The Doctrine of Chances is a book on probability theory by 18th-century French mathematician Abraham de Moivre, published in 1733. De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Protestants. The book's title came to be synonymous with probability theory, and accordingly the phrase was used in Thomas Bayes' famous posthumous paper An Essay Toward Solving a Problem in the Doctrine of Chances, wherein a version of Bayes' theorem was first introduced.
The second edition of de Moivre's book introduced the concept of normal distributions as approximations to binomial distributions. In effect de Moivre proved a weak version of the central limit theorem. Sometimes his result is called the theorem of de Moivre-Laplace.