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.
On the numerical values of the roots of the equation cosx = x
