THEORY OF POLYCONIC PROJECTIONS/ 



97 



meridians and orthogonal parallels. In figure 30 let P 

 and P' be the projections of the poles, the middle point 

 of the line PP' , APA'P^ the circumference described upon 

 PP' as a diameter, A A' the diameter perpendicular to 

 PP^ ; in addition, let S be the center of the projection of any 

 parallel, TJ and J7', Z> and B' , F and F' the points where 

 this projection intersects, respectively, the circimiference 



Fig. 



-Geometrical relations between orthogonal circular meridians and parallels, 

 first figure. 



APA'P^, the line PP\ and the perpendicular erected at S 

 upon this line; finally, let V be the intersection of PP' 

 with UU\ and let U^ be symmetrical to Z7 with respect to 

 0, so that U'U^ is parallel to PP' 



The point D being the bisector of the arc UDU', UD 

 will bisect the angle formed by the chord TJU^ and the 

 tangent OU; the point A' being the bisector o^ the arc 



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