Heuristic principle enunciated by Gottfried Wilhelm Leibniz
In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by
Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali.[1]Henk J. M. Bos describes it as the principle to the effect that in a sum involving
infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded.[2] Thus, if is finite and is infinitesimal, then one sets
Similarly,
where the higher-order term dudv is discarded in accordance with the TLH. A recent study argues that Leibniz's TLH was a precursor of the
standard part function over the
hyperreals.[3]