|Book IV Proposition 11|
Then, since each of the angles ACD, CDA is double of the angle CAD, and they have
been bisected by the straight lines CE, DB, therefore
the five angles DAC, ACE, ECD, CDB, BDA are equal to one another.
But equal angles stand on equal circumferences; [III.26] therefore
the five circumferences AB, BC, CD, DE, EA are equal to one another.
But equal circumferences are subtended by equal straight lines; [III.29] therefore
the five straight lines AB, BC, CD, DE, EA are equal to one another;
the pentagon ABCDE is equilateral.
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