  We generalize Monge's theorem for $n+1$ pairwise homothetic convex bodies in
$E^n$ in place of three disks in $E^2$. We also present a version for
homotheties for pairs of vertices of a non degenerate simplex in $E^n$. It
includes a reverse of Monge's theorem. Moreover, we give an analogon of Monge's
theorem on the $n$-dimensional sphere.
