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Book III   Proposition 30
But equal straight lines cut off equal circumferences, the greater equal to the greater, and the less to the less; [III.28]
and each of the circumferences AD, DB is less than a semicircle;
therefore
    the circumference AD is equal to the ciecumference DB.

Therefore
    The given circumference has been bisected at the point D.

Being what it was required to do.
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