How is Euclid's geometry different from any other geometry?

Answer by  Clement (1453)

Euclid's geometry is the "traditional" geometry you study at school. One of its basic axioms states that for a given line and a point not on this line there exists a unique other line parallel to the first one. Non-Euclidean geometries reject this axiom.

Answer by  oddrobot (10)

Euclid's geometry is the geometry of two planes. For every point on the graph of an equation, there is only one corresponding answer to the solution of the equation. Also for every solution to an equation, there is only one corresponding point on the graph of the equation. Other geometries may contain more than two planes.