548 
[964 
964. 
ON THE NINE-POINTS CIRCLE OF A SPHERICAL TRIANGLE. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. xxvn. (1895), 
pp. 35—39.] 
The definition is in effect given in Hart’s paper, “ Extension of Terquem’s theorem 
respecting the circle which bisects three sides of a triangle,” Quarterly Mathematical 
Journal, t. IV. (1861), pp. 260, 261, viz. if we have a spherical triangle ABC, then we 
have a circle (i.e. a small circle of the sphere), say the nine-points circle, meeting the 
sides BG, CA, AB in the points F, L; G, M; H, N respectively, where 
cos\c sin \a 
cos ^rb sin\a 
(which equations agree with BF + FO = BC), and 
cos 2"C sin £a 
tan \BL = 
cos ^b + cos-|c cos ’ 
cos ^b sin\a 
tan CL — 
cos c -t- cos\acos 
(which equations agree with BL + CL = BC); and with the like formulae for the points 
G, M: and H, N: respectively. 
If, as usual, the sides of the triangle are called a, b, c, and for shortness we 
write