In Part Three, Diamond attempts to describe how societies that got agriculture first used that advantage to also get "guns, germs, and steel." In other words, he describes how the development of agriculture led to the development of technology and of infectious diseases. He also links agriculture to the development of centralized governments. All of these things allowed such societies to dominate other societies.
Diamond advances his argument by making these connections. He shows how the presence of livestock in human communities led to the evolution of infectious diseases. He shows how agriculture led to larger populations and, in turn, to technology. He shows how these larger populations led to the need for centralized government.
Diamond advances his argument, then, by showing how the development of agriculture leads to the development of the more proximate causes of European dominance.