1 
177] SOLUTION OF A MECHANICAL PROBLEM. 
Combining with these the equations 
x cos a + r) sin a — p = 0, 
79 
p 
and 
w, 
we ] 
. 
X, 
y> 
1 
t 
A, 
H, 
L 
V, 
H, 
B, 
M 
1, 
L, 
M, 
n 
= 0 
for the equation of the required line x cos a + y sin a. — p = 0. Replacing L, M, A, H, B 
hy their values, the equation is readily transformed into 
1=0 
X , 
y > 
1 
X 
V, 
1 
a, 
b, 
1 
a, 
b, 
1 
a', 
b\ 
1 
a', 
v, 
1 
where the summation extends to each pair of points (a, b) and {a', b'). This is, in 
fact, an extension of the harmonic relation of a point and line with respect to a triangle.