|
|
| Line 1: |
Line 1: |
| 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.
| |
| | author1-link = Henk J. M. Bos
| |
| | arxiv =
| |
| | doi = 10.1007/BF00327456
| |
| | issue =
| |
| | journal = [[Archive for History of Exact Sciences]]
| |
| | pages = 1–90
| |
| | title = Differentials, higher-order differentials and the derivative in the Leibnizian calculus
| |
| | volume = 14
| |
| | year = 1974}}</ref> Thus, if <math>a</math> is finite and <math>dx</math> is infinitesimal, then one sets
| |
| :<math>a+dx=a</math>. | |
| Similarly,
| |
| :<math>u\,dv+v\,du+du\,dv=u\,dv+v\,du,</math>
| |
| 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
| |
| | last1 = Katz | first1 = Mikhail
| |
| | author1-link = Mikhail Katz
| |
| | last2 = Sherry | first2 = David
| |
| | author2-link =
| |
| | arxiv = 1205.0174
| |
| | doi = 10.1007/s10670-012-9370-y
| |
| | issue =
| |
| | journal = [[Erkenntnis]]
| |
| | pages =
| |
| | title = Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond
| |
| | volume =
| |
| | year = 2012}}</ref>
| |
| | |
| ==See also==
| |
| *[[Law of Continuity]]
| |
| *[[Adequality]]
| |
| | |
| == References ==
| |
| {{reflist}}
| |
| | |
| | |
| {{Gottfried Wilhelm Leibniz}}
| |
| {{Infinitesimals}}
| |
| | |
| [[Category:History of calculus]]
| |
| [[Category:Gottfried Leibniz]]
| |
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.