De Moivre on the Law of Normal Probability

Abraham de Moivre (1667-1754) left France at the revocation of the Edict of Nantes and spent the rest of his life in London. where he solved problems for wealthy patrons and did private tutoring in mathematics. He is best known for his work on trigonometry, probability. and annuities. On November 12, 1733 he presented privately to some friends a brief paper of seven pages entitled “Approximatio ad Summam Terminorum Binomii a + b\n in Seriem expansi.” Only two copies of this are known to be extant. His own translation, with some additions, was included in the second edition (1738) of The Doctrine of Chances, pages 235–243. This paper gave the first statement of the formula for the “normal curve,” the first method of finding the probability of the occurrence of an error of a given size when that error is expressed in terms of the variability of the distribution as a unit, and the first recognition of that value later termed the probable error. It shows, also, that before Stirling, De Molvre had been approaching a solution of the value of factorial n.