# Who came up with the Euler-Lagrange equation first?

Could someone explain who came up with the specific equation first?

http://en.wikipedia.org/wiki/Euler-Lagrange

makes it sound like Lagrange got it first, in 1755, then sent it to Euler.

but:

http://en.wikipedia.org/wiki/Calculus_of_variations

sort of makes it sound like Euler got it first in the 1730s.

It seems like a straightforward question, but I can't find an answer anywhere. Who came up with the equation, Euler or Lagrange? And what precisely did the other man contribute to get his name on there?

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Jacobi would know.... :-) –  Mariano Suárez-Alvarez Jul 31 '12 at 16:57
Have you seen this? –  Ｊ. Ｍ. Jul 31 '12 at 17:02
This has been asked also here mathoverflow.net/questions/103623/… –  Mariano Suárez-Alvarez Jul 31 '12 at 18:57
some interesting papers I found : Fraser1, Fraser2, Hanc –  Raymond Manzoni Jul 31 '12 at 22:22

Euler's derivation approximated a curve by $N$ points and then let $N$ go to infinity to find extremals. This method was somewhat tedious in its implementation and Euler himself was interested in finding a method that did not rely on any geometry as his method did.