  Denoting by $\mathcal{E}\subseteq \R^2$ the set of the pairs
$(\lambda_1(\Omega),\lambda_2(\Omega))$ for all the open sets
$\Omega\subseteq\R^N$ with unit measure, and by $\Theta\subseteq\R^N$ the union
of two disjoint balls of half measure, we give an elementary proof of the fact
that $\partial\E$ has horizontal tangent at its lowest point
$(\lambda_1(\Theta),\lambda_2(\Theta))$.
