Transcendental law of homogeneity
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 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.[3]
See also
- Law of continuity
- Adequality
References
- ^ Leibniz Mathematische Schriften, (1863), edited by C. I. Gerhardt, volume V, pages 377–382)
- ^ Bos, Henk J. M. (1974), "Differentials, higher-order differentials and the derivative in the Leibnizian calculus", Archive for History of Exact Sciences, 14: 1–90, doi:10.1007/BF00327456, S2CID 120779114
- ^ Katz, Mikhail; Sherry, David (2012), "Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond", Erkenntnis, 78 (3): 571–625, arXiv:1205.0174, doi:10.1007/s10670-012-9370-y, S2CID 254471766
- v
- t
- e
philosophy
- Alternating series test
- Best of all possible worlds
- Calculus controversy
- Calculus ratiocinator
- Characteristica universalis
- Compossibility
- Difference
- Dynamism
- Identity of indiscernibles
- Individuation
- Law of continuity
- Leibniz wheel
- Leibniz's gap
- Leibniz's notation
- Lingua generalis
- Mathesis universalis
- Pre-established harmony
- Plenitude
- Sufficient reason
- Salva veritate
- Theodicy
- Transcendental law of homogeneity
- Rationalism
- Universal science
- Vis viva
- Well-founded phenomenon
- De Arte Combinatoria (1666)
- Discourse on Metaphysics (1686)
- New Essays on Human Understanding (1704)
- Théodicée (1710)
- Monadology (1714)
- Leibniz–Clarke correspondence (1715–1716)
This article about the history of mathematics is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e