Statistical Science

Maty’s Biography of Abraham De Moivre, Translated, Annotated and Augmented

David R. Bellhouse and Christian Genest

Full-text: Open access

Abstract

November 27, 2004, marked the 250th anniversary of the death of Abraham De Moivre, best known in statistical circles for his famous large-sample approximation to the binomial distribution, whose generalization is now referred to as the Central Limit Theorem. De Moivre was one of the great pioneers of classical probability theory. He also made seminal contributions in analytic geometry, complex analysis and the theory of annuities. The first biography of De Moivre, on which almost all subsequent ones have since relied, was written in French by Matthew Maty. It was published in 1755 in the Journal britannique. The authors provide here, for the first time, a complete translation into English of Maty’s biography of De Moivre. New material, much of it taken from modern sources, is given in footnotes, along with numerous annotations designed to provide additional clarity to Maty’s biography for contemporary readers.

Article information

Source
Statist. Sci., Volume 22, Number 1 (2007), 109-136.

Dates
First available in Project Euclid: 1 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1185975640

Digital Object Identifier
doi:10.1214/088342306000000268

Mathematical Reviews number (MathSciNet)
MR2394478

Zentralblatt MATH identifier
1246.01019

Citation

Bellhouse, David R.; Genest, Christian. Maty’s Biography of Abraham De Moivre, Translated, Annotated and Augmented. Statist. Sci. 22 (2007), no. 1, 109--136. doi:10.1214/088342306000000268. https://projecteuclid.org/euclid.ss/1185975640


Export citation

References

  • Agnew, D. C. A. (1871). Protestant Exiles from France in the Reign of Louis XIV, 2nd ed. Reeves and Turner, London.
  • Anonymous (1695). The Royal Academies: Encourag'd by several of the Nobility, and many other very Eminent Persons. A Collection for Improvement of Husbandry and Trade 6 134.
  • Anonymous (1731). A View of the Town: Or, Memoirs of London, 2nd ed. Moore, London.
  • Archibald, R. C. (1926). A rare pamphlet of Moivre and some of his discoveries. Isis 8 671--683.
  • Baker, S. (1756). A Catalogue of the Entire and Valuable Library of Martin Folkes, Esq. London.
  • Ball, W. W. R. (1889). A History of the Study of Mathematics at Cambridge. Cambridge Univ. Press.
  • Barnard, G. A. (1958). Thomas Bayes---A biographical note. Biometrika 45 293--295.
  • Bayle, P. (1696). Dictionnaire historique et critique. Reinier Leers, Rotterdam.
  • Bellhouse, D. R. (2007a). Lord Stanhope's papers on the Doctrine of Chances. Historia Math. 34 173--186.
  • Bellhouse, D. R. (2007b). Banishing Fortuna: Montmort and De Moivre. To appear.
  • Bellhouse, D. R., Renouf, E. M., Raut, R. and Bauer, M. A. (2007). De Moivre's knowledge community: An analysis of the subscription list to the Miscellanea Analytica. To appear.
  • Bernoulli, J. (1710). Extrait d'une lettre de M. Herman à M. Bernoulli datée de Padoüe le 12 juillet 1710. Mémoires de Mathématique et de Physique Tirez de Registres de l'Académie Royale des Sciences Année 1710 (Paris, 1732).
  • Burney, C. (1789). A General History of Music from the Earliest Ages to the Present Period 4. London.
  • Cheyne, G. (1703). Fluxionum Methodus Inversa: Sive Quantitatum Fluentium Leges Generaliores. J. Matthew, London.
  • Climenson, E. J. (1906). Elizabeth Montagu: The Queen of the Bluestockings, her Correspondence from 1720--1761. John Murray, London.
  • Cook, A. (1998). Edmond Halley: Charting the Heavens and the Seas. Clarendon Press, Oxford.
  • Cooper, W. D. (1862). Lists of Foreign Protestants, and Aliens, Resident in England 1618--1688. From Returns in the State Paper Office. Camden Society, London.
  • Cotes, R. (1722). Harmonia Mensurarum, Sive, Analysis & Synthesis per Rationum & Angulorum Mensuras Promotae: Accedunt alia Opuscula Mathematica. Cambridge, England.
  • Cyriaque de Mangin, C. (1620). Quatre livres de la géométrie pratique. Paris.
  • Daw, R. H. and Pearson, E. S. (1972). Studies in the history of probability and statistics. XXX. Abraham De Moivre's 1733 derivation of the normal curve: A bibliographical note. Biometrika 59 677--680.
  • De Moivre, A. (1695). Specimina Quaedam Illustria Doctrinae Fluxionum sive Exempla quibus Methodi istius usus et Praestantia in Solvendis Problematis Geometricis Elucidatur, ex Epistola Peritissimi Mathematici D. Ab. de Moivre Desumpta. Philosophical Transactions 19 52--57.
  • De Moivre, A. (1704). Animadversiones in G. Cheynaei Tractatum de Fluxionum Methodo Inversa. Edward Midwinter, London.
  • De Moivre, A. (1711). De Mensura Sortis. Philosophical Transactions 27 213--264.
  • De Moivre, A. (1717). Proprietates Quaedam Simplices Sectionum Conicarum ex Natura Focorum deductae; cum Theoremate Generali de Viribus Centripetis; quorum ope Lex Virium Centripetarum ad Focos Sectionum Tendentium, Velocitates Corporum in Illis Revolventium, & Descriptio Orbium Facillime Determinantur. Philosophical Transactions 30 622--628.
  • De Moivre, A. (1718). The Doctrine of Chances, or, a Method of Calculating the Probability of Events in Play. Pearson, London.
  • De Moivre, A. (1722). De Fractionibus Algebraicis Radicalitate Immunibus ad Fractiones Simpliciores Reducendis, Deque Summandis Terminis Quarumdam Serierum Aequali Intervallo a Se Distantibus. Philosophical Transactions 32 162--178.
  • De Moivre, A. (1725). Annuities upon Lives, or, the Valuation of Annuities upon any Number of Lives, as also, of Reversions to which is added, an Appendix Concerning the Expectations of Life, and Probabilities of Survivorship. W.P., London.
  • De Moivre, A. (1730). Miscellanea Analytica de Seriebus et Quadraturis. J. Tonson and J. Watts, London.
  • De Moivre, A. (1733). Approximatio ad Summam Terminorum Binomii $\overlinea + b ^n$ in Seriem expansi. London.
  • De Moivre, A. (1738). The Doctrine of Chances: or, a Method of Calculating the Probability of Events in Play, 2nd ed. Woodfall, London.
  • De Moivre, A. (1743). Annuities upon Lives: With Several Tables, Exhibiting at One View, the Values of Lives for Several Rates of Interest. Woodfall, London.
  • De Moivre, A. (1756). The Doctrine of Chances: Or, a Method of Calculating the Probability of Events in Play, 3rd ed. Millar, London. Reprinted in 1967 by Chelsea, New York.
  • De Morgan, A. (1846). On a point connected with the dispute between Keil and Leibnitz about the invention of fluxions. Philosophical Transactions Roy. Soc. Lond. 136 107--109.
  • De Morgan, A. (1857). Dr Johnson and Dr Maty. Notes and Queries 4 341.
  • Deslandes, A. F. (1713). Poetae Rustiantis Literatum Otium. Lintot, London.
  • Des Maizeaux, P. (1720). Recueil de diverses pièces, sur la philosophie, la religion naturelle, l'histoire, les mathématiques, &c. Par Mr.s. Leibniz, Clarke, Newton, & autres auteurs célèbres 2. Sauzet, Amsterdam.
  • Ditton, H. (1706). An Institution of Fluxions. Botham, London.
  • Ewles-Bergeron, P. (1997). Edward Mangin's list of Huguenot names, 1841. Proc. Huguenot Society 26 611--634.
  • Fiske, D. W. (1902). The Lost Manuscript of the Reverend Lewis Rou's `Critical Remarks upon the Letter to the Craftsman on the Game of Chess.' Landi Press, Florence.
  • Fitz-Adam, A. (1755--1757). The World. Dodsley, London.
  • de Fontenelle, B. (1719). Éloge de M. de Montmort. Histoire de l'Académie royale des sciences. Année 1719 (Paris, 1721) 83--93.
  • Formey, S. (1748). Éloge de Monsieur Naudé. Histoire de l'Académie royale des sciences et de belles lettres de Berlin, 1746. Ambroise Haude, Berlin.
  • de Fouchy, G. (1754). Éloge de M. Moivre. Histoire de l'Académie royale des sciences. Année 1754 (Paris, 1759) 175--184.
  • Fournier, G. (1643). Euclidis sex Primi Elementorum Geometricorum Libri, in Commodiorem Formam Contracti Demonstrati. Hénault, Paris.
  • Frederick II, King of Prussia. (1789). Posthumous Works of Frederic II. King of Prussia 9. Correspondence. Letters between Frederic II and M. Jordan. Robinson, London.
  • Gowing, R. (1983). Roger Cotes---Natural Philosopher. Cambridge Univ. Press.
  • Guicciardini, N. (1989). The Development of Newtonian Calculus in Britain 1700--1800. Cambridge Univ. Press.
  • Haag, E. and Haag, E. (1846--1859). La France protestante. J. Cherbuliez, Paris. Reprinted in 1966 by Slatine Reprints, Geneva.
  • Hald, A. (1984). A. de Moivre: `De Mensura Sortis' or `On the Measurement of Chance.' Internat. Statist. Rev. 52 229--262.
  • Hald, A. (1990). A History of Probability and Statistics and Their Applications before 1750. Wiley, New York.
  • Halley, E. (1695). An easie demonstration of the analogy of the logarithmick tangents to the meridian line or sum of the secants. Philosophical Transactions 19 202--214.
  • Halley, E. (1705). Astronomiae cometicae synopsis. Philosophical Transactions 24 1882--1899. Reprinted in Oxford, 1705. Reprinted and translated into English, 1705 under the title A Synopsis of the Astronomy of Comets. London.
  • Halley, E. (1715). Observations of the late total eclipse of the sun on the 22d of April last past, made before the Royal Society at their house in Crane-Court in Fleet-Street, London. Philosophical Transactions 29 245--262.
  • Harrison, J. (1978). The Library of Isaac Newton. Cambridge Univ. Press.
  • Huguenot Society (1914). Conversions et reconnoissances faites a l'Église de la Savoye 1684--1702. Publications of the Huguenot Society 22. Spottiswoode, London.
  • Huguenot Society (1923). Letters of denization and acts of naturalization for aliens in England & Ireland 1701--1800. Publications of the Huguenot Society 27. Sherratt and Hughes, Manchester.
  • Huguenot Society (1929). Register of the Church of West Street. Publications of the Huguenot Society 32. Butler and Tanner, Frome.
  • Huygens, C. (1657). De Ratiociniis in Ludo Aleae. In Francisci a Schooten Exercitationum Mathematicarum libri quinque (F. van Schooten, ed.) 517--524. Elsevier, Leiden.
  • Jacquelot, I. (1712). A Specimen of Papal and French Persecution. S. Holt, London.
  • Jordan, C.-E. (1735). Histoire d'un voyage littéraire fait en 1733 en France, en Angleterre et en Hollande. Adrien Moetjens, The Hague, The Netherlands. Reprinted in 1968 by Slatkine Reprints, Geneva.
  • Kahle, L. M. (1735). Elementa Logicae Probabilium Methodo in Usum Scientiarum et Vitae Adornata. Officina Rengeriana, Halle.
  • King, G. (1804). Natural and Political Observations and Conclusions upon the State and Condition of England, 1696. Stockdale, London. Reprinted in The Earliest Classics, 1973, Gregg International, Farnborough.
  • Knobloch, E. (1998). Mathematics at the Prussian Academy of Sciences 1700--1810. In Mathematics in Berlin (H. G. W. Begehr, H. Koch, J. Kramer, N. Schappacher, E.-J. Thiele, eds.) 1--8. Birkhaüser, Berlin.
  • Lamy, B. (1701). Traité de perspective, sont les fondemens de la peinture. Anisson, Paris.
  • Lasocki, D. (1989). The life of Daniel De Moivre. The Consort 45 15--17.
  • Le Blanc, J.-B. (1747). Letters on the English and French Nations. J. Brindley, London.
  • Le Gendre, F. (1657). L'Arithmétique en sa perfection, mise en pratique selon l'usage des financiers, banquiers, & marchands.
  • Leibniz, G. W. (1962). Mathematische Schriften. Olms, Hildesheim, Germany.
  • Lewis, W. S. (1941). Three Tours through London in the Years 1748, 1776, 1797. Greenwood, Wesport.
  • Lillywhite, B. (1963). London Coffee Houses. George Allen and Unwin, London.
  • Maclaurin, C. (1982). The Collected Letters of Colin MacLaurin. Shiva, Nantwich, England.
  • MacPike, E. F. (1932). Correspondence and Papers of Edmond Halley. Clarendon Press, Oxford.
  • Maty, M. (1755). Mémoire sur la vie et sur les écrits de Mr. Abraham de Moivre. Journal britannique 18 1--51.
  • de Montaigne, M. (1754). Essais de Montaigne, avec les notes de M. Coste 4. Nourse and Vaillant, London.
  • de Montmort, P. R. (1708). Essay d'analyse sur les jeux de hazard. Quillau, Paris.
  • de Montmort, P. R. (1713). Essay d'analyse sur les jeux de hazard, 2nd ed. Quillau, Paris.
  • Motteux, P. A. (1740). Remarques de Pierre Le Motteux sur Rabelais. London.
  • Murdoch, T. (1992). The Dukes of Montagu as patrons of the Huguenots. Proc. Huguenot Society 25 340--355.
  • Newton, I. (1687). Philosophiae Naturalis Principia Mathematica. Pepys and Streater, London.
  • Newton, I. (1718). Opticks; or, a Treatise of the Reflections, Inflections and Colours of Light, 2nd ed. Innys, London.
  • Newton, I. (1720). Traité d'optique sur les réflexions, réfractions, inflexions, et couleurs de la lumière. Par m. Le chev. Newton traduit de l'anglois par M. Cost, sur la seconde édition, augmentée par l'auteur. P. Humbert, Amsterdam.
  • Newton, I. (1722). Traité d'optique: sur les réflexions, réfractions, inflexions, et les couleurs, de la lumière/par Monsieur le Chevalier Newton. Traduit par M. Coste, sur la seconde édition angloise, augmentée par l'auteur. Seconde édition françoise, beaucoup plus correcte que la première. Montalant, Paris.
  • Newton, I. (1959--1977). The Correspondence of Isaac Newton. Cambridge Univ. Press.
  • Newton, I. (1967--1981). The Mathematical Papers of Isaac Newton. Cambridge Univ. Press.
  • Osborne, T. (1742). A Catalogue of a Choice and Valuable Collection of Books: Being the Libraries of a late eminent Serjeant at Law and of Dr. Edmund Halley. London.
  • Ozanam, J. (1725). Récréations mathématiques et physiques. C. Jombert, Paris.
  • Pearson, K. (1978). The History of Statistics in the 17th and 18th Centuries against the Changing Background of Intellectual, Scientific and Religious Thought. Charles Griffin and Company, London.
  • Pepusch, J. C. (1746). Of the various genera and species of music among the antients, with some observations concerning their scale. Philosophical Transactions 44 266--274.
  • Pope, A. (1734). An Essay on Man, Being the First Book of Ethic Epistles. John Wright, London.
  • Prestet, J. (1675). Éléments de mathématiques. André Pralard, Paris.
  • Rigaud, S. J. (1841). Correspondence of Scientific Men of the Seventeenth Century. Oxford Univ. Press. Reprinted 1965 by Georg Olms, Hildesheim, Germany.
  • Rigg, J. M. and Bakewell, S. (2004). Mark Duncan (d. 1640). In Oxford Dictionary of National Biography. Oxford Univ. Press. Available at www.oxforddnb.com/view/article/8226.
  • Rohault, J. (1682). Oeuvres posthumes de Mr. Rohault. Guillaume Desprez, Paris.
  • Royal Commission on Historical Manuscripts (1910). Manuscripts of the House of Lords. New Series 5 1702--1704. H. M. Stationary Office, London.
  • Royal Commission on Historical Manuscripts (1912). Manuscripts of the House of Lords. New Series 6 1704--1706. H.M. Stationary Office, London.
  • Sanford, V. (1936). François le Gendre, Arithméticien. Osiris 1 510--518.
  • Schneider, I. (1968). Der Mathematiker Abraham de Moivre (1667--1754). Archive for History of Exact Sciences 5 177--317.
  • Schneider, I. (2001). Abraham De Moivre. In Statisticians of the Centuries (C. C. Heyde and E. Seneta, eds.) 45--51. Springer, New York.
  • Schneider, I. (2004). Abraham De Moivre (1667--1754). In Oxford Dictionary of National Biography. Oxford Univ. Press. Available at www.oxforddnb.com/view/article/18893.
  • Schneider, I. (2005). Abraham De Moivre, Doctrine of Chances (1718, 1738, 1756). In Landmark Writings in Western Mathematics 1640--1940 (I. Grattan-Guinness, ed.) 105--120. Elsevier, Amsterdam.
  • Shuttleworth, J. (1709). A Treatise of Opticks Direct. Midwinter, London.
  • Simpson, T. (1737). A New Treatise of Fluxions. Gardner, London.
  • Simpson, T. (1740). The Nature and Laws of Chance. Edward Cave, London.
  • Simpson, T. (1742). The Doctrine of Annuities and Reversions. Nourse, London.
  • Smiles, S. (1868). The Huguenots: Their Settlements, Churches and Industries in England and Ireland, 2nd ed. John Murray, London.
  • Society for the Diffusion of Useful Knowledge. (1837). The Penny Cyclopaedia of the Society for the Diffusion of Useful Knowledge 8. Charles Knight, London.
  • Squire, J. (1742). A Proposal for Discovering our Longitude. Vaillant and Needham, London.
  • Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press of Harvard Univ. Press, Cambridge, MA.
  • Stirling, J. and Tweedie, C. (1922). James Stirling: A Sketch of His Life and Works Along with His Scientific Correspondence. Clarendon Press, Oxford.
  • Stratford, M. (1987). Daniel Demoivre (c. 1675--c. 1720) and his music. The Consort 43 13--16.
  • Sunderland, C. S. (1881--1883). Bibliotheca Sunderlandiana: Sale Catalogue of the Truly Important and very Extensive Books Known as the Sunderland or Blenheim Library, sold by Auction by Messrs Puttick and Simpson, London, W.C. Norman and Son, London.
  • Taylor, B. (1793). Contemplatio Philosophica: A Posthumous Work of the Late Brook Taylor LLD FRS. Bulmer, London.
  • Tilmouth, M. (1957). The Royal Academies of 1695. Music and Letters 38 327--334.
  • Twiss, R. (1787). Chess. Robinson, London.
  • Venn, J. and Venn, J. A. (1922--1954). Alumni Cantabrigienses. Cambridge Univ. Press.
  • Walker, H. M. (1934). Abraham de Moivre. Scripta Mathematica 2 316--333. Reprinted in the Chelsea reprint of the third edition of The Doctrine of Chances.
  • Wilford, J. (1723--1729). The Monthly Catalogue Being a General Register of Books, Sermons, Plays, Poetry, and Pamphlets, Printed and Published in London, or the Universities. John Wilford, London.
  • Wollenschläger, K. (1933). Der mathematische Briefwechsel zwischen Johann I Bernoulli und Abraham de Moivre. Verhandlungen der Naturforschenden Gesellschaft in Basel 43 151--317.