Euclid's Elements - Book III, Proposition 31

Author:
mtpberg
Topic:
Circle
An angle inscribed in (see Definition 8) a semicircle is a right angle. An angle inscribed in a segment larger than a semicircle is acute. An angle inscribed in a segment smaller than a semicircle is obtuse. Furthermore, the angle of (see Definition 7) a segment larger than a semicircle is obtuse, and the angle of a segment smaller than a semicircle is acute.