramidis ſecant ſeſe in eaſdem rationes. </s>
              <s>Vocetur
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              autem punctum hoc centrum dictæ pyramidis. </s>
            </p>
            <p type="main">
              <s>Sit pyramis ABCD, cuius vertex A, baſis autem
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              triangulum BCD, axes AE, BM, CL, DN, vnde qua­
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              tuor triangulorum, quæ ſunt circa pyramidem ABCD,
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              centra erunt grauitatis E, L, M, N. </s>
              <s>Dico quatuor li­
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              neas AE, BM, CL, DN, ſecare ſe ſe in vno puncto in
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              eaſdem rationes, quas prædixi, & quæ ſequuntur. </s>
              <s>Nam ex
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              puncto A, ducatur recta ALH, quæ ob trianguli ABD,
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              centrum L, ſecabit latus BD, bifariam in puncto H; iun­
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              cta igitur CE, & producta conueniet cum ALH, vt in
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              puncto H. eadem ratione iunctæ AM, BE, & productæ
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              conuenient in medio lateris CD, conueniant in puncto K,
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              necnon AN, DE, in medio ipſius BC, vt in puncto G.
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              </s>
              <s>Quoniam igitur ob triangulorum centra, eſt vt CE ad EH,
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              ita AL ad LH, dupla enim eſt vtraque vtriuſque, ſeca­
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              bunt ſeſe rectæ AE, CL, inter eaſdem parallelas; quare
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              vt AF ad FE, ita erit CF ad FL, circum æquales angu
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              los ad verticem: triangula igitur AFL, CFE; & reci­
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              proca, & æqualia inter ſe erunt. </s>
              <s>Cum igitur ſit vt AL ad
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              LH, ita CE ad EH, hoc eſt vt triangulum AFL ad
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              triangulum FLH, (ſi ducatur FH) ita triangulum CFE,
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              ad triangulum FEH, erunt inter ſe æqualia triangula
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              FEH, FLH. </s>
              <s>Quare vt triangulum AFH, ad triangu­
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              lum FLH, hoc eſt vt AH ad HL, ita erit triangulum
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              AFH ad triangulum FEH, hoc eſt AF ad FE: ſed re­
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              cta AH, eſt tripla ipſius LH; igitur & AF, erit ipſius FE, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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