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the angle BAD is equal to the angle in the segment AEB, for the latter too is itself a right angle, being an angle in a semicircle. [III.31]
But
the angle BAD is also equal to the angle at C.
Therefore
the angle AEB is also equal to the angle at C.
Therefore again
the segment AEB of a circle has been described on AB admitting an angle equal to the angle at C.
Being what it was required to do.
