 Leibniz conceived of differentials \(\Dx , \Dy\) as variables ranging over differences. This enabled him to take the important step of regarding the symbol \(\D\) as an operator acting on variables, so paving the way for the iterated application of \(\D \), leading to the higher differentials \(\D\Dx = \D^2 x\), \(\D^3 x = \D\D^2 x\), and in general \(\D^{n+1}x = \D\D^{n}x\). Leibniz supposed that the first-order differentials \(\Dx\), \(\Dy\),…. were incomparably smaller than, or infinitesimal with respect to, the finite quantities \(x\), \(y\),…, and, in general, that an analogous relation obtained between the \((n+1)^{\textrm{th}}\)-order differentials \(\D^{n+1}x\) and the \(n^{\textrm{th}}\)-order differentials \(\D^n x\). He also assumed that the \(n^{\textrm{th}}\) power \((\Dx )^n\) of a first-order differential was of the same order of magnitude as an \(n^{\textrm{th}}\)-order differential \(\D^{n} x\), in the sense that the quotient \(\D^{n} x/(\Dx )^n\) is a finite quantity.