THEORY OF POLYCONIC PROJECTIONS. 



65 



M 



'/'V 



/ ^--7 



j--^ 



/ ^ 



/ \ 



I'll 



/ \ / 



m* 



-v^ 



^<- 



\B 



Fig. 23. — Sphere showing intersection of given lines. 



In figure 23 let Z be the zenith, and C the center of the 

 sphere and let MM' be the arc of a great cu*cle joining the 

 points M and M', HE is the point of projection, m and 

 m' are evidently the projections of M and M\ Produce 

 the chord MM' until it meets mm' produced in R; then 

 RO is evidently in the plane of the great circle MM', and 

 also in the primitive plane. Therefore, the points 

 and 0' lie on the projection of the great circle and the 

 projection is fully determined, since it is a circle passing 

 through m, m', u, and 0', If MM' is parallel to mm'\ 

 then evidently 00' is also parallel to each of these lines. 



