Abstract

The mathematical content of Leibniz's analysis situs has not been well understood. I characterize Leibniz's mathematical achievement by comparing analysis situs to the methods favored by seventeenth century geometers and to the nineteenth century Erlangen Program. I show that while Leibniz has the concept of transformation he has not isolated the concept of topological transformation. Nor does he have the Erlangen Program conception of geometry as the study of invariants of transformation groups. I also discuss the role of analysis situs in Leibniz's empirical methodology; in particular, I point to the use of transformations to determine primitives for mechanical explanation of natural phenomena