 He then supposed there was a means of saying what the distance was infinitesimally, by generalising the formula for \(ds\) from 2 to \(n\) variables. (He even allowed that entirely different formulae be used, but we shall not describe that part of his theory, which lay fallow for many years). Next, he generalized the intrinsic property of curvature to higher dimensions; essentially, the \(n\)-dimensional object has lots of 2-dimensional surfaces to which the Gaussian theory applies, so a notion of curvature of a \(n\)-dimensional object at a point can be derived from a consideration of the 2-dimensional surfaces that pass through the point.