Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding of this mechanism, we approach a technology as a body of knowledge consisting of interlinked inventions. Technological cumulativeness can then be understood as the extent to which inventions build on other inventions within that same body of knowledge. The cumulativeness of a technology is therefore characterized by the structure of its knowledge base, which is different from, but closely related to, the size of its knowledge base. We analytically derive equations describing the relation between the cumulativeness and the size of the knowledge base. In addition, we empirically test our ideas for a number of selected technologies, using patent data. Our results suggest that cumulativeness increases proportionally with the size of the knowledge base, at a rate that varies considerably across technologies. Furthermore, this rate is inversely related to the rate of invention over time. This suggests that cumulativeness increases relatively slowly in rapidly growing technologies. In sum, the presented approach allows for an in-depth, systematic analysis of cumulativeness variations across technologies and the knowledge dynamics underlying technology development.