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The history of the Euler-Lagrange Equation in Calculus of ..

Did Euler and Lagrange really come up with the Euler Equation in the calculus of variations. I have seen later work by Weierstrass, Zermeerlo and others that indicates that the Euler- equation was not known by them in its present form! I guess I am wrong but tell me!
All the best
Karl-Gustaf Lofgren
Professor of Economics
Umeå University, Umeå, Sweden.


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