Mathematical Treasure: Abraham De Moivre's Doctrine of Chances

 Written by Abraham de Moivre (1667–1754), The Doctrine of Chances: A Method of Calculating the Probabilities of Events in Play was an early work in probability theory. It first appeared in Latin in 1711, with the first English edition published in 1718. Below is the title page of the 1738 English 2nd edition, “fuller, clearer, and more correct than the first.”

Next is an image of page 1 with the statement, “Wherefore, if we constitute a Fraction whereof the Numerator be the number of Chances whereby an Event happen, and the Denominator the number of all Chances whereby it may either happen or fail, that Fraction will be a proper designation of the Probability of happening.”

The next two images show some sample problems from the book. First is the solution to the problem “to find the Probability of throwing an Ace in two throws” on page 9, followed by a problem about three “Gamesters” on page 43.

Page 211 below contains a notation different from what is used today for \( (a + b)^2 \) and then the start of a section about annuities.

Images from a copy of the 1756 4th edition of The Doctrine of Chances, in which the normal distribution first appears, can also be found in Convergence.

A complete digital scan of the 1738 2nd edition of The Doctrine of Chances is available in the Linda Hall Library Digital Collections. The call number is QA273 .M63 1738.

Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The Linda Hall Library makes available all existing digital images from its collection that are in the public domain to be used for any purpose under the terms of a Creative Commons License CC by 4.0. The Library’s preferred credit line for all use is: “Courtesy of The Linda Hall Library of Science, Engineering & Technology.”

Index to Mathematical Treasures