Unique reconstructibility of convex compact sets from their projections (Q806044)

The n-dimensional convex sets \(V_ 1\) and \(V_ 2\) are orthogonally projected onto some given hyperplanes. It is proved if there exists a translation which transforms the image of \(V_ 1\) into the image of \(V_ 2\) for all of these projections then \(V_ 1\) can be translated into \(V_ 2\).