685] 
295 
685. 
ON MR COTTERILL’S GONIOMETRICAL PROBLEM. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. xv. (1878), 
pp. 196—198.] 
The very remarkable formulae contained in Mr Cotterill’s paper, “A goniometrical 
problem, to be solved analytically in one move, or more simply synthetically in two 
moves,” Quarterly Mathematical Journal, t. vii. (1866), pp. 259—272, are presented in 
a form which, to say the least, is not as easily intelligible as might be; and they 
have not, I think, attracted the attention which they well deserve. 
Using his notation, except that I write for angles small roman letters, in order 
to be able to have the corresponding italic small letters and capitals for the sines 
and cosines respectively of the same angles, we consider nine angles 
a, b, c, 
d, e, f, 
x, y, z, 
which are such that the sum of three angles in the same line, or in the same 
column, is an odd multiple of 7r. Of course, any four angles such as a, b, d, e are