 In “On the Facts Underlying Geometry,” Helmholtz investigates a related, but distinct question. He agrees with Riemann that geometry is not possible unless we can compare figures to each other and measure them, and that measurement is not possible unless at least some properties of the figures we are measuring do not change when the figures move. Helmholtz asks, what are the most general axioms of geometry that must hold for such motions, motions preserving the spatial properties of figures, to be possible?