518 HYDRO GRAPHICAL SURVEYING [afi>. b. 



Bisect C K G in K N, making GKNorXKZ = i convergency, 



Then E where K N intersects P F is on the parallel K C, or P K = P K. 



Bisect K P E in P X. 



Now M K Z = K Z P + K P Z, 



but M K Z = 90° + I Convergency (by construction) and 

 K P Z = i Convergency ; 



.-. 90° + i Conv = K Z P + i Conv ; 

 .-. K Z P = 90° = P Z E, 



and as K P Z = Z P E and P Z is common, the As K Z P & P Z E are equal 

 and similar ; 



/. P E = P K. 



Q. E. D. 



