THEORY OF POLYGON IC PROJECTIONS. 



65 



This same problem can be solved by the method of 

 descriptive geometry in the following way: 



Fig. 25.— Projection of great circle through two points on stereographic projection, 

 second method. 



In figure 25 BO is the trace of the great circle plane on 

 the horizontal plane; we need to determine, then, this 

 trace of the plane of ilf , M' and the center of the sphere. 

 n and n', "p and ^p' are determined as before; from p let fall 

 the perpendicular pq^ upon "WE and from p' , the perpen- 

 dicular 2^'2'j prolong Otti to r, making Or^Oq, and pro- 

 long Om' to r' , vndSmg Or' = 0(1', r and r' are then the 

 orthographic horizontal projections of the given points M 

 and M' on the sphere. Draw S' U parallel to WE; let 

 fall the perpendiculars r's' and rs and prolong them, 

 making S' T = p'q' and S T=pq, T and T are the ortho- 

 graphic vertical projections of M and M', and TT' is the 



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