ABSTRACT
The intuitive idea of a limit is quite old. In ancient Greece, the so-called method of exhaustion was used by Archimedes, around 225 BC, to calculate the area under a parabola. In the 17th century, Newton and Leibniz based much of the calculus they developed on the idea of taking limits. In spite of the success that calculus brought to the natural sciences, it also drew heavy criticism due to the use of infinitesimals (infinitely small numbers). It was not until 1821, when Cauchy published Cours d’analyse, probably the most influential textbook in the history of analysis, that calculus achieved the rigor that is quite close to modern standards.
