[SOLVED] Advanced Multivariable Calculus: Constrained Extrema Test

Hello,

I'm reading C.H. Edwards' "Advanced Calculus of Several Variables". I don't understand completely his proof of theorem II.8.9, concerning a "second derivative test" for constrained (Lagrange multiplier) maximum-minimum problems. Specifically, i don't understand the last paragraph of the proof, explaining why the condition on delta can be satisfied. I'd appreciate a more detailed and more formal treatment of this point.

This theorem, in its general form as presented in Edwards, is hard to find in other books. So i've emailed Prof. Edwards, asking him for a clarification of the point stated above, offering in exchange a list of typos and other errors i'd found in the book. But it's been several days now, and i haven't received any answer from him.