Date of Award
Doctor of Philosophy
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 (contrary to what is often claimed) 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.
Solomon, Graham Timothy, "Leibniz's Analysis Situs In Mathematical Context" (1990). Digitized Theses. 1872.