I. On a new geometry of space

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, byx, 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, byt, y v for instance. The equationtx +uy +vz = 1 represents, in regardingx, y, z as variable,t, u , v as constant, a plane by means of its points. The three constantst, u, v are the coordinates of this plane. The same equation, in regardingt, u, v as variable,x, y, z as constant, represents a point by means of planes passing through it. The three constantsx, y, z are the coordinates of this point.