On the projecting cones of stereographic projection

Abstract

In a grammastereographic projection, any plane is projected as an arc of a great circle, that is, an arc passing through two diametrically opposite points of the projection circle. This circle represents one circular section of the cone having its center at the point of convergence of the rays; the other circular section of the same cone is the diametral circle of the sphere in the plane being projected. Apparently, no crystallographer has yet noted that these projecting cones are not cones of a general nature, but are special cones, known as the cones of Pappus, who first noted their simple construction. The two special axes of the projecting cone are perpendiculars to both circular sections, that is, perpendiculars to both the given plane and the projection plane (see the article).

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