SYMMBDIAN POINT OF A TRIANGLE. 61 



Hence we have the series of eij nations — 



a^ ( (px^dS+b-^ ^' i'py-'dS+c' i j' 'pz"-dS= g (a') V, ' 



from which we obtain the following: — 



C i px'dS = a^r, i ipy-'dS=b^-V,i ipz^dS=c^-V. (37) 



kMmilarly by solving tor I I 'II — 'II " ' ^^^^^^ 



the equations — 





we find — 



5 



r 





(38) 



5.— ON THE SYMMEDIAN POINT OF A TEIANGLE. 

 By EVELYN G. HOGG, M,A., Christ's College, Cliristchurch, N.Z. 



1. The axis of homology of any point P (a'/S'y') with respect to 

 the triangle of reference ABC has for equation — 



- + '^ + - =0. 

 a' /?' y' 



If this line pass through the fixed point (a^^^y^), the locus of P is 

 the conic 



^o p. To , 



a P 7 



In particular the circle ABC is the locus of points whose axes of 

 homology with respect to the triangle ABC pass through the symmedian 

 point 8 (a&c) of that triangle. 



