In a paper of 1921, C. Segre characterized the Veronese surface as the only non-developable surface in P⁵ such that all its curves are principal. This results was later extended by Terracini in a paper of 1942, in which he gave a similar differential-geometric characterization of 1-defective higher dimensional varieties. I'll try to explain how these results can be interpreted as a sort of infinitesimal Terracini lemma, and how they can be extended to higher defective varieties.