  In the article "On the linearizability of 3-webs" (Nonlinear analysis 47,
(2001) pp.2643-2654), published in 2001, we studied the linearizability problem
for 3-webs on a 2-dimensional manifold. Four years after the publication of our
article, V.V.Goldberg and V.V.Lychagin in the paper "On linearization of planar
three-webs and Blaschke's conjecture" (C.R.Acad. Sci. Paris, Ser. I. vol. 341.
num 3 (2005)) obtained similar results by a different method and criticized our
article by qualifying the proofs incomplete. However, they obtained false
result on the linearizability of a certain web. We present here the complete
version of our work with computations and explicit formulas, because we deem
that their opinion concerning our work is unjustified.
