Axiomatic geometry

A method of computing certain out-of-the-way distances or heights based on similarity of geometric figures and attributed to Thales presaged more conceptual approach to geometry taken by Euclid in his Elements, one of the most influential books ever written. Euclid introduced certain axioms or postulates, expressing primary or self-evident properties of points, lines, and planes. He proceeded to rigorously deduce other properties by mathematical reasoning. The typical feature of Euclid's approach to geometry was its rigour. In the twentieth century, David Hilbert employed obvious reasoning in his attempt to update Euclid and provide modern foundations of geometry.