History of geometry
Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, "The Elements" is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.
History of science in classical antiquity
The first step in this emphasis upon a model was that of the followers of Pythagoras (approximately 582 – 507 BC), who saw number as the fundamental unchanging entity underlying all the structure of the universe. For Pythagoras and his followers matter was made up of ordered arrangements of point/atoms, arranged according to geometrical principles into triangles, squares, rectangles, and so on... Even on a larger scale, the parts of the universe were arranged on the principles of a musical scale and a number. For example, the Pythagoreans held that there were ten heavenly bodies because ten is a perfect number, the sum of 1 + 2 + 3 + 4. Thus with the Pythagoreans we find number emerging as the rational basis for an orderly universe — as the first proposal for a scientific ordering principle of the cosmos.
Like the Pythagoreans, Plato (c. 427–c. 347 BC) found the ordering principle of the universe in mathematics, specifically in geometry. A later account has it that Plato had inscribed at the entrance to his school, the Academy, "Let no man ignorant of geometry enter." The story is a myth, but like all myths it has a grain of truth, for in his writings Plato repeatedly tell us of the importance of geometry.