The reuse of ontologies is critical to their value as a means of knowledge representation. Unfortunately, reuse also still poses a considerable challenge for the ontological community. One reason for this is the lack of a formal definition of reuse. How can we attempt to perform or even assist this sort of ontology design, if we have no clear understanding of what constitutes reuse, and what does not? In this work we aim to remedy this situation by providing a formal definition of the concepts of reuse and reusability. Beyond providing a clear understanding of these concepts, part of the resulting definition is a characterization of the operations of reuse that can be leveraged to determine how a given ontology(s) must be reused to satisfy some specified requirements. This serves not only to provide direction for the task of reuse, but also to assess the implications of reusing an ontology(s), a priori. Collectively, the solutions presented in this paper serve as a major step in improving the current state of reuse.