Progressive expansion of the number domain

Over two millenia there have been three important expansions of the number domain. First, about 450 BC, Pythagoreans proved the existence of irrational numbers; their initial goal was to calculate the diagonal of a unit square. Secondly, in the late middle ages, European mathematicians came progressively to admit the possibility of one negative solution among those of linear systems of equations. Thirdly, in 1572, the Italian algebraist Rafael Bombelli used imaginary numbers in order to obtain a real (and positive) root for a particular form of the cubic equation.