Deb Russell explains on About.com that Euclid is famous for his treatise on geometry entitled “Elements,” which makes him one of the most renowned teachers in mathematics. His work has served as a significant foundation for mathematics teachers for more than 2,000 years.
All the rules used in geometry are based on Euclid’s writings, expounds Russell. "Elements" includes the Number Theory, the Eudoxus’ Theory of Irrational Numbers and Solid Geometry, among other theories. In 1482, the first edition of this treatise was printed in a logical and coherent framework. Since then, more than 1,000 editions have been printed. In the early 1900s, schools stopped using "Elements," although its theories continue to be used. The treatise discusses the Euclidean algorithm, which is one of the oldest algorithms known. This algorithm is used to determine the greatest common divisor of two integers.
The Encyclopedia Britannica states that Euclid is the most prominent mathematician of Greco-Roman antiquity. He compiled his treatise from several works of earlier men, including Hippocrates of Chios and Theudius. Although Euclid based his work upon his predecessors, the entire design of his treatise was his own, resulting in the creation of the five regular solids known as the Platonic solids.