Euclid's Elements - Book III, Proposition 31

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.

 

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circle  element  euclid 
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15 – 18
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English (United States)
 
 
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