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Laplace's theory of errors

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References

  1. P.S. Laplace Exposition du système du monde (1796). Œuvr. compl., t. 6. Paris, 1884. (Reprint of the 1835 edition.)

  2. P.S. Laplace Traité de Mécanique céleste, 1798–1825. Œuvr. compl., tt. 1–5, 1878–1882. Separate volumes first publ. in 1798, 1798, an 11, 1805 and 1825.

  3. P.S. Laplace Théorie analytique des probabilités. Paris, 1812, 1814, 1820 and Œuvr. compl., t. 7, No. 1–2, 1886. This work consists of two livres and the references are to livre 2 (t. 7, No. 2 of the Œuvr. compl.). From the second edition onward the main text is preceded by a preface which also has appeared repeatedly separately (see [4]). Also, from the third edition, the main text is followed by four supplements. The first three of them are entered separately below [5], [6], [7].

  4. P.S. Laplace Essai philosophique sur les probabilités. See [3]. Œuvr. compl., t. 7, No. 1, separate pagination.

  5. Supplément premier (to [3]). Sur l'application du calcul des probabilités à la philosophie naturelle. (1816). Œuvr. compl., t. 7, No. 2, pp. 497–530. Essentially compiled from two memoirs, both published in 1815 and reprinted in Œuvr. compl., t. 13 (1904), pp. 98–116 and 117–120, respectively.

    Google Scholar 

  6. Deuxième supplément (to [3]). Application du calcul des probabilités aux opérations géodésiques (1818). Œuvr. compl., t. 7, No. 2, pp. 531–580. A first version of this Supplément appeared in the same year (1818) and is mentioned (but not reprinted) in Œuvr. compl., t. 13.

    Google Scholar 

  7. P.S. Laplace Troisième supplément (to [3]). Application des formules géodésiques de probabilité, à la méridienne de France. (S.a.). Œuvr. compl., t. 7, No. 2, pp. 581–616. Section 1 of this Supplément was published separately in 1820 and is mentioned (but not reprinted) in Œuvr. compl., t. 13; another memoir [30] publ. in 1819 is reprinted with a reference to this Supplément.

  8. P.S. Laplace Précis de l'histoire de l'astronomie. Paris, 1821.

  9. Recherches sur l'integration des équations différentielles aux différences finies etc. 1773 (1776). Œuvr. compl., t. 8, 1891, pp. 69–197.

    Google Scholar 

  10. Mémoire sur la probabilité des causes par les événements. (1774). Ibidem, pp. 27–65.

    Google Scholar 

  11. Mémoire sur les probabilités, 1778 (1781). Œuvr. compl., t. 9, 1893, pp. 383–485.

    Google Scholar 

  12. Mémoire sur la détermination des orbites des comètes, 1780 (1784). Œuvr. compl., t. 10, 1894, pp. 93–146.

    Google Scholar 

  13. Mémoire sur la chaleur. (1784). Ibidem, pp. 149–200. See pp. 157 and 178.

    Google Scholar 

  14. Mémoire sur la figure de la terre, 1783 (1786). Œuvr. compl., t. 11, 1895, pp. 3–32.

    Google Scholar 

  15. Mémoire sur les inégalités séculaires des planètes et des satellites, 1784 (1787). Ibidem, pp. 49–92.

    Google Scholar 

  16. Théorie de Jupiter et de Saturne, 1785 (1788). Ibidem, pp. 95–207.

    Google Scholar 

  17. Sur l'équation séculaire de la Lune, 1786 (1788). Ibidem, pp. 243–271.

    Google Scholar 

  18. Théorie des satellites de Jupiter, suite, 1789 (1792). Ibidem, pp. 415–473.

    Google Scholar 

  19. Sur quelques points du système du monde. (1789). Ibidem, pp. 477–558.

    Google Scholar 

  20. Mémoire sur le flux et reflux de la mer, 1790 (1797). Œuvr. compl., t. 12, 1898, pp. 3–126.

    Google Scholar 

  21. Mémoire sur le flux et reflux de la mer, 1818 (1820). Ibidem, pp. 473–546.

    Google Scholar 

  22. Mémoire sur les intégrales définies etc., 1810 (1811). Ibidem, pp. 357–412.

    Google Scholar 

  23. Mémoire sur les approximations des formules, etc., 1809 (1810). Ibidem, pp. 301–345.

    Google Scholar 

  24. Mémoire sur les approximations des formules, etc. supplément, 1809 (1810). Ibidem, pp. 349–353.

    Google Scholar 

  25. Mémoire sur la diminution de l'obliquité de l'écliptique, etc., 1811 (1809). Œuvr. compl., t. 13, 1904, pp. 44–70.

    Google Scholar 

  26. Sur l'inégalité à longue période du mouvement lunaire, 1813 (1811). Ibidem, pp. 79–84

    Google Scholar 

  27. Sur la détermination des orbites des comètes, 1824 (1821). Ibidem, pp. 265–267.

    Google Scholar 

  28. Mémoire sur le flux et reflux lunaire atmosphérique, 1830 (1827). Ibidem, pp. 342–358.

    Google Scholar 

  29. Rapport sur l'ouvrage de Du Séjour, etc. (1775). Written by Laplace, D'Alembert, Borda and Bézout. Œuvr. compl., t. 14, 1912, pp. 333–339.

    Google Scholar 

  30. Mémoire sur l'application du calcul des probabilités aux observations, etc. (1819). Ibidem, pp. 301–304.

    Google Scholar 

  31. P.S. Laplace Letter to F.T. Schubert dated 5 Nov. 1811. In occasional series Nauchnoe nasledstvo, vol. 1, 1948, p. 802. In orig. French with Russ. transl.

2. Other authors

  1. Bernoulli, D., Dijudicatio maxime probabilis, etc. (1778). Engl. transl.: Biometrika, Vol. 48, No. 1–2, 1961, pp. 3–18.

    Google Scholar 

  2. Bertrand, J., Calcul des probabilités. Paris, 1888.

  3. Bienaymé, I.J., A l'appui de la découverte de Laplace sur la loi de probabilité dans la méthode des moindres carrés. C.r. Acad. roy, sci. Paris, t. 37, 1853, pp. 309–324. Reprint: J. math. pures et appl., t. 12, 1867, pp. 158–176.

    Google Scholar 

  4. De Bruijn, N.G., Asymptotic methods in analysis. Amsterdam, 1958.

  5. Cauchy, A.L., Sur le système des valeurs qu'il faut attribuer à deux éléments, etc. (1824). Oeuvr. compl., ser. 2, t. 2. Paris, 1958, pp. 312–322.

    Google Scholar 

  6. Cauchy, A.L., Sur le système des valeurs qu'il faut attribuer à divers éléments, etc. 1814 (1831). Oeuvr. compl., ser. 2, t. 1. Paris, 1905, pp. 358–402.

    Google Scholar 

  7. Chebyshev, P. L., Theory of probability. Lectures delivered in 1879–1880 as written down by A. M. Liapunov. Edited by A. N. Krylov. Moscow-Leningrad, 1936. (In Russian.)

  8. Czuber, E., Theorie der Beobachtungsfehler. Leipzig, 1891.

  9. Deming, W. E., Statistical adjustment of data. New York-London, 1944.

  10. De Morgan, A., Theory of probabilities. Enc. Metropolitana, Vol. 2. London, 1845, pp. 393–490.

    Google Scholar 

  11. Eisenhart, C., The meaning of “least” in least squares. J. Wash. Acad. Sci., Vol. 54, No. 2, 1964, pp. 24–33.

    Google Scholar 

  12. Eisenhart, C., Gauss. Intern. Enc. of the Soc. Sciences, Vol. 6, pp. 74–81, 1968. Ed., D. L. Sills.

    Google Scholar 

  13. Gauss, C. F., Theoria motus, etc. (1809). German transl. in: Abhandlungen zur Methode der kleinsten Quadrate. Hrsg. A. Börsch und P. Simon. Berlin, 1887 (pp. 92–117).

  14. Gauss, C. F., Disquisitio de elementis ellipticis Palladis, etc. (1811). German transl.: Abhandlungen, pp. 118–128.

  15. Gauss, C.F., Bestimmung der Genauigkeit der Beobachtungen (1816). Abhandlungen, pp. 129–138.

  16. Gauss, C. F., Brief nach Encke 25 Febr. 1819. Werke, Bd. 12, pp. 200–201. Göttingen-Berlin, 1929.

    Google Scholar 

  17. Gauss, C.F., Theoria combinationis, etc. (1823–1828). German transl.: Abhandlungen, pp. 1–91.

  18. Gauss, C.F., Brief nach Bessel 28 Febr. 1839. Werke, Bd. 8, pp. 146–147. Göttingen-Leipzig, 1900.

    Google Scholar 

  19. Gauss, C.F., “Selbstanzeige” of pt. 1 of [48] (1821). Werke, Bd. 4. Göttingen, 1880, pp. 95–100.

    Google Scholar 

  20. Gauss, C.F., “Selbstanzeige” of pt. 2 of [48] (1823). Ibidem, pp. 100–104.

    Google Scholar 

  21. Goussac, A.A., La préhistoire et les débuts de la théorie de la représentation approximative des fonctions. Hist.-math. essays, Vol. 14, 1961, pp 289–348. (In Russian.)

    Google Scholar 

  22. Idel'son, N.I., Method of least squares etc. Moscow, 1947. (In Russian.)

  23. Kolmogorov, A.N., La méthode de la médiane dans la théorie des erreurs. Recueil math. (Moscow), t. 38, No. 3–4, 1931, pp. 47–49. (In Russian; French summary on p. 50.)

    Google Scholar 

  24. Lancaster, H.O., Forerunners of the Pearson x 2. Austr. J. Stat., Vol. 8, No. 3, 1966, pp. 117–126.

    Google Scholar 

  25. Lancaster, H.O., Development of the notion of statistical dependence. Math. chronicle (N. Z.), Vol. 2, pts 1–2, 1972, pp. 1–16.

    Google Scholar 

  26. La Vallée Poussin, C.I., Sur la méthode de l'approximation minimum (1911). Russ. transl.: Proc. Moscow inst. land surv., Vol. 9, 1960, pp. 227–236.

    Google Scholar 

  27. Linnik, Ju. W., Method of least squares, etc. Oxford a.o., 1961. (Orig. in Russian, 1958 (and 1962).)

  28. Markov, A.A., Law of large numbers and method of least squares (1898). Selected works, pp. 231–251. Leningrad, 1951. (In Russian.)

  29. Meadowcroft, L.V., On Laplace's theorem on simultaneous errors. Messenger of Math., Vol. 50, No. 1, 1920, pp. 40–48.

    Google Scholar 

  30. Molina, E.C., The theory of probability: Some comments on Laplace's Théorie analytique. Bull. Amer. Math. Soc., Vol. 36, No. 6, 1930, pp. 369–392.

    Google Scholar 

  31. Pitman, E.J.G., Estimation of the location and scale parameters etc. Biometrika, Vol. 30, No. 3, 1939, pp. 391–421.

    Google Scholar 

  32. Plackett, R.L., The discovery of the method of least squares. Biometrika, Vol. 59, No. 2, 1972, pp. 239–251.

    Google Scholar 

  33. Poisson, S.D., Sur la probabilité des résultats moyens des observations. Conn. des tems 1827 (1824), pp. 273–302.

  34. Poisson, S.D., Recherches sur la probabilité des jugements, etc. Paris, 1837.

  35. Rietz, H.L., On a certain law of probability of Laplace. Proc. Intern. congr. mathematicians Toronto 1924. Toronto, 1928, Vol. 2, pp. 795–799.

    Google Scholar 

  36. Sarhan, A.E., & B.G. Greenberg, Rectangular distributions. In: Contributions to Order Statistics, pp. 383–390. Ed., Sarhan & Greenberg, New York-London, 1962.

  37. Schneider, I., Der Mathematiker A. de Moivre. Arch. Hist. Ex. Sci. Vol. 5, No. 3–4, 1968, pp. 177–317.

    Google Scholar 

  38. Sheynin, O.B., J.H. Lambert's work on probability, Ibidem, Vol. 7, No. 3, 1971, pp. 244–256.

    Google Scholar 

  39. Sheynin, O.B., On the mathematical treatment of observations by L. Euler. Ibidem, Vol. 9, No. 1, 1972, pp. 45–56.

    Google Scholar 

  40. Sheynin, O.B., D. Bernoulli's work on probability, Rete. Strukturgeschichte der Naturwissenschaften Bd. 1, No. 3–4, 1972, pp. 273–300.

    Google Scholar 

  41. Sheynin, O.B., Finite random sums (a historical essay). Arch. Hist. Ex. Sci., Vol. 9, No. 4–5, 1973, pp. 275–305.

    Google Scholar 

  42. Sheynin, O.B., R.J. Boscovich's work on probability. Ibidem, , Vol. 9, No. 4–5, 1973, pp. 306–324.

    Google Scholar 

  43. Sheynin, O.B., Mathematical treatment of astronomical observations (a hist. essay). Ibidem, , Vol. 11, No. 2–3, 1973, pp. 97–126.

    Google Scholar 

  44. Sheynin, O.B., On the prehistory of the theory of probability. Ibidem, , Vol. 12, No. 2, 1974, pp. 97–141.

    Google Scholar 

  45. Sheynin, O.B., La delta fonction de Dirac chez Laplace. Hist.-math. essays, Vol. 20, 1975, pp. 303–308. (In Russian.)

    Google Scholar 

  46. Sheynin, O.B., P.S. Laplace's work on probability. Arch. Hist. Ex. Sci., Vol. 16, 1976, pp. 137–187.

    Google Scholar 

  47. Stigler, S.M., Gergonne's 1815 paper, etc. Hist. math., Vol. 1, 1974, pp. 431–447. (Orig. publ. in 1973.)

    Google Scholar 

  48. Stigler, S.M., Laplace, Fisher, and the discovery of the concept of sufficiency. Biometrika, Vol. 60, No. 3, 1973, pp. 439–445.

    Google Scholar 

  49. Stigler, S.M., Newcomb, P. Daniell, and the history of robust estimation 1885–1920. J. Amer. Stat. Assoc., Vol. 68, No. 344, 1973, pp. 872–879.

    Google Scholar 

  50. Todhunter, I., History of mathematical theory of probability, etc. (1865). Reprints: New York, 1949, 1965.

  51. Todhunter, I., On the method of least squares. Trans. Cambr. Philos. Soc., Vol. 11, pt 2, 1869, pp. 219–238.

    Google Scholar 

  52. Tsinger (Tsinguer), V. Ya., Method of least squares. (Diss.). Moscow, 1862. (In Russian.)

    Google Scholar 

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Sheynin, O.B. Laplace's theory of errors. Arch. Hist. Exact Sci. 17, 1–61 (1977). https://doi.org/10.1007/BF00348401

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