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.
is infinitesimal, then one sets Similarly, where the higher-order term du dv is discarded in accordance with the TLH.
A 2012 study argues that Leibniz's TLH was a precursor of the standard part function over the hyperreals.
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