The Doctrine of Chances: or, A Method of Calculating the Probabilities of Events in Play. The third edition, Fuller, Clearer, and more Correct than the Former.

London: printed for A. Millar,, 1756. Bound for the Earl of Abergavenny Third and fullest edition of de Moivre's important work on the theory of probability, including his final, improved version of his Annuities upon Lives. In the Doctrine, first published in 1718, de Moivre made an early and important contribution to the calculus of games of chance and probability theory, setting out "a series of algebraic and analytic tools for the theory of probability... which foreshadowed Boolean algebra" (ODNB) and other concepts. His introduction contains an overview of main concepts such as probability, conditional probability, expectation, dependent and independent events, the multiplication rule, and the binomial distribution. The book is dedicated to Sir Isaac Newton, whose priority in the dispute between Newton and Leibniz over the development of infinitesimal calculus de Moivre had defended. The work on annuities, first published in 1725, was equally pioneering, and influenced Lagrange and Laplace. The binding was executed for George Neville, Earl of Abergavenny (1727-85), with his badge of a Tudor rose and a portcullis, each surmounted by an Earl's coronet, as supralibros and on the spine labels (see Davenport, English Heraldic Book-Stamps, p. 303). Quarto (290 x 223 mm). Later 18th-century sprinkled calf, neatly rebacked and recornered with original spine laid down, green and black labels, gilt in compartments, covers with narrow Greek-key gilt border, marbled endpapers. Engraved medallion portrait of author to title page, reproducing Dassier's 1741 medal. Title with early signature "F. Foljambe", and note "examination prize St. John. Coll Camb". Front joint peeling a little, binding firm, light soiling and spotting to sig. S else contents clean and fresh. An excellent copy. ESTC T33063; Kress 5546.