A generalization of a Theorem of A. Rogers

Generalizing a Theorem due to A. Rogers {ro1}, we are going to prove that if for a pair of convex bodies K₁,K₂⊂, n≥ 3, there exists a hyperplane H and a pair of different points p₁ and p₂ in H such that for each $(n-2)$-plane M⊂ H, there exists a mirror which maps the hypersection of K₁ defined by \ p₁,M\ onto the hypersection of K₂ defined by \ p₂,M\, then there exists a mirror which maps K₁ onto K₂.