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Ibn al-Fahhād and the Great Conjunction of 1166 AD

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Abstract

Farīd al-Dīn Abu al-Ḥasan ‘Alī b. al-Fahhād’s astronomical tradition as represented in the prolegomenon to his Alā’ī zīj (1172 AD) shows his experimental examination of the theories of his predecessors and testing the circumstances of the synodic phenomena as derived from the theories developed in the classical period of medieval Middle Eastern astronomy against his own observations. This work was highly influential in late Islamic astronomy and was translated into Greek in the 1290s. He evaluated al-Battānī’s Ṣābi’ zīj (d. 929 AD) and al-Khāzinī’s Sanjarī zīj (fl. 1115 AD) with regard to the conjunction between Jupiter and Saturn in 1166 AD and found the errors of, respectively, about 35 and 10 days in the times predicted, which are verified by a recalculation on the basis of these works and modern theories. His inspection of the four solar theories established by his Islamic predecessors with respect to the quantitative differences between their predicted times for the occurrence of the vernal equinoxes is also correct. His calculation of the parameters of the solar and lunar eclipses in April 1176 has the errors of up to 1 h in the time and one digit in the magnitude. A general result of this study is that solely the evaluation of the synodic phenomena could mislead the judgment about the reliability and worthiness of the contemporary theories.

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Notes

  1. See Mozaffari (2014a).

  2. For example, see Saliba (1986) and Mozaffari (2018a, b, c, 2019).

  3. See Mozaffari (2019).

  4. The observation reports from these two astronomers in Ibn Yūnus’s Ḥākimī zīj only reflect a minor portion of their fruitful careers, mostly marking the beginning and end of their observational periods: from Ḥabash, two observations from 829–830 AD (a conjunction between Saturn and Jupiter and a single observation of Venus) and two observations from 864 AD (a conjunction of Jupiter and the star Regulus, α Leo, and a conjunction of Venus and Mars); from the Banū Amājūr: eight random observations of conjunctions, occultations, and near appulses made between 885 AD and 919 AD and two periodic observations in 918–919 AD (Jupiter with the star Vega, α Lyr, and Mars with the star Sirius, α CMa). See Ibn Yūnus, Zīj, L: pp. 98–99, 108–109, F1: f. 10r; Caussin de Perceval (1804), pp. 104–111, 154–158, 157–162; Delambre (1879, p. 83, 87–89).

  5. See Pingree (1962, 1963, 1968), Kennedy (1958, pp. 259–260, 1962), Kennedy and van der Waerden (1963) and Kennedy and Pingree (1971).

  6. For example, Levi Ben Gerson (1288–1344 AD) computed the date and longitude of the Great Conjunction of 1226 AD, according to which it should have occurred on 9 March, at λ = 303;37°, and also made a prognostication for that of 1345 AD, which was expected to take place on 28 March, 1;17h after noon, at λ = 319;44°. Another Jewish scholar, Abraham Bar Ḥiyya, dates the first on 14 February 1226 (see Goldstein and Pingree 1990, pp. 11, 15, 19, 21, 42–43, 44–45). In reality, both conjunctions occurred four days earlier than the estimated ones; the first on 5 March at 4:40 MLT (for Orange, Southern France: φ ≈ 44;8°, L ≈ 4;49°) at λ ≈ 302;58° and the second on 24 March about 20 min after noon at λ ≈ 319;1°.

  7. Ibn Yūnus, Zīj, L: p. 108; Caussin de Perceval (1804, pp. 154–155) and Delambre (1879), p. 87. The report only says: “there was a conjunction on Friday, Rūz Dhībāzar, the 29th day of the month of Rabī‘I in the year 214 al-Hijra, which is the year 198 Yazdigird,” without referring to the celestial bodies engaged, but a conjunction between Jupiter and Saturn occurred on that day at about 17:45 MLT when the two planets arrived at a longitude of 128;32°. Moreover, the date is in error, since 29 Rabī‘I 214 H is equivalent of Sunday, 6 June 829, according to the civil Hijra calendar, or a day earlier, Saturday, 5 June 829, according to the astronomical Hijra calendar, none of which is a Friday. It should be 4 June 829 (JDN 2024005), which is 8 Urdībihisht (the 2nd month) 198 Y; Dhībāzar (or Dībāzar) is the name of the 8th day of each month in the Persian calendar, and Rūz means “day” in Persian.

  8. Ibn Yūnus, Zīj, L: pp. 119–120, Caussin de Perceval (1804, pp. 210–215), Delambre (1879, p. 92). It was the first of the triple conjunctions of the two superior planets about the time; the two others took place on 7 March and 1 June 1008, which Ibn Yūnus does not refer to.

  9. Wābkanawī, Zīj, T: ff. 2r–v, 134v–135r, Y: ff. 2v–3r, 235v–236r, P: 2v–3r, ff. 205r–v. On Muḥyī al-Dīn’s observations, esp. see Mozaffari (2018a). On Wābkanawī, see Mozaffari (2013a) and Mozaffari and Zotti (2013).

  10. Ibn al-Fahhād, Zīj, pp. 7–9.

  11. Ibn al-Fahhād, Zīj, p. 60.

  12. See Mozaffari (2017, pp. 16–18), wherein the longitudes of the planetary apogees in the Alā’ī zīj are also discussed. The fragment is on the derivation of the solar parameters, which has been already discussed in Mozaffari (2013b, Part 1, pp. 322) (Table 1, no. 8), 328–329, where it is referred to as “Anonymous.”

  13. It is clearly acknowledged in the prolegomenon to the Mulakhkhaṣ zīj (K: f. 1v) that this work is dependent upon the ‘Alā’ī zīj. Note that it is probable that both Shāmil zīj and Ṣinā‘at were written by Athīr al-Dīn al-Abharī himself. The epoch of all of these works is the year 600 Y, the beginning of which is 18 January 1231. The values for the longitudes of the planetary apogees in them exceed those in the ‘Alā’ī zīj by 0;53,38°, which is in agreement with a precessional/apogeal motion of 1° in every 66 years and the interval of 59 Persian years between their epoch and that of the ‘Alā’ī zīj, 541 Y (Abharī, Mulakhkhaṣ, K: ff. 66r–v, 67v, 70v, 72v, 74v, 76v, U: f. 33v, F: f. 82r; Shāmil, P: ff. 23r–v, F2: ff. 44r–v, D: f. 17r, Pa: f. 22v; Ṣinā‘at, P1: ff. 48v, 65–66v, 74v–75r, N: pp. 83, 114–116, 136–137, I: ff. 40v, 55–56v, 64v–65r—the tables are missing from MSS P2 and Pa).

  14. See van Dalen (2004).

  15. Al-Fārisī, C: f. 57r; see, also, Kennedy (1956, p. 132, no. 54) and Dalen (2004, p. 829).

  16. For example, the epoch longitude values of the planetary apogees in the ‘Umdat (al-Maghribī, ‘Umdat, M: ff. 23v, 24v, 25v, 26v, 27r) are more than Ibn al-Fahhād’s values, given presently in this paper, by 1;21,17°, so that all of the values are ended with zero in the seconds; by a precessional rate 1°/66y and 90 years intervening the epoch of the ‘Umdat, i.e., the end of 600 Y, and that of the ‘Alā’ī zīj, i.e., 541 Y, it should be about 1;21,49°. It seems that either the rounded increment of 1;22° was added to Ibn al-Fahhād’s truncated epoch longitudes or, inversely, a truncated increment of 1;21° was added to the rounded Ibn al-Fahhād’s longitude values. In the Īlkhānī zīj, Ibn al-Fahhād’s value for the daily mean anomalistic motion of Mercury, 3;6,24,22,7,59°, was used (Īlkhānī zīj, C: 132, P: f. 45v, M1: f. 80v).

  17. Muḥyī al-Dīn gives the differences in the lunar mean longitude between his trio lunar eclipses (7 March 1262, 7 April 1270, and 24 January 1274) as 30;57,18° and 277;44,27°, respectively (see Mozaffari 2014b), both of which are in agreement with a daily mean motion of 13;10,35,1,55,32° which is equal to Ibn al-Fahhād’s value (see Dalen 2004, p. 832), which appears to have been in turn adopted from the Mumtaḥan zīj (see below, the prolegomenon, passage [VI]).

  18. This work was written in Shiraz. Kamālī, F: ff. 230r–v (some instructions in VIII.7), 231v–233r, 234r (the solar, lunar, and planetary mean positions and apogee longitudes for 13 Adhar 1614 Alexander/23 Rajab 702 al-Hijra/13 Khurdād 672 Yazdigird (= 13 March 1303, JDN 2197050) as well as their mean motions in 20 solar years), 240r–241r (equation tables), G: ff. 247v, 248v–249r, 252r, 253v.

  19. This work was written in Yazd, seemingly, in the 1290s. It is preserved nowadays in a unique manuscript in Tehran, Library of Parliament, no. 184, and is neither be confused with Wābkanawī’s Zīj al-Muḥaqqaq al-Sulṭānī, nor with Ulugh Beg’s Sulṭānī zīj (see Mozaffari 2019, pp. 72–73, notes 28 and 29). The materials related to the ‘Alā’ī zīj can be found on ff. 76v–77r, 78v, 80r–v (some instructions, respectively, in III.1, III.4, and III.9), 81r (the solar, lunar, and planetary mean positions for Sunday, the beginning of the year of 217 Jalālī/11 Khurdād 664 (= 13 March 1295, JDN 2194128)), 81v (the differences in mean motions between various zījes), 123v–124r, 171v (equation tables), 172v–174r (the solar, lunar, and planetary apparent angular diameters).

  20. This hypothesis was put forward for the first time in Mozaffari (2013a), but still awaits the final confirmation by comparing the relevant surviving Persian and Greek texts.

  21. See Pingree (1985–1986). The late Prof. Pingree mistakenly assumed that the original ‘Alā’ī zīj was in Arabic and thus thought of Shams al-Bukhārī (i.e., Wābkanawī) as the author of its alleged Persian version/adaptation used by Chioniades (ibid, Vol. 1, pp. 8, 16, and 18).

  22. See below, notes 50 and 51.

  23. Pingree (1985–1986, Vol. 1, pp. 53, 57, 69, 179).

  24. Pingree (1985–1986, Vol. 1, Chapters 32–36: pp. 131–169). 5MCSE, no. 07846. 5MCLE, no. 07961.

  25. Pingree (1985–1986, Vol. 1, pp. 98–101).

  26. Kennedy (1956, pp. 128: no. 23, 132: no. 53, 133: nos. 58, 62, 134: no. 64, 135: no. 84) gives this information from the prolegomenon of Wābkanawī’s Muḥaqqaq zīj (T: f. 3r, Y: ff. 4r–v, P: f. 4r) and Maḥmūd b. Abū Bakr al-Fārisī’s Zīj al-mumtaḥan al-Muẓaffarī (C: f. 57r); the latter has been translated in Kunitzsch and Langermann 2003, pp. 160–162.

  27. Ibn al-Fahhād, Zīj, pp. 3–5.

  28. The historical northeastern region in the ancient and medieval Persia, including part of Central Asia, Afghanistan, and the Khurāsān province of the present-time Iran.

  29. A recomputation from the tables of the mean positions and motions of Saturn in the ‘Alā’ī zīj (Ibn al-Fahhād, Zīj, pp. 94, 97, 101) results in the value of 50;38,12° for the mean eccentric anomaly at the given date, which added to the longitude of the apogee (see below, note 31), yields the value of 298;35,14° for the mean longitude.

  30. Text: …;53,…; a scribal error in writing down the alphanumerics with similar forms: . A recomputation from the tables gives 327;13,50°.

  31. 248;1,43° at the epoch (Ibn al-Fahhād, Zīj, p. 73; Mozaffari 2017, p. 18); so for the given date: 247;57,2° (NB. the rate of precession adopted in the ‘Alā’ī zīj = 1° in 66 Egyptian/Persian years of 365 days, without leap years).

  32. Text: …;…,53; a scribal error due to the confusion between the Abjad symbol for zero and 53/نج, attested by the value given for the true longitude of Saturn in ‘Alā’ī zīj I.60: p. 59, in which the derivation of the parameters of this conjunction is discussed, as well as the time computed for the conjunction (see below, Sect. 3). A recomputation yields 291;11,1°. In his commentary on the Greek translation of ‘Alā’ī zīj I.60, the late Prof. Pingree (1985–1986, Vol. 1, p. 378) reaches a figure of 291;10,4°, close to Ibn al-Fahhād’s calculated value, but neglecting three quantities necessary to take into account in the derivation of the longitude of a planet on the basis of Ptolemy’s interpolation scheme (explained in ‘Alā’ī zīj I.28: pp. 22–23): the difference in the epicyclic equation, the interpolation coefficient, and the apogeal motion.

  33. Entering the table of the coefficient of the southern latitude of Saturn with the adjusted eccentric anomaly of 45;46,39°, the value of 0;6 is extracted therefrom, and the table of the southern latitude of the planet gives the value of 2;7° opposite the adjusted epicyclic anomaly of 332;5,23° (Ibn al-Fahhād, Zīj, p. 109). Thus, the latitude of the planet  =   0;6 · 2;7°   =  0;12,42°.

  34. Text: 305;…,…; a scribal error due to the confusion between the Abjad symbol for zero and 5/ه. The mean eccentric anomaly derived from the tables   =  122;54,55°, which, added to the longitude of the apogee (see below, note 36), amounts to the value of 300;33,57° for the mean longitude.

  35. A recomputation from the tables of the mean positions and motions of Jupiter (Ibn al-Fahhād, Zīj, pp. 110, 117) results in 325;15,6°.

  36. At the epoch: 177;43,43°, and hence for the given time: 177;39,2°.

  37. My recomputation with interpolation in the equation tables of the ‘Alā’ī zīj results in 291;12,53°, which, similar to the value we have derived for the longitude of Saturn (note 32), exceeds Ibn al-Fahhād’s registered value by a single arc-minute. The late Prof. Pingree (1956–1986, Vol. 1, pp. 380) arrives at 291;11,48°, again close to Ibn al-Fahhād’s calculated value, but neglecting three essential quantities mentioned earlier in note 32.

  38. Text: …;…,7; a scribal error in registering the Abjad numerals: . The value of 0;8 is derived from the table of the coefficient of the southern latitude of Jupiter for the adjusted eccentric anomaly of 118;22,40°, and the value of 1;8° can be found in the table of the southern latitude of the planet opposite the adjusted epicyclic anomaly of 329;47,21° (Ibn al-Fahhād, Zīj, p. 125). Thus, the latitude of the planet = 0;8 · 1;8° = 0;9,4°. The correct value is given in ‘Alā’ī zīj I.60 (see below, Sect. 3).

  39. In ‘Alā’ī zīj I.60: p. 59, this quantity is given to the arc-seconds (see below, Sect. 3).

  40. Ptolemy’s parallactic instrument in Almagest V.12 (Toomer [1984] 1998, pp. 244–247), the so-called triquetrum in the medieval period.

  41. The modern longitudes in this paper have been computed by means of the software Alcyone Ephemeris (version 4.3; see http://www.alcyone.de for details), which is based on an analytical ephemeris by Steve Moshier adjusted to the Jet Propulsion Laboratory Development Ephemeris 406 (JPL DE 406; see Standish 1998). These fulfill the minimum requirements with regard to the degree of precision needed for our historical survey.

  42. Khāzinī, Kayfiyyat al-i‘tibār, in: Zīj, V: ff. 16v–17r.

  43. Khāzinī, Kayfiyyat al-i‘tibār II.4, in: Zīj, V: f. 8r.

  44. Khāzinī, Kayfiyyat al-i‘tibār, in: Zīj, V: ff. 16v–17r.

  45. For example, a single observation of Mars with the star Procyon (α CMi) on 1 January 919 (JDN 2056723) and the periodic observations of Jupiter with the star Vega (α Lyr) from 13 July (JDN 2056551) to 9 September 918 (JDN 2056609); see Ibn Yūnus, Zīj, L: pp. 98–99; Caussin de Perceval (1804, pp. 104–111) and Delambre (1879), p. 83.

  46. See Mozaffari (2019).

  47. Ibn al-Fahhād, Zīj, pp. 57–59; the Greek translation in Pingree (1956–1986, Vol. 1, pp. 241–243).

  48. Text: …;…,49; a scribal error in registering the Abjad numerals: , quickly understood from the value immediately given for the relative angular velocity.

  49. The late Prof. Pingree (1956–1986, Vol. 1, pp. 377–381) comments that the longitudes of the two planets are for noon on 11, not 10, December 1166. The reason is that he takes the wrong date 5 Bahman 535 Y = 14 Ṣafar 562 H, according to the astronomical Hijra calendar (the epoch: 15 July 622, JDN 1948439), given in I.60, as equal to Saturday, 10 December 1166, while it was Friday, 9 December 1166.

  50. In the Greek translation, there can be found some scribal errors, and also the numerical values are rounded to arc-minutes, except for β and θ, so that without access to the original text, it can not be easily known how the author has derived a figure of 8;15h for the time of the conjunction (e.g., see Pingree’s comment 1956–1986, Vol. 1, p. 380). It is not known whether the numerical values had been registered in the round numbers in the manuscript(s) available to Wābkanawī or he himself rounded them. If the latter is the case, it merits mentioning, furthermore, that the true daily motion of Jupiter is given as 0;14°, and hence it appears that the manuscript(s) in the possession of Wābkanawī suffered from the copying error already mentioned in note 48.

  51. This visual experience cannot be found in the Greek translation; instead, strictly adhering to the computational outputs, we are told: “the difference (between) the 2 latitudes was larger than (half) of the 2 diameters. From this it was clear that Saturn was not about to be eclipsed by being concealed by Jupiter. The southern latitude of Saturn was the maximum [!? SMM: greater than that of Jupiter?]; therefore it was known that the passage of Saturn [SMM: Jupiter?] is to the northern side [!?]” (Pingree 1956–1986, Vol. 1, p. 243; the additions in square brackets are mine). It is not known whether this passage comes from an earlier version of the ‘Alā’ī zīj, which had presumably prepared prior to the observation of the Great Conjunction of 1166 AD, and of which Wābkanawī used about a century later, and Ibn al-Fahhād later replaced it by the note stemmed from his interesting observational experience, or, conversely, this passage is Wābkanawī’s and was substituted for the original note during his tutorial course for Chioniades.

  52. See Mozaffari (2018a, pp. 604, 614–615).

  53. Shīrwān is a region of eastern Caucasian land (see the entry by W. Barthold and C. E. Bosworth in EI2: Vol. 9, pp. 487–488). The terrestrial coordinates φ = 39;56° N, L = 48;55° E point toward a spot nearly in the middle of the region.

  54. See Goldstein (2004).

  55. Said and Stephenson (1995, p. 128).

  56. See Stephenson (1997, pp. 488–490) and Steele (2000, p. 115).

  57. See Mozaffari (2016, pp. 304–305).

  58. Khāzinī, Zīj, L: f. 105v.

  59. Khāzinī’s base meridian is Qubba, 90° distant from the western shore of the Encompassing Sea.

  60. It is marginally worthwhile that the main reason for the positive shift in al-Battānī’s ephemerides of Jupiter is the large error of ~ + 1;6° in al-Battānī’s value for the mean longitude of the planet (for 1–1–880 AD: 229;58°; Modern: 228;52°) and the continuous increase in it seems to be partly due to the fact that his value for the daily motion in longitude of the planet is larger than the true value by ~ 0;0,0,1° (al-Battānī: 0;4,59,16,54,54,57°. Modern values: for the beginning of the Common Era: 0;4,59,15,54,26,…°, and for 2000 AD: 0;4,59,15,57,32,…°, as computed from the formula given in Simon et al. 1994, p. 678).

  61. See Mozaffari (2018b, esp. pp. 216–221).

  62. Mozaffari (2018b, pp. 228–229, 236). It merits noting that Ibn al-Fahhād should know Bīrūnī’s works which were very influential to the late medieval Islamic astronomers; although no direct reference to Bīrūnī can be found throughout the ‘Alā’ī zīj, some materials in this work comes from Bīrūnī; for example, a double-argument table for the half-diameters of the Moon and Earth’s shadow in it is computed on the basis of Bīrūnī’s formula in al-Qanūn VII.11.1 (Bīrūnī 1954–1956, Vol. 2, pp. 857–871. Bīrūnī’s formula is also cited in Kamālī’s Zīj, V.11: F: ff. 140v–141r, G: ff. 136r–v). But, it is not known whether he did not encounter Bīrūnī’s rejection of the Mumtaḥan solar theory or why he neglected it.

  63. For example, according to Aristotle, both the father and the Sun are moving principles in the generation of a man, as he says, e.g., in Physics (194 b 13) that “Man is begotten by man and by the Sun as well.”

  64. Ibn al-Fahhād, Zīj, pp. 30–35.

  65. 5MCSE, No. 07555.

  66. 5MCLE, No. 07660.

  67. Already mentioned in Mozaffari and Steele (2015, pp. 347–348, note 17).

  68. Passingly mentioned in A. Tihon’s entry on Chioniades (Koertge 2008, Vol. 2, p. 121).

  69. Only referred to in S.M.R. Ansārī’s article “Astronomy in medieval India” (Selin 2016, pp. 718–719).

  70. Only mentioned in P.G. Schmidl’s entry on al-Fārisī, R. Mercier’s entry on “Shams al-Bukhārī,” van Dalen’s entry on Wābkanawī (Hockey et al. 2014, pp. 699–700, 1986, 2273).

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Acknowledgements

I would like to express my very great appreciation to Prof. Benno van Dalen (Munich, Germany), to whom we owe our entire knowledge of Ibn al-Fahhād’s astronomical tradition after the late Prof. D. Pingree published the Greek translation of the ‘Alā’ī zīj in the 1980s. He showed me the scans of the unique manuscript of this work preserved in the Salar Jung Library in India. The historical ephemerides from the Islamic zījes used in this article have been computed with the aid of his very useful PC program “Historical Horoscopes.” Also, I would like to express my deep gratitude to Julio Samsó Moya (Spain), David A. King (Germany), James Evans, George Saliba, John Steele, Dennis Duke, and Noel Swerdlow (USA) for their constructive encouragement and support. This work was financially supported by the Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under research Project No. 1/6275-7.

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Mozaffari, S.M. Ibn al-Fahhād and the Great Conjunction of 1166 AD. Arch. Hist. Exact Sci. 73, 517–549 (2019). https://doi.org/10.1007/s00407-019-00232-0

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