|Book III Proposition 25|
The line EA was proved equal to each of EB, EC;
the three straight lines EA, EB, EC are equal to one another.
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]
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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