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Book IV   Proposition 15
Therefore
    the six angles EGD, DGC, CGB, BGA, AGF, FGE are equal to one another.

    But equal angles stand on equal circumferences; [III.26] therefore
    the six circumferenced AB, BC, CD, DE, EF, FA are equal to one another.

    And equal circumferences are subtended by equal straight lines; [III.29] therefore
    the six straight lines are equal to one another.

Therefore
    The hexagon ABCDEF is equilateral.
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