Further theorems on the relationships between linear and stereographic projections

Abstract

One theorem states that the distance from the gnomonostereographic projection to the linear projection in a certain plane is equal to the distance from the latter to the vanishing point of the rays. The proof reduces to the fact that the vanishing point of the rays Z, the gnomonostereographic projection P, and the midpoint of the linear projection of the plane O constitute the vertices of an isosceles triangle, having the first two points at its base, and this, in turn, reduces to proving the equality of the angles at the base.

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