  We show that a convex pyramid in R^n with apex at 0 can be brought to the
first quadrant by a finite sequence of monomial blowing-ups if and only if its
intersection with the opposite of the first quadrant is 0. The proof is
non-trivially derived from the theorem of Farkas-Minkowski. Then, we apply this
theorem to show how the Newton diagrams of the roots of any Weierstrass
polynomial are contained in a pyramid of this type. Finally, if n = 2, this
fact is equivalent to the Jung-Abhyankar theorem.
