Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard 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 newton
In 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.
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