MOIVRE, ABRAHAM de (1667–1754), mathematician, was the son of a surgeon at Vitry in Champagne, where he was born on 26 May 1667. His education was begun by the Christian Brothers, but he was sent at the age of eleven to the protestant university of Sedan, and was there during four years trained by Du Rondel in Greek. A year's study of logic at Saumur followed; then, after a course of physics in 1684 at the College d'Harcourt in Paris, and a trip to Burgundy, he devoted himself to mathematics under Ozanam in Paris, where his parents were then settled. The revocation of the edict of Nantes in 1685, however, led to his temporary seclusion in the priory of St. Martin, and on his release, 27 April 1688, he repaired to London. A call at the Earl of Devonshire's, with a recommendatory letter, chanced to introduce him to Newton's 'Principia.' He procured the book, divided it into separate leaves for convenience of transport in his pocket, and eagerly studied it on the peregrinations intervening between the lessons and lectures by which he earned a subsistence. In 1692 he became known to Halley, and shortly afterwards to Newton and Nicolas Faccio [q. v.] His first communication to the Royal Society was in March 1695, on some points connected with the 'Method of Fluxions' (Phil. Trans. xix. 52), and he was elected a fellow in 1697. His 'Animadversiones in D. Georgii Cheynæi Tractatum de Fluxionum Methodo inversa,' published in 1704, procured him the notice of Bernoulli. The rejoinder of George Cheyne [q. v.] was purely personal, and De Moivre left it unnoticed.
De Moivre's essay, 'De Mensura Sortis,' presented to the Royal Society in 1711 (ib. xxvii. 213), originated in a suggestion by Francis Robartes, later earl of Radnor, that he should deal on broader principles with the problems treated by Montmort in his 'Essai d' Analyse sur les Jeux de Hasard,' Paris, 1708. The resulting controversy with this author terminated amicably. De Moivre pursued the investigation in his 'Doctrine of Chances,' published in 1718, in the preface to which he indicated the nature of 'recurring series.' He introduced besides the principle that the probability of a compound event is the product of the probabilities of the simple events composing it, and the whole subject, Todhunter remarks,' owes more to him than to any other mathematician, with the single exception of Laplace (History of the Theory of Probability, p. 193). The first edition of the work was dedicated to Sir Isaac Newton; subsequent enlarged editions, dedicated to Lord Carpenter [see Carpenter, George, Lord Carpenter], appeared in 1738 and 1756.
De Moivre came next to Halley as a founder of a science of life-contingencies. His 'Annuities upon Lives,' first published in 1725, with a dedication to the Earl of Macclesfield [see Parker, Thomas, Earl Of Macclesfield], was reissued, corrected and improved, in 1743, 1750, 1752, and 1756, and in an Italian version by Fontana, at Milan, in 1776. The merit and usefulness of his celebrated hypothesis, that 'the decrements of life are in arithmetical progression,' were maintained by Francis Baily [q. v.] in chap. ix. of his 'Doctrine of Life-Annuities,' 1813, against the strictures of Price and De Morgan. The appearance of Simpson's 'Doctrine of Annuities' in 1742 gave occasion to a groundless imputation of plagiarism made by De Moivre in the second edition of his work; it was, however, successfully refuted, and silently omitted from subsequent editions. De Moivre's most important work, 'Miscellanea Analytica,' London, 1730, was his last. He demonstrated in it his method of recurring series, created 'imaginary trigonometry,' through the invention of the theorem known by his name, and generalised Cotes's 'Theorem on the Property of the Circle' (p. 17). Naude's presentation of the book to the Berlin Academy of Sciences procured the election by acclamation of its author as a member of that body on 23 Aug. 1735.
Leibnitz, who made De Moivre's acquaintance in London, vainly endeavoured to secure for him a professorial position in Germany; and his foreign origin similarly barred the way to his promotion in England. So he continued all his life to support himself by teaching, and answering questions on the chances of play and the values of annuities. Bernoulli wrote of him to Leibnitz in 1710 as struggling with want and misery; yet he was one of the commissioners appointed by the Royal Society in 1712 to arbitrate on the claims of Newton and Leibnitz to the invention of the infinitesimal calculus. He was the intimate friend of Newton, who used to fetch him each evening, for philosophical discourse at his own house, from the coffee-house in St. Martin's Lane (probably Slaughter's), where he spent most of his time (Brewster, Life of Newton, i. 248); and Newton's favourite method in his old age of dealing with questioners about the 'Principia' was to refer them to
