Fermat, Roberval and Desargues took exception in their various ways to the methods employed in the geometry, and to the demonstrations of the laws of refraction given in the Dioptrics and Meteors.
The dispute on the latter point between Fermat and Descartes was continued, even after the philosopher's death, as late as 1662.
In another question connected with this, the problem of drawing tangents to any curve, Descartes was drawn into a controversy with Pierre (de) Fermat (1601-1663), Gilles Persone de Roberval (1602-1675), and Girard Desargues (1593-1661).
Fermat and Descartes agreed in regarding the tangent to a curve as a secant of that curve with the two points of intersection coinciding, while Roberval regarded it as the direction of the composite movement by which the curve can be described.
It was really cute to see that the theorem, first referred to in Fermat 's notebook in 1637 (!
How would you define fermat? Add your definition here.