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MOIVRE, Abraham de (1667-1754). The Doctrine of Chances: or, A Method of Calculating the Probability of Events in Play. London: W. Pearson, for the Author, 1718.
Half-sheet 4o printed work-and-turn (251 x 191 mm). Collation: s2 (1 title, +_ dedication to Newton), A2 a-c2 (preface, without c2 presumably blank); B-Z2 Aa-Yy2 (text). Engraved title-page vignette, engraved head- and tail-pieces. Contemporary English panelled calf (rebacked, some edgewear).
Provenance: James Stirling (1692-1770), mathematician who developed "Stirling's formula" from Moivre's investigations (his signature and inscription on the title-page: "Ja: Stirling Ex dono Authoris 1727," mathematical notation on one margin, and notation on final leaf verso [see below]).
FIRST EDITION. PRESENTATION COPY TO THE MATHEMATICIAN JAMES STIRLING, AND CONTAINING MOIVRE'S MANUSCRIPT LISTING OF ERRATA AT END. De Moivre left France after the revocation of the Edict of Nantes in 1685 and spent the remainder of his life in London. He was among the intimate friends of Newton, to whom this book is dedicated. The Doctrine of Chances was Moivre's first book and was based on "De mensura sortis," a short memoir which was published in the Philosophical transactions in 1711. It was essentially a gambler's manual "giving a systematic presentation of the arithmetic principles upon which are based the solution of problems concerning the advantage of players and the size of wager which may be lain in a wide variety of games of chance" (Walker).
This copy was presented to James Stirling, author of Methodus differentialis (1730), which contains "Stirling's formula," based on Moivre's investigations into the approximate behavior for large n of the terms of the symmetrical binomial (1 + 1)n, in which Moivre found the constant A = 2-21/125 = 2.168. Moivre's approximation was published in Miscellanea analytica in 1730 (see lot 679). "It is clear from De Moivre's account that he had the practical equivalent to 'Stirling's formula' before Stirling turned to this problem and that it was in response to De Moivre's investigation that Stirling took up this question" (Stigler, p. 73). Stirling developed his more elegant "formula" published as Methodus Differentialis (1730). The final verso at end CONTAINS 22 LINES OF MANUSCRIPT ERRATA IN DE MOIVRE'S HAND. A note below in Stirling's hand reads: "These Errata are written by the Author." AN IMPORTANT ASSOCIATION COPY. Babson/Newton 181; Stigler, pp. 70-88; Walker, pp. 12-13; Norman 1529.
Half-sheet 4
Provenance: James Stirling (1692-1770), mathematician who developed "Stirling's formula" from Moivre's investigations (his signature and inscription on the title-page: "Ja: Stirling Ex dono Authoris 1727," mathematical notation on one margin, and notation on final leaf verso [see below]).
FIRST EDITION. PRESENTATION COPY TO THE MATHEMATICIAN JAMES STIRLING, AND CONTAINING MOIVRE'S MANUSCRIPT LISTING OF ERRATA AT END. De Moivre left France after the revocation of the Edict of Nantes in 1685 and spent the remainder of his life in London. He was among the intimate friends of Newton, to whom this book is dedicated. The Doctrine of Chances was Moivre's first book and was based on "De mensura sortis," a short memoir which was published in the Philosophical transactions in 1711. It was essentially a gambler's manual "giving a systematic presentation of the arithmetic principles upon which are based the solution of problems concerning the advantage of players and the size of wager which may be lain in a wide variety of games of chance" (Walker).
This copy was presented to James Stirling, author of Methodus differentialis (1730), which contains "Stirling's formula," based on Moivre's investigations into the approximate behavior for large n of the terms of the symmetrical binomial (1 + 1)