XVII. On a new geometry of space

Abstract I. On Linear Complexes of Right Lines. 1. Infinite space may be considered either as consisting of points or transversed by planes. The points, in the first conception, are determined by their coordinates, by x, y, z for instance, taken in the ordinary signification; the planes, in the second conception, are determined in an analogous way by their coordinates, introduced by myself into analytical geometry, by t, u, v for instance. The equation tx + uy + vz + 1 = 0 represents, in regarding x, y, z as variable and t, u, v as constant, a plane by means of its points. The three constants t, u, v are the coordinates of this plane. The same equation, in regarding t, u, v as variable, x, y, z as constant, represents a point by means of planes passing through it. The three constants are the coordinates of the point.