This article suggests that 16th‐century sources describing astronomical instruments may be analyzed in terms of ‘geometrical tools’, that is discrete arrangements of lines and curves that solve particular problems. Geometrical tools provided a means for innovation. By playing, literally, with such tools, mathematicians could invent new instruments or add new functions to existing instruments. For a case study of this process, I shall consider the rectangular astrolabe, first proposed in 1515 by Johannes Stabius and reconfigured in several other versions over the course of the 16th century. Geometrical tools, I conclude, are revealed in diagrams found in the sources, not in the accompanying texts.