2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71578We generalize the classical Terracini's Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the $d$-Veronese embedding of the projective 3-space.Algebraic Geometry14N05text