Annuities on Lives: with Several Tables, Exhibiting at One View, the Values of Lives, for Different Rates in Interest

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by Abraham de Moivre

Annuities on Lives
George Wythe bookplate.jpg
Title not held by The Wolf Law Library
at the College of William & Mary.
Author Abraham de Moivre
Published London:
Date 1752
Edition 4th
Volumes volume set

The French mathematician Abraham de Moivre (1667-1754) was born in Vitry-le-François, Champagne to a Huguenot family.[1] He "pioneered the development of analytical trigonometry - for which he formulated his theorem regarding complex numbers - [and] devised a means of research into the theory of probability."[2] As an 18-year-old, he was imprisoned for his faith after King Louis XIV revoked the Edict of Nantes which had given Protestants the right to worship without persecution. He spent a year in prison and fled to England upon his release.

In London, de Moivre became a close friend of Sir Isaac Newton and Edmund Halley. In 1697, de Moivre was elected to the Royal Society and in 1712 was appointed to settle the bitter dispute between Newton and Gottfried Leibniz over the priority for the systematization of calculus. Although a talented mathematician, de Moivre spent the majority of life in relative poverty, prevented by his French nationality from obtaining a position at an English university.[3] He died in London on November 27, 1754 at the age of 87.

De Moivre first published Annuities on Lives, a work primarily concerned with mortality statistics, in 1725. In it, de Moivre "laid the mathematical foundations of the theory of annuities." He "devised formulae based on a hypothesized law of mortality and constant rates of interest on money."[4] It is considered a valuable contribution to the field particularly because of de Moivre's

derivation of formulas for annuities based on a postulated law of mortality and constant rates of interest on money. Here one finds the treatment of joint annuities on several lives, the inheritance of annuities, problems about the fair division of the costs of a tontine, and other contracts in which both age and interest on capital are relevant.[5]

Subsequent editions were published in 1743, 1750, 1752 and 1756.

Evidence for Inclusion in Wythe's Library

Wythe references "the accurate Demoivre" in his decision for the case of Aylett v. Aylett:

In adjusting the proportion, which a tenent for life ought to have of the purchase money, for which an estate of inheritance should be sold, would a court, at this day, regard the rules observed in such cases by the courts formerly, or have recourse to the problems and tables invented and formed for that purpose by the accurate Demoivre, Halley or Price?[6]

We do not know that he definitely owned one of de Moivre's works, nor which one it might have been. The Brown Bibliography[7] lists the both the 4th edition (1752) of Annuities on Lives and the 1st edition The Doctrine of Chances, or A Method of Calculating the Probability of Events in Play published in 1718. Brown notes:

Wythe's comment above also refers to three books on the subject of which this title and the Price are recorded in Jefferson's library. The Halley title is unknown at this time. While Wythe owned the Price, whether he owned, or only used, the de Moivre is unknown.
Also Jefferson owned the second de Moivre title in his library which he sold to the Library of Congress in 1815: #32. De Moivre's Doctrine of chances, 4to. However, even though Jefferson owned the second book, the way Wythe cites the three books on prices is unclear as to which of the two [de Moivre] titles he is citing.[8]

The Wolf Law Library has yet to procure either title by de Moivre.

See also


  1. “Moivre, Abraham De (1667-1754)”, The Hutchinson Dictionary of Scientific Biography (Abington, United Kingdom: Helicon, 2014), accessed April 14, 2015.
  2. Ibid.
  3. Eli Maor, Trigonometric Delights (Princeton: Princeton University Press, 2011), 80.
  4. “Moivre, Abraham De (1667-1754)”.
  5. “Moivre, Abraham De”, in, accessed June 16, 2023.
  6. George Wythe, Decisions of Cases in Virginia, By the High Court of Chancery, With Remarks Upon Decrees by the Court of Appeals, Reversing Some of Those Decisions (Richmond, Virginia: J. W. Randolph, 1852), 228.
  7. Bennie Brown, "The Library of George Wythe of Williamsburg and Richmond," (unpublished manuscript, May, 2012) Microsoft Word file. Earlier edition available at:
  8. Ibid.

External Links

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