At the age of nineteen he communicated to Leonhard Euler his idea of a general method of dealing with "**isoperimetrical**" problems, known later as the Calculus of Variations.

The calculus of variations lay undeveloped in Euler's mode of treating **isoperimetrical** problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the analytical investigation of the planetary movements.

In 1696 he proposed the famous problem of **isoperimetrical** figures, and offered a reward for its solution.

The family quarrel about the problem of **isoperimetrical** figures above mentioned began about this time.