60 U. S. COAST AND GEODETIC SURVEY. 



tance f, then AF = a tan | and AF' = a tan ^ (r-p) 



= a cot ?; but OJ. = a, and so we have 

 OP:OA=OA:AP\ 

 THis establishes the validity of the construction. 



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y 



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V^ 



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As a basis for the next problem we shall prove that if a 

 plane passes through the poles of two great circles it cuts 

 off equal arcs on the two circles. n-nnt 



In figure 21 let P be the pole of the great circle CEC 

 and let P' be the pole of BED' with the center of the 



