In the eighteenth century calculus was a formidable and somewhat mysterious machine. Euler summed divergent series and drew correct results from them; Lagrange tried to base everything on power series; books spoke of “infinitely small” quantities that were zero when convenient and non-zero when not. It worked, but nobody could explain exactly why. The Cours d’analyse In 1821 Cauchy published the Cours d’analyse de l’École royale polytechnique, with the lessons he gave to future engineers. In the preface he announced his intention of giving analysis “all the rigour that is demanded in geometry”. Everything begins with a definition: