Fermat developed his method(s) of adequality in late 1620s. Fermat's manuscript was deposited in the library of d'Espagnet at Bordeaux. One of the methods involved the double-root idea for finding tangent lines, minima/maxima, and other applications. The method was communicated to Mercenne's circle in Paris around 1637. Jean Itard mentioned in his article from the 1970s that Fermat's method was superior to that of Descartes because the latter used normal directions to solve the same type of problems, whereas in truth the problems are affine in nature and should not involve finding the normal direction. Descartes' methods were therefore unnecessarily complicated. Conifold's answer is inaccurate on this point.

Fermat developed his method(s) of adequality in late 1620s. Fermat's manuscript was deposited in the library of d'Espagnet at Bordeaux. One of the methods involved the double-root idea for finding tangent lines, minima/maxima, and other applications. The method was communicated to Mercenne's circle in Paris around 1637. Jean Itard mentioned in his article from the 1970s that Fermat's method was superior to that of Descartes because the latter used normal directions to solve the same type of problems, whereas in truth the problems are affine in nature and should not involve finding the normal direction. Descartes' methods were therefore unnecessarily complicated. Conifold's answer is inaccurate on this point.