2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165299We prove an inequality of the form $γ_n\geq C_n(γ_{n-1})$ giving a lower bound for the Hermite constant $γ_n$ in dimension $n$ in terms of $γ_{n-1}$. Iterating this inequality yields a new proof of the Minkowski-Hlawka bound.24 pages, to appear in Internation Journal of Number TheoryNumber Theory10E05, 10E20text