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Book III   Proposition 25
    The line EA was proved equal to each of EB, EC;
therefore
    the three straight lines EA, EB, EC are equal to one another.
Therefore
    the circle drawn with center E and distance one of the straight lines EA, EB, EC will also pass through the remaining points and will have been completed. [III.9]

Therefore,
    given a segment of a circle, the complete circle has been described.

And it is manifest that the segment ABC is less than a semicircle, because the center E happens to be outside it.
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