Cite a book in general and then a chapter in particular
As Najib Idrissi commented, I have also similar approach in my field of Computer Science.

In one of my paper, I had to cite the book twice in the following way.

"The application domains have expanded in various horizons considering the applicability of the this approach and has led the community to look for problems in .... \cite{FullBook}. One of the prinicipal advantage of using such an approach lies in its computational complexity which has been found to be O(n^2).\cite[Chapter 2, Proof:3.2]{Book}"