DE. PLUCKER ON A NEW GEOMETRY OE SPACE. 
737 
By putting successively r 
y'= 
af= 00 , 
the same equation becomes 
C+E#+Dy=0, 1 
B+Far-D 2 = 0, 1 (18) 
A-1>-Ez=0.J 
Accordingly these equations represent the planes corresponding to points moved to an 
infinite distance along OZ, OY, OX. 
By combining each of the equations (18) with (17), we get the rays conjugate to the 
axes of coordinates OZ, OY, OX, forming a triangle, the angles of which fall within the 
three planes of coordinates, XY, XZ, YZ, into the corresponding points. 
24. By putting 
w — 00 , 
the equation (15), representing a point corresponding to any given point d), becomes 
D£+Ew— Fw=0, 
and then indicates that the point corresponding to the infinitely distant plane of space 
falls itself, at an infinite distance, along a direction which may be represented by the 
equations 
x y z 
D — E = F’ 
(19) 
while, if rectangular coordinates were supposed, 
D^+E < y+F2!=0 
represents the plane perpendicular to it. 
We shall call this direction the characteristic direction of the complex. It is invariably 
connected with the complex. 
25. By putting successively 
tf = 00 , 
v! = 00 , 
— co , 
we get, in order to represent within the planes of coordinates YZ, XZ, XY, the points 
corresponding to these planes, the following equations : 
Cu— Bv— Dw=0, j 
a-Av-Ew=0, ......... (20) 
B£— Au— Fw=0. I 
