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| 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'' (see C. I. Gerhardt GM volume V, pages 377-382). [[Henk J. M. Bos]] describes it as the principle to the effect that in a sum involving [[infinitesimal]]s of different orders, only the lowest-order term must be retained, and the remainder discarded.<ref>{{citation
| | My name's Amparo Vosburg but everybody calls me Amparo. I'm from Poland. I'm studying at the university (2nd year) and I play the Lap Steel Guitar for 8 years. Usually I choose songs from the famous films :D. <br>I have two sister. I like Bird watching, watching movies and Baton twirling. |
| | last1 = Bos | first1 = Henk J. M.
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| | author1-link = Henk J. M. Bos
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| | arxiv =
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| | doi = 10.1007/BF00327456
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| | issue =
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| | journal = [[Archive for History of Exact Sciences]]
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| | pages = 1–90
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| | title = Differentials, higher-order differentials and the derivative in the Leibnizian calculus
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| | volume = 14
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| | year = 1974}}</ref> Thus, if <math>a</math> is finite and <math>dx</math> is infinitesimal, then one sets
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| :<math>a+dx=a</math>. | |
| Similarly,
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| :<math>u\,dv+v\,du+du\,dv=u\,dv+v\,du,</math>
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| 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 [[hyperreal]]s.<ref>{{citation
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| | last1 = Katz | first1 = Mikhail
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| | author1-link = Mikhail Katz
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| | last2 = Sherry | first2 = David
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| | author2-link =
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| | arxiv = 1205.0174
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| | doi = 10.1007/s10670-012-9370-y
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| | issue =
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| | journal = [[Erkenntnis]]
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| | pages =
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| | title = Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond
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| | volume =
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| | year = 2012}}</ref>
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| ==See also==
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| *[[Law of Continuity]]
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| *[[Adequality]]
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| == References ==
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| {{reflist}}
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| {{Gottfried Wilhelm Leibniz}}
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| {{Infinitesimals}}
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| [[Category:History of calculus]]
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| [[Category:Gottfried Leibniz]]
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My name's Amparo Vosburg but everybody calls me Amparo. I'm from Poland. I'm studying at the university (2nd year) and I play the Lap Steel Guitar for 8 years. Usually I choose songs from the famous films :D.
I have two sister. I like Bird watching, watching movies and Baton twirling.