Then 

 but 

 Therefore 



THEORY OF POLYCONIC PROJECTIONS. 



DC : EM=DO : EO=DB : EH, 

 DC=DB. 

 EM=EH, 



AEGE=\ (arc OZ + arc ZF)=^+i arc EJB 

 AERO = Tr- Z.ERO = Tr- ZDBO^TT-^siTcOLACB 

 = 7r-i (arc OLACBK-eiTc BK) 



=-7r —-rir +2 arc BK =4 + ^^^ -^^• 



Therefore 



ZEGH= ZEHG 

 and 



EH=EG, 



In a similar way it can be proved that 



EM^EF. 

 But, since 



EH=EM, 



EG = EF, 



therefore the projection of D is the center of the circle that 

 maps the given circle. D is, of course, the apex of the cone 

 tangent to the sphere along the given circle. 



'file stereographic horizon projection can be constructed ' 

 either by computation of the radii and centers or directly 

 by graphic construction. The formulas for computation 

 are for the meridians 



p^ = a sec a co^ec X 

 Xia= —cb sec a cot X 

 Vjn= —a tan a 



