This book offers a new interpretation of Hermann von Helmholtz s work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz s Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature completely comprehensible, which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question by drawing on the theory...