In solving optimisation problems in function spaces, Euler made extensive use of this `method
of finite differences'. By replacing smooth curves by polygonal lines, he reduced the problem of
finding extrema of a function to the problem of finding extrema of a function of n variables, and
then he obtained exact solutions by passing to the limit as n ! 1. In this sense, functions can
be regarded as `functions of infinitely many variables' (that is, the infinitely many values of x(t)
at different points), and the calculus of variations can be regarded as the corresponding analog of
differential calculus of functions of n real variables.