Farkas proved his famous result (which, nowadays, is fundamental in optimization theory) in 1902 and called it *Grundsatz der einfachen Ungleichung* which may be translated as *fundamental theorem of simple inequalities* (where simple means linear, I know that *Grundsatz* can also be translated as *principle*, but reading Farkas, I strongly believe that fundamental theorem fits better).


*Question.* Who was the first to call his fundamental theorem the **Farkas' lemma**?




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I have edited the question because of the comments which concern the former formulation of a *relegation*.



Who called Farkas' fundamental theorem a lemma?
This is the earliest reference I have located:


[Minkowski-Farkas Lemma in Banach Spaces](https://cowles.yale.edu/sites/default/files/files/pub/cdp/m-0416.pdf), L. Hurwicz (1952).


The same result was also referred to as the Minkowski-Farkas-Weyl theorem in the 1950's, for example in


[The strong Minkowski-Farkas-Weyl theorem for vector spaces over ordered fields](https://pubmed.ncbi.nlm.nih.gov/16590290/), A. Charnes and W.W. Cooper (1958).


The three authors are associated with this result in view of the following contributions:


* H. Minkowski, *Geometrie der Zahlen* (Leipzig, 1896).
* J. Farkas, *Über die Theorie der einfachen Ungleichungen*, Journal für die reine und angewandte Mathematik, **124**, 1-27 (1902).
* H. Weyl, *Elementare Theorie der konvexen Polyeder*, Comm. Helvet., **7**, 290-306 (1935).


