Fermat, Pierre (1601-1665).    

    Fermat was a famous French lawyer. He produced great contributions in the field of Calculus. He and the French philosopher, Rene Descartes (1596-1650) are considered the inventors of analytic geometry. It was Fermat and Descartes who introduced the point of view that is characteristic of analytic geometry. They considered curves defined by equations as well as by geometric properties. Moreover, they made extensive use of the close association between algebra of equations and the geometry of the curves.

    Fermat and Descartes used only what corresponds to the positive half of the modern horizontal coordinate axis and did not use an explicit vertical axis. To plot a point corresponding to positive solutions of an equation in two unknowns A and E, Fermat measured the distance A along a horizontal line from a fixed point. The fixed point corresponded to the origin in a modern coordinate plane. He then measured the distance E along a line at a fixed angle, but not necessarily a right angle, to the horizontal line.

Fermat used infinitesimals to find the tangent lines to curves as early as 1636.