Exercise 4, § 2

Let C be a convex cone with vertex 0 in a vector space E; if $(x_i)_{1 \leq i \leq n}$ is a finite family of points of C such that $\sum_{i=1}^n \lambda_i x_i = 0$ for a family of numbers $\lambda_i > 0$, then C contains the vector subspace of E generated by the $x_i$.