‎MOIVRE (A. De)‎
‎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, Millar, 1756, un volume grand in 4 (24 cm x 30) relié en pleine basane (reliure de l'époque), (restaurations maladroites aux coiffes), (2), 11pp., (1pp.), 348pp.‎

Reference : 3725

‎---- Troisième édition REVUE, AUGMENTEE ET CORRIGEE ---- EX-LIBRIS C.V.L. CHARLIER, auteur d'un ouvrage sur le calcul des probabilités ---- EXEMPLAIRE GRAND DE MARGES ---- "De Moivre's work on the theory of probability surpasses anything done by any other mathematician except Laplace. His principal contributions are his investigations respecting the duration of play, his theory of recurring series and his extension of the value of Bernouillis theorem by the aid of Sterling's theorem". (Cajori) ---- "The first edition of this work contains 175 pages, the second edition 258 pages and the third 348 pages. The following list will indicate the parts which are new in the third edition : the Remark pages 30/33 and pages 48 & 49, the greater part of the second Corollary pages 64/66, the Examples page 88 ; the Scholium page 95, the Remark page 149 and pages 151/159, the fourth Corollary page 162, the second Corollary pages 176/179, the note at the foot of page 187, the Remark pages 251/254. The part on life annuities is very much changed. The Introduction is very much fuller than the corresponding part of the first edition. In his third edition De Moivre draws attention to the convenience of approximating to a fraction with a large numerator and denominator by continued fractions, which he calls "the Method proposed by Dr Wallis, Huygens and others". He gives the rule for the formation of the successive convergents... This third edition contains 74 problems exclusive of those relating to life annuities (in the first edition there were 53 problems)... The pages 220/229 contains one of De Moivre's most valuable contributions to mathematics, namely that of Recurring series... Pages 261/328 are devoted to Annuities on lives ; an Appendix finishes the book, occupying pages 329/348 : this also relates principally to annuities, but it contains a few notes on the subject of probability...". (Todhunter). A very full account of the above third edition will be found in Todhunter's History of the theory of probability"**3725/ARM3‎