Lagrange and Legendre

On 12 August 1755 a 19-year-old, one Ludovico de la Grange Tournier of Turin, wrote Euler a brief letter to which was attached an appendix containing mathematical details of a very beautiful and revolutionary idea (see Lagrange [1755] and Euler [1755]). He saw how to eliminate from Euler’s methods of 1744 the tedium and need for geometrical insight and to reduce the entire process to a quite analytic machine or apparatus, which could turn out the necessary condition of Euler and more, almost automatically. This basic idea of Lagrange ushered in a new epoch in the calculus of variations. Indeed after seeing Lagrange’s work, Euler dropped his own method, espoused that of Lagrange, and renamed the subject the calculus of variations.1