  In this work, we obtain an unexpected geometric characterization of
sphericity of a real-analytic Levi-nondegenerate hypersurface $M\subset\mathbb
C^{2}$. We prove that $M$ is spherical if and only if its Segre\,(-Webster)
varieties satisfy an elementary combinatorial property, identical to a property
of straight lines on the plane and known in Projective Geometry as the {\em
Desargues Theorem}.
