Euclid

Elements, by Euclid (c. 330-c. 260 B.C.), is the most enduring and influential mathematical work of all time. In it, the ancient Greek mathematician incorporated the work of earlier mathematicians plus many of his original teachings.

Elements is divided into thirteen books: the first six cover plane geometry (the geometry of two-dimensional figures); seven to nine address arithmetic and number theory (number theory is the study of nonzero whole numbers and their relationships to one another); ten treats irrational numbers (numbers that cannot be expressed as ratios of whole numbers); and eleven to thirteen discuss solid geometry (geometry of three-dimensional objects).

In presenting his theorems Euclid used the "synthetic approach."