The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived numer- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling’s series to series solution of differential equations, from the Euler–Maclaurin summation formula to the Lagrange inversion theorem, from Laplace’s theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be found unacceptable today, thus, if we look back to the theory of series prior to Cauchy without reconstructing internal motivations and the concep- tual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a ma- gician or diviner rather than the penetrating and complex work of great mathematicians.