Fermat applied his method of tangents to many difficult problems. The method has the form of the nowstandard method of differential calculus, though it begs entirely the difficult theory of limits .

I had a hint of this method [of fluxions] from Fermat's way of drawing tangents, and by applying it to abstract equations, directly and invertedly, I made it general.
isaac newtonIn mathematics he was greater Than Tycho Brahe, or Erra Pater: For he, by geometric scale, Could take the size of pots of ale; Resolve, by sines and tangents straight, If bread and butter wanted weight; And wisely tell what hour o' th' day The clock doth strike, by algebra.