544 
writing only the first (or indeed any one) of the tree equations (90) or 
(91), and then appending an ‘“‘ &c.’’; for the Jaw which has been just 
stated will always enable us to recover (or deduce) the other two. We 
may therefore briefly but sufficiently express several of the foregoing re- 
sults, by writing, 
a = (100), &c.; a’=(011), &.; a” = (011), &c.; ay = (111), ee] 
A, = (10001), &c. ; 4,=(10010), &c.; a’; =(10001), &e.; (92) 
4’, = (10010), &e. | 
Plane ave =[01100], &.; Line av,a’ = [011], &. ; (93) 
to which we may add these other symbols of planes and lines, each sup- 
posed to be followed by an ‘‘ &e.’’: 
plane sop = [10001]; scx =[10010]; trace =sce=[100]; (94) 
plane px’B,c’c, = [11101] ; EB/B,C'C, = [11110]; ie (95 
trace = B/ e/a” = [111] } ) 
plane aB,C.C,B, = [01111]; trace = aa” = [011]; (96) 
this line 4” passing also, by (77), through the two points B, and ¢ ; 
‘plane B,¢:D, =[21111]; B.D, =[21111]; trace=n,a"=[211]; (97) 
plane a’'B,B, = [21111] 3 trace = A/By = [21 1]; 
plane a/c,C2 = [21111]; trace = A/C) = [211] 2 (98) 
where it may be noticed that the symbol for a’c,c,, or for a/c), may be 
deduced from that for 4’B,B, or for 4’Bo, by simply interchanging the 
second and third coefficients, or coordinates. It is easy to see that the 
quinary symbol for the plane axc itself is on the same plan [00011], the 
equation of that plane being w=; and it will be remembered that, by 
[18.], the ternary symbol for the point p, in that plane is (111). 
[21.] A right Line A in Space may be regarded in two principal 
views, as follows. Ist, it may be considered as the locus of a variable 
point ¥, collinear with two given points Py), P\; and in this view, the 
symbol 
to(Po) + t,(P1), (comp. (72),) 
for the variable point upon the line, may be regarded as a Local Symbol 
(or Point-Symbol) of the Line A itself. Thus 
(0é2’), or (Oy), (99) 
may either represent an arbitrary point on the line sc; or, as a local 
symbol, that line itself. Or IInd, we may consider a line A as a hinge, 
round which a plane I turns, so as to be always collinear ['7.] with two 
gwen planes M1), II, through the line ; and then a symbol of the form 
tof Hy | + é,[11,], (comp. (25),) 
