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Al-bīrūnī and The Mathematical Treatment of Observations

Published online by Cambridge University Press:  24 October 2008

Extract

The classical theory of errors can be divided into stochastic and determinate parts, or branches. The birth of the first of therse became inevitable after Bradley's idea of cultivating astronomy and natural science in general by “regular series of observations and experiments” became universally accepted. Such scholars as Lambert, Simpson, Lagrange, Daniel Bernoulli and Euler were responsible for the development of the stochastic theory of errors while Laplace and Gauss completed its construction. About fifty or sixty years ago it was included into mathematical statistics.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1992

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References

1 Bradley, J., “A letter… concerning an apparent motion observed in some of the fixed stares”, in Rigaud, S.P., Miscellaneous works an correspondence of J. Bradley, Philosophical Transations of the Royal Society of London 45, (Oxford, 1832), pp. 1741, see on p. 17.Google Scholar

2 Cotes, R., “Aestimatio errorum in mixta mathesi per variations partium tiranguli plani et sphaerici (1722) ”, in Opera miscellanea (London, 1768), pp. 1058.Google Scholar

3 Sheynin, O.B., “D. Bernoulli's work on probability”, in Studies in the Histry of Statistics and Probability (London, 1977), vol. II, pp. 105–32, see in § 5.2.Google Scholar

4 Sheynin, O.B., “Mathematical treatment of astronomical observations: a historical essay”, Archive for Histry of Exact Sciences, 11 (1973): 97126.CrossRefGoogle Scholar

5 Ptolemy, , Almagest, Engl. transl. by Taliaferro, R.C., Great Books of the Western World 16, (Chicago, 1952), pp. 5465.Google Scholar

6 Ibid., Book 4, §1, p. 108.

7 Ibid., Book 4, §9, pp. 135–7.

8 Bīrūnī, Al, The Determination of the Coordinates of Posotions for the Correction of Distances between Cities, Engl. transl. by Ali, Jamal (Beirut, 1967).Google Scholar

9 Ibid., on pp.51 and 152.

10 Cf. § 2.1.Google Scholar

11 Al-Bīrūnī, Correction of Distances between Cities, pp. 39 and 155.Google Scholar

12 Ibid., p. 129.

13 Ibid., pp. 115–16.

14 Ibid., pp. 191 and 199.

15 Al-Bīrūnī, , “al-Qānūn al Mas'ūdī”, in Selected Works, Russian transl. by Bulgakov, P.G., Rozhankaya, M.M. and Rozenfeld, B.A. (Tashkent, 19731976), vol, V; part 1 of the volume (1973) comparies Books 1–5 of the Qānūn and part 2 (1976) includes the remainder.Google Scholar

16 Ibid., Book 7, chap. V, p. 778.

17 Ibid., Book 6, chap. II, p. 614.

18 Ibid., Book 4, chap. XV, pp. 366–7.

19 Al-Khāzinī, “The book of the balance of wisdom (Kniga vesov mudrosti),” Russian transl. by Rozhanskaya, and Levinova, I.S., Nauchnoye nasledstvo (Moscow, 1983), vol. VI, pp. 15140.Google Scholar

20 Ibid., p. 106.

21 Bourne, W., A Regiment for the Sea and other writings on navigation (1574), ed. Taylor, E.G.R. (Cambridge, 1963), pp. 135314, esp. on p. 208.Google Scholar

22 Kepler, J., Neue Astronomie (1609), Übers und eingeleit. Caspar, M. (Munich and Berlin, 1929), p. 209.Google Scholar

23 Huygens, C., “Horlorium oscillatorium sive de motu pendulorum (1673),” in Œuvres complètes (La Haye, 1934), t. XVIII, pp. 27438, see part 1 and part 4, Proposition 26 rewspectively.Google Scholar

24 Cf. § 1.Google Scholar

25 Galilei, G., History and Demonstrations Concerning Sunspots (1613), transl. with introd. and notes by Drake, S. (New York, 1957), pp. 88144.Google Scholar

26 Ptolemy, Almagest.Google Scholar

27 Ibid., Book 1, īrūnī, Correction of Distances between Cities.

28 Ibid., p. 51.

29 Ibid., p. 51.

30 Ibid., pp. 155–6.

31 Cf. al-Khāzinī, “Book of the balance of wisdom,” p. 112.Google Scholar

32 Al-Bīrūnī, “al-Qāuūn al-Mas'ūdī”, Book 6, VI, p. 631.Google Scholar

33 Ibid., chap. VI, pp. 636–7.

34 Al-Bīrūnī, Correction of Distances between Cities, p. 83.Google Scholar

35 Ibid., p. 203.

36 Ibid., on pp. 46–51.

37 Ptolemy, Almagest, Book 4, § 6, p. 123; Book 10, āzinī, “The book of the balance of wisdom”, pp. 60–2.Google Scholar

38 Al-Khāzinī, “The book of the balance of wisdom,” pp. 60–2.Google Scholar

39 Galilei, G., Dialogue Concerning the Two Chif World Systems (1632), transl. by Drake, S. (Berkeley and Los Angeles, 1962).Google Scholar

40 Cf. § 3.2.Google Scholar

41 Kepler, Neue Astronomie, p. 197.Google Scholar

42 Ibid., p.166.

43 Ibid., on p.113.

44 SeeEisenhart's, C. discussion of invited papersa on the history of statistics, 40th Session of International Statistical Intitute 1975, Bulletin ISI, 46 (1976): 355–7.Google Scholar

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