Euclidean geometry is a mathematical system attributed to the
Alexandria. Euclid's text
Elements was the first systematic discussion of
geometry. It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing
axioms, and then proving many other
theorems) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could fit together into a comprehensive deductive and logical system.
The Elements begin with
plane geometry, still often taught in
secondary school as the first
axiomatic system and the first examples of
formal proof. The Elements goes on to the
solid geometry of three
dimensions, and Euclidean geometry was subsequently extended to any finite number of
dimensions. Much of the Elements states results of what is now called
number theory, proved using geometrical methods.
For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute sense. Today, however, many other self-consistent geometries are known, the first ones having been discovered in the early 19th century. It also is no longer taken for granted that Euclidean geometry describes physical space. An implication of
Einstein's theory of
general relativity is that Euclidean geometry is only a good approximation to the properties of physical space if the
gravitational field is not too strong.