The Doctrine of Chances

For the rule of evidence in law, see doctrine of chances.

The Doctrine of Chances was the first textbook on probability theory, written by 18th-century French mathematician Abraham de Moivre and first published in 1718.^[1] De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. 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 Towards Solving a Problem in the Doctrine of Chances, wherein a version of Bayes' theorem was first introduced.

The Doctrine of Chances

Front page of first edition
Author	Abraham de Moivre
Language	English
Genre	Mathematics
Publication date	1718

Editions

The full title of the first edition was The Doctrine of Chances: or, A Method of Calculating the Probability of Events in Play. It was published in 1718, by W. Pearson, and ran for 175 pages. Published in 1738 by Woodfall and running for 258 pages, 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 special case of the central limit theorem. Sometimes his result is called the theorem of de Moivre–Laplace. A third edition was published posthumously in 1756 by A. Millar and ran for 348 pages.^[2] Additional material in the third edition included an application of probability theory to actuarial science in the calculation of annuities.^[1]