Valerio, Luca, De centro gravitatis solidorvm libri tres

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            <p type="main">
              <s>
                <pb xlink:href="043/01/045.jpg" pagenum="37"/>
              trum grauitatis. </s>
              <s>Si enim non eſt, erit aliud, eſto G: &
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              iunctatur EG, producatur ad partes G, in infinitum vſ­
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              que ìn F. </s>
              <s>Quoniam igitur E, eſt centrum grauitatis vnius
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              partis AC, & G, totius AB; erit reliquæ partis CD, in
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              linea GF centrum grauitatis: ſed & in puncto E; eiuſ­
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              dem igitur magnitudinis AB, duo centra grauitatis erunt.
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              </s>
              <s>Quod fieri non poteſt; totius igitur AB, erit centrum gra
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              uitatis idem E. </s>
              <s>Manifeſtum eſt igitur propoſitum. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XIX.
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              </s>
            </p>
            <p type="main">
              <s>Omnis trianguli rectilinei idem eſt centrum
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              grauitatis, & figuræ. </s>
            </p>
            <p type="main">
              <s>Sit triangulum rectilineum ABC, cuius centrum G.
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              </s>
              <s>Dico G, eſse centrum grauitatis trianguli ABC. </s>
              <s>Si enim
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              fieri poteſt, ſit aliud punctum N, centrum grauitatis trian
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              guli ABC, & per punctum G, ducantur rectæ AF, BD,
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              CE, & DHE, ERF, FKD,
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              K
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              LH, & NG. </s>
              <s>Quo­
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              niam igitur quæ ab angulis A, B, C, ductæ ſunt rectæ
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              lineæ per G, ſecant bifariam latera AB, BC, CA; erit
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              triangulum EDF, ſimile triangulo ABC, ob latera pa­
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              rallela vt ſunt EF, AC. </s>
              <s>Et quoniam triangulum EDF,
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              dimidium eſt cuius vis trium parallelogrammorum AF,
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              BD, CE, æqualia inter ſe erunt ea parallelogramma
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              omnifariam ſumpta, quorum centra grauitatis H, K, R;
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              intelligantur autem tria parallelogramma AF, BD, CE,
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              diſtincta penitus, ita vt inter ſe congruant ſecundum tria
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              triangula DEF, inter ſe congruentia: trium igitur trian
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              gulorum DEF, inter ſe congruentium & centra grauita­
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              tis inter ſe congruent in puncto M. </s>
              <s>Quoniam igitur in­
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              ter duas parallelas EF, KH, ſecant ſe rectæ lineæ FH,
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              LR, in puncto G; erit vt FG, ad GH, ita RG, ad GL; </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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