  We show that high Veronese subrings of any commutative graded ring have a
Grobner basis with all relations of degree 2. (The d-th Veronese subring of a
ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means
we take d sufficiently large, say at least half the regularity of the ideal
defining the original ring.) This gives another proof of Backelin's theorem
that such Veronese subrings are Koszul algebras (= wonderful rings), i.e., that
the minimal resolution of the residue field of such a ring is linear.
