THEORY OF POLYCONIC PROJECTIONS. 



99 



line; the same is true of the three points Z>^ 21, G, 

 as also of G, D, M' and of G' , M\ B' , The three points 

 Z)', G, G' are thus the vertices of a triangle the altitudes of 

 which intersect in Z> and the feet of these perpendiculars 

 are at 0, M' ^ and M. 



Let us construct the angle FOl equal to that which the 

 meridian PMP' makes with the straight line meridian 

 PP'\ the three points P', G, 1 will be in a straight line, 



Fig. 31.— Geometrical relations Detween orthogonal meridians and parallels, 

 second figure. 



because the angle OP'G which subtends the arc PMG upon 

 the circumference T is equal to half the angle formed 

 by the chord PP' with the tangent at P' ] that is, to half 

 the angle POI; hence upon the circumference it ought 

 to subtend an arc equal to PP, that is to say, that the pro- 

 longation of P'G ought to pass through /. We have, then, 

 to determine directly the point G, a process analogous to 



