  In this paper we prove an infinitesimal version of the classical Terracini
Lemma for 3--secant planes to a variety. Precisely we prove that if
  $X\subseteq \PP^r$ is an irreducible, non--degenerate, projective complex
variety of dimension $n$ with $r\geq 3n+2$, such that the variety of osculating
planes to curves in $X$ has the expected dimension $3n$ and for every
$0$--dimensional, curvilinear scheme $\gamma$ of length 3 contained in $X$ the
family of hyperplanes sections of $X$ which are singular along $\gamma$ has
dimension larger that $r-3(n+1)$, then $X$ is $2$--secant defective.
