Transcendental law of homogeneity explained

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. Thus, if

a is finite and dx is infinitesimal, then one setsa + dx = a.

Similarly,

udv + vdu + dudv = udv + vdu,

where the higher-order term du dv 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.

See also

• Law of continuity
• Adequality

Notes and References

1. Leibniz Mathematische Schriften, (1863), edited by C. I. Gerhardt, volume V, pages 377–382)