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Book I   Proposition 21
Then, since in any triangle two sides are greater than the remaining one, [1.20]
    therefore, in the triangle ABE, the two sides BA, AE are greater than BE. Let EC be added to each;
    therefore BA, AC are greater than BE, EC. (continue)

Again, since, in the triangle DEC, the two sides DE, EC are greater than DC, let BD be added to each;
    therefore BE, EC are greater than BD, DC. (continue)

Since BA, AC were proved greater than BE, EC and BE, EC are greater than BD, DC;
    therefore BA, AC are (much) greater than BD, DC.
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