  Let $\nu_d : \mathbb{P}^n \longrightarrow \mathbb{P}^N$ be the Veronese
mapping of degree $d$ where $N = {n+d \choose n} -1$. By an elementary approach
it is shown that $\nu_d$ is an isomorphism of $\mathbb{P}^n$ onto the
projective variety defined by the $2$-minors of a matrix.
