326 A. Mukhopadhyay — Memoir on Plane Analytic Geometry. [No 3, 



Z.AB'C' = — - — ^— A. Then, in order to find the envelope of B'C, take 

 o 



AC, AB as the axes of x and y respectively, so that the equation of B'C is 



^+^=1 (^^) 



Now, we have from the geometry of the figure 



AC'zz-^sinf^-^-A), (100) 



sin A \ 3 / ^ ^ 



AB' = -Arsin 

 sm A 



while 

 gives 



sm 

 c 



in + ^), (101) 



c = AB = AC' + C'B 

 in (I-.- a) sin(| + ._B) 



sin A sin B 



sm 



= ^ : T V r— 5- I- cos S 



Sin A sm B J 



["•(I-b)~(I-»)]. 



+ \ ^-^ — '- : — -. hsm 



1^ sm B sm A J 



which may be written in the form 



where 



- = Pcos(9-i-Qsin^, (102) 



P = l + ^ (cot A + cotB) (103) 



Q= i (cot A- cot B) (104) 



The equation of B'C in (99), therefore, reduces to 



sin A sin A _ . , ^' 



which may be written 



I X sin ^— - Aj +2/ sin ^ j cos B-\- j ?/ cos - - a? cos f-;^ - A\ | sin & 



