More theorems on the relationships between linear and stereographic projections

Abstract

One theorem is that the distance of a gnomostereographic from a linear projection in a certain plane is equal to the distance from the last point of convergence of the rays. The proof boils down to the fact that the vanishing point of the rays Z, the gnomostereographic projection P and the midpoint of the linear projection of the plane O constitute the vertices of an isosceles triangle having the first points at the base, and this, in turn, comes down to proving the equality of the angles at the base.