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Book III   Proposition 15
And, since
    the two sides ME, EN are equal to the two sides FE, EG, and the angle MEN greater than the angle FEG,
therefore
    the base MN is greater than the base FG. [I.24]
But
    MN was proved equal to BC;
therefore
BC is greater that FG.

Therefore, of AD, BC, FG,
the diameter AD is greatest and BC greater than FG.

Being what it was required to prove.
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