Of the branches of mathematics, geometry has, from the earliest Hellenic period, been given a curious position that straddles empirical and exact science. Its standing as an empirical and approximate science stems from the practical pursuits of artistic drafting, land surveying and measuring in general. From the prominence of visual applications, such as figures and constructions in the twentieth century Einstein’s General Theory of Relativity holds that the geometry of space-time is dependent upon physical quantities. On the other hand, earlier on in history, the symmetry and perfect regularity of certain geometric figures were taken as representative of a higher order knowledge than that afforded by sense experience. Concerns with figures and constructions, instead of with numbers and computations, rendered geometry amenable to axiomatic formulation and syllogistic deduction, establishing a paradigm of demonstrative visual and intuitive knowledge that has spanned two millennia.