"'Geometry' means 'measure of the earth.' In ancient Egypt, from which Greece inherited this study, the Nile would flood its banks each year, covering the land and obliterating the orderly marking of plot and farm areas. This yearly flood symbolized to the Egyptian the cyclic return of the primal watery chaos, and when the waters receded the work began of redefining and re-establishing the boundaries. This work was called geometry and was seen as a re-establishment of the principle of order and law on earth. Each year the areas measured out would be somewhat different. The human order would shift and this was reflected in the ordering of the earth. The Temple astronomer might say that certain celestial configurations had changed so that the orientation or location of a temple had to be adjusted accordingly. So the laying of squares upon the earth had, for the Egyptian, a metaphysical as well as a physical and social dimension. This activity of 'measuring the earth' became the basis for a science of natural law as it is embodied in the archetypal forms of circle, square, and triangle.

Geometry is the study of spatial order through the measure and relationships of forms. Geometry and arithmetic, together with astronomy, the science of temporal order through the observation of cyclic movement, constituted the major intellectual disciplines of classical education. The fourth element of this great fourfold syllabus, the Quadrivium, was the study of harmony and music. The laws of simple harmonics were considered to be universals which defined the relationship and interchange between the temporal movements and events of the heavens and the spatial order and development on earth."—Robert Lawlor, Sacred Geometry