With the develoment of analytic geometry in the seventeenth century, space come to be regarded as a collection of points, and with the creation of the classical non-Euclidean geometries in the ninteenth century, mathematicians accepted the situation that there is more than one geometry.but space was still regarded as a locus in which figures could be compared with one another. The central idea became that of a group of congruent transformations of space into itself , and a geometry came to be regarded as the study of those properties of configurations of points which remain unchanged when, in Section 9-8 ,how this point of view was expanded by Felix Klein (1849-1929) in his Erlanger Programm of 1872. In the Erlanger Programm a geometry was defined as the invariant theory of a transformation group, This concept synthesized and generalized all earlier concepts of geometry, and supplied a singularly neat classification of a large number of important geometries.
At the end of the nineteenth century, with the development of the idea of a branch of matnematics as an abstract boody of theorems deduced from a set of postulates each geometry became, from point of view, a particular branch of mathematics.