110 
THEORY OF COLLINEATIONS. 
ae AA AB k-1 : dA dB 
The limits of [Gsq, andj, are respectively [—,. =, 
t. The normal form of type II then becomes 
% Ye LO x Yy i) 
A AB eA A 5B. SSB 
DEN Ey AN UE ys 
isis ‘ds ds ds ds 
Al” B’ 1 ki A” All Br 1 ki Bi 
v= ’ Yi = 
x yo i @ 5 
A Bion st (Same denominator. ) 
dA dB 
rae vee ee 
ds ds 
All Br a k! 
But - and 
= are the direction cosines of the tangent to s 
at A, 7. e., cosine and sine of its angle with the positive 
x-axis, and may be replaced by « and 3 respectively ; we have 
also a?+ B= 1. 
Fic. 20. 
