  Going one step further in Zak's classification of Scorza varieties with
secant defect equal to one, we characterize the Veronese embedding of $\P^n$
given by the complete linear system of quadrics and its smooth projections from
a point as the only smooth irreducible complex and non-degenerate projective
subvarieties of $\P^N$ that can be projected isomorphically into $\P^{2n}$ when
$N\geq\binom{n+2}{2}-2$.
