 Lobachevskii argued firstly that geometry was a science of bodies in space, and that space is three-dimensional. The most primitive concept was that of contact, and its opposite, a cut separating two bodies. Two bodies not in contact are separated and a suitable third body in contact with both of them measures the distance between them -- a concept that was otherwise undefined. With it, however, he could define a sphere with its centre at a given point as the collection of all points equidistant from that given point. He then showed how to define a plane capturing the intuition that a plane is the collection of points in space that lie the same distance from two given points. In his terms, given two points, a plane is the set of points common to two spheres of equal radius, one centred on one of the points and the other on the other. A line can be defined similarly using circles on the same plane.