This paper presents an analysis of the systematic astronomical observations performed by Muḥyī al-Dīn al-Maghribī (d. 1283 AD) at the Maragha observatory (northwestern Iran, ca. 1260–1320 AD) between 1262 and 1274 AD. In a treatise entitled Talkhīṣ al-majisṭī (Compendium of the Almagest), preserved in a unique copy at Leiden, Universiteitsbibliotheek (Or. 110), Muḥyī al-Dīn explains his observations and measurements of the Sun, the Moon, the superior planets, and eight reference stars. His measurements of the meridian altitudes of the Sun, the superior planets, and the eight bright stars were made using the mural quadrant of the observatory, and the times of their meridian transit using a water clock. The mean absolute error in the meridian altitudes of the Sun is ~ 3.1′, of the superior planets ~ 4.6′, and of the eight fixed stars ~ 6.2′. The clepsydras used by Muḥyī al-Dīn could apparently fix time intervals with a precision of ± 5 min. His estimation of the magnitudes of three lunar eclipses observed in Maragha in 1262, 1270, and 1274 AD is in close agreement with modern data.
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Sayılı  1988, pp. 187–223; some necessary corrections to Sayılı’s historical arguments have already been given in Mozaffari and Zotti 2013. It appears that the performance of astronomical observations in Maragha predates the foundation of the observatory there by around a century; in his treatise on the stereographic projection of the celestial sphere (the fundamental basis of the astrolabe), Ibn al-Ṣalāḥ al-Hamadhānī (d. 1153 AD) said that at Maragha he found a value of 23;35° for the obliquity of the ecliptic (see Lorch 2000, p. 401; Mozaffari and Zotti 2013, p. 51, note 10).
Īlkhānī zīj, T: Suppl. P: f. 31v.
This table has recently been analyzed; see Mozaffari 2016a. For the two star tables in the Mumtaḥan zīj and their relation to Ibn al-A‘lam (d. 985 AD), see Mozaffari 2016–2017.
Wābkanawī, Zīj, T: f. 89v, Y: f. 155r, P: 135r.
See Mozaffari 2013a.
Wābkanawī, Zīj, T: ff. 2r–v, 134v–135r, Y: ff. 2v–3r, 235v–236r, P: 2v–3r, ff. 205r–v.
Pingree 1985–1986, Vol. 1, Chapters 32–36: pp. 131–169.
In ‘Alā’ī zīj I.35 and I.36: pp. 30–35, Ibn al-Fahhād shows how to compute the parameters of the solar eclipse of 11 April 1176 and the lunar eclipse of 25 April 1176. On their accuracy, see Mozaffari and Steele 2015, pp. 347–348, note 17.
Pingree 1985–1986, Vol. 1, Chapters XVII–XXII: pp. 307–333.
Ibn al-Fuwaṭī, Vol. 5, p. 117. A quotation from Mālik b. Anas can be found in Muḥyī al-Dīn’s ‘Umdat, f. 24r (above the table of the anomaly of Saturn).
Of them, Ibn al-Fuwaṭī (Vol. 1, 146–147) mentions ‘Izz al-Dīn al-Ḥasan b. al-Shaykh Muḥammad b. al-Shaykh al-Ḥasan al-Wāsiṭī al-‘aṭṭār Shaykh Dār Sūsīyān.
See Suter 1900, p. 155; Brockelmann 1937–1942, Vol. 1, p. 626; 1943–1949, S1, p. 868; Sarton 1927–1948, Vol. 2, Part 2, pp. 1015–1016; Sezgin 1978, p. 292; Rosenfeld and İhsanoğlu 2003, p. 226. Some of his mathematical works were studied; e.g., see Hogendijk 1993. S. Tekeli’s short entry on al-Maghribī in DSB (Gillipsie et al., Vol. 9, p. 555) covers only his mathematical works. See, also, M. Comes’ entry in BEA (Hockey et al. 2007, pp. 548–549).
See Mozaffari 2017, p. 6.
On the basis of the date of a Ptolemaic star table found in it for the end of 630 Y/9 January 1262; al-Maghribī, ‘Umdat, f. 137r.
al-Maghribī, ‘Umdat, f. 1v.
See Mozaffari 2016a, p. 300.
Kamālī, Ashrafī zīj, F: ff. 231v, 232r, G: f. 248v; Kāshī, Khāqānī zīj, IO: f. 104r. Kāshī refers to Muḥyī al-Dīn as the sage/wise (ḥakīm).
Ibn al-Fuwaṭī, Vol. 5, p. 117.
Mozaffari and Zotti 2013 introduces all the indications of these terms, as found in the works written either during the lifetime of the Maragha observatory or afterward.
See Mozaffari 2016b.
Except, perhaps, for his value of 23;30° for the obliquity of the ecliptic, resulting from the measurements of the maximum and minimum annual solar noon altitudes performed on three successive days after the two dates of 12 June and 7 December 1264 (Sect. 4.1.1, nos. 1 and 2, Sect. 5.1, and Table 1); Muḥyī al-Dīn’s altitude values, 76;9,30° and 29;9,30°, strictly result in the value 23.5° for the obliquity of the ecliptic. In the Īlkhānī zīj (C: p. 203, T: f. 102v, P: f. 59v, M1: f. 104v, M2: f. 89v), al-Ṭūsī remarks that “on the basis of our observations, the obliquity of the ecliptic exceeds 23;30° by a small amount, and we estimated it to be 23;30°.” (The emphasis is added.) Also, in his Risāla fī kayfiyyat al-irṣād (The treatise on how to make [astronomical] observations) (P: f. 7v, N: f. 41r), al-‘Urḍī says that the same value was known from the continuous observations at Maragha.
al-Maghribī, Talkhīṣ, f. 2r.
Sayılı 1960 , p. 205.
al-Maghribī, Adwār, M: f. 55v.
al-Maghribī, Adwār, M: f. 124v.
Ibn al-Fuwaṭī, Vol. 5, p. 117.
The contents of the treatise were introduced in Saliba 1983. The computations related to the eccentricity of the Sun and of Jupiter were addressed in the two critical studies by G. Saliba (1985, 1986). For al-Maghribī’s solar theory, see Mozaffari 2013b, pp. 318, 330; 2018, esp. pp. 229, 235. For his lunar measurements, see Mozaffari 2014a.
Taqī al-Dīn’s only comment on Talkhīṣ can be found on f. 50v. On his observations, see Mozaffari and Steele 2015.
In Talkhīṣ III.11: ff. 49r–50v, Muḥyī al-Dīn explains in detail how to compute the ecliptic coordinates of a celestial body from its meridian altitude and the time of its meridian transit or from its altitude and azimuth.
Al-Maghribī, Talkhṣ, f. 31r.
Al-Maghribī, Talkhīṣ, f. 31r.
Al-Maghribī, Talkhīṣ, f. 58r.
Al-Maghribī, Talkhīṣ, f. 58r.
Al-Maghribī, Talkhīṣ, f. 59r; also, translated in Saliba 1985, p. 118.
Al-Maghribī, Talkhīṣ, f. 59r; also, translated in Saliba 1985, p. 118.
Al-Maghribī, Talkhīṣ, f. 59r; also, translated in Saliba 1985, pp. 118–119.
Al-Maghribī, Talkhīṣ, f. 60r.
Al-Maghribī, Talkhīṣ, f. 69v.
Al-Maghribī, Talkhīṣ, f. 69v.
Al-Maghribī, Talkhīṣ, f. 69v.
Al-Maghribī, Talkhīṣ, f. 69v.
Al-Maghribī, Talkhīṣ, f. 78v.
Al-Maghribī, Talkhīṣ, f. 85v.
Al-Maghribī, Talkhīṣ, ff. 111r–111v. All of the emphases in the quotations are ours.
Al-Maghribī, Talkhīṣ, f. 112r.
Al-Maghribī, Talkhīṣ, ff. 112r–112v.
Al-Maghribī, Talkhīṣ, f. 112v.
Al-Maghribī, Talkhīṣ, ff. 112v–113r.
Al-Maghribī, Talkhīṣ, f. 113r.
Al-Maghribī, Talkhīṣ, f. 113v.
Al-Maghribī, Talkhīṣ, ff. 113v–114r.
Al-Maghribī, Talkhīṣ, f. 123r.
Al-Maghribī, Talkhīṣ, f. 123r.
Al-Maghribī, Talkhīṣ, f. 123v.
Al-Maghribī, Talkhīṣ, f. 128r.
Al-Maghribī, Talkhīṣ, f. 128v.
Al-Maghribī, Talkhīṣ, f. 128v.
Al-Maghribī, Talkhīṣ, f. 132v.
Al-Maghribī, Talkhīṣ, ff. 132v.
Al-Maghribī, Talkhīṣ, f. 133r.
In the analysis of these observations, allowance should be made for atmospheric refraction and parallax, especially when a celestial body is setting, rising, or is at a low altitude. Maragha is 1550 m above sea level where the average atmospheric pressure is ~ 850 mbar. The changes in temperature at the different times are also taken into account, based on weather reports for the 2000 s. Throughout this paper, the true modern values are derived from the software Alcyone Ephemeris 4.3 which is well suited for historical investigations.
The modern times and magnitudes of the eclipses are based on Espanek and Meeus, NASA’s Five Millennium Catalog of Lunar Eclipses, nos. 07878, 07897, and 07907.
Making observations of this kind seems to have been a characteristic of planetary research ever since Antiquity (for Babylonian observations of the appulses of the planets to the stars, see Jones 2004). Even in the telescopic era, the astronomers found that “of all the celestial observations that have hitherto been made, none are so capable of perfect exactness, as the near appulses of the Moon and planets to the fixed stars” (Halley 1720–1721, p. 209).
E.g., Alī b. Amājūr’s single observations of Mercury and Venus with Antares on 24 December 918 and Mars with Procyon on 1 January 919 (Ibn Yūnus, Zīj, L: p. 99; Caussin 1804, pp. 108–111; Delambre 1819, p. 83) and periodic observations of Jupiter with Vega and Mars with Sirius from 13 July to 9 September 918 (Ibn Yūnus, Zīj, L: pp. 98–99; Caussin 1804, pp. 104–107; Delambre 1819, p. 83). The majority of other planetary observational records are the closeness of the planets to Regulus. Examples: A conjunction of Jupiter with Regulus was observed by Ḥabash on 6 September 864 (Ibn Yūnus, Zīj, L: p. 108; Caussin 1804, pp. 155–156; Delambre 1819, p. 87); Māhānī found Saturn 2/3° in longitude behind Regulus on 28 August 858 (Ibn Yūnus, Zīj, L: p. 96; Caussin 1804, pp. 94–97; Delambre 1819, p. 80); an occultation of Regulus by Venus on 10 September 885 (Ibn Yūnus, Zīj, L: p. 109, F1: f. 10r (the only observation of the Banū Amājūr that is mentioned in MS. F1 of the Ḥākimī zīj); Caussin 1804, pp. 157–158; Delambre 1819, p. 87) and a conjunction of Mars with Regulus on 20 September 909 (Ibn Yūnus, Zīj, L: p. 109; Caussin 1804, pp. 161–162; Delambre 1819, p. 89) were observed by Alī b. Amājūr; and eight conjunctions of Regulus with Venus and five with Mars were observed by Ibn Yūnus during 987–1002 AD (Ibn Yūnus, Zīj, L: pp. 113–120; Caussin 1804, pp. 179–211; Delambre 1819, pp. 90–92). The other two conjunctions of the planets with Regulus are reported by a thirteenth-century Yemenite astronomer, al-Kawāshī: Jupiter-Regulus on 5 October 1279 and Mars-Regulus on 16 June 1282 (see King and Gingerich 1982, pp. 124, 126–127).
Al-Maghribī, Talkhīṣ, f. 127r.
Muḥyī al-Dīn could determine the daily motion in longitude of a planet by deriving its longitudes from its horizontal coordinates measured at the same time on two successive nights, according to his method. From his values for the motional parameters and orbital elements of Saturn, the longitude of Saturn at noon on 2 and 3 October 1270 in Maragha were, respectively, 139;44,11° and 139;49,28° (modern: 139;39,55° and 139;45,11°); both sets of values result in a daily longitudinal motion of 0;5°.
Al-Maghribī, Talkhīṣ, f. 127r.
From Muḥyī al-Dīn’s parameter values, the longitudes of the planet at the noon of the two days 27 and 28 June 1271 were, respectively, 139;53,42° and 140;00,28° (modern: 140;7,57° and 139;14,28°).
Al-Maghribī, Talkhīṣ, f. 131v.
Ibn Yūnus, Zīj, L: p. 114; Caussin 1804, pp. 181–183.
Toomer  1998, p. 464.
See Clark and Stephenson 1977, p. 133; in the Planetary Hypotheses, Ptolemy presents Hipparchus’s estimates of the apparent diameters of the planets, in which the diameter of Jupiter at its mean distance from the earth is given as 1/12 of that of the sun (Goldstein 1967, p. 11). Some theoretical estimates of the other sort were proposed for the practical purposes in Islamic astronomy; for instance, a table for the angular diameters of the planets can be found in al-Fahhād’s ‘Alā’ī zīj (composed ca. 1172 AD), p. 182, which was also copied in Wābkanawī’s Zīj, T: f. 170v, the Ashrafī zīj, f. 92v, and the anonymous Sulṭānī zīj, f. 172v. The table gives the diameters for the true epicyclic anomaly of the planets at the mean distance of the center of the epicycle from the Earth. The tabular values for the diameter of Jupiter run from a minimum of 2′ 56″ to a maximum of 4′ 21″.
Al-Maghribī, Talkhīṣ, f. 135r.
See Mozaffari and Zotti 2013, p. 82.
Al-‘Urḍī was aware of the fact that the smallest subdivision marked off on an instrument, easily readable by an unaided eye, should correspond to a length of ~ 1 mm. In his description of the solstice armilla (“Two Circles” in Almagest I.12: Toomer  1998, pp. 61–62), al-‘Urḍī makes an interesting remark about the subdivisions, which confirms our estimation; its inner diameter is equal to 5 cubits (about half of the diameter of the mural quadrant) and 4 fingers in both width and thickness: “If the diameter of the smallest circle drawn on the two [lateral] surfaces of the ring is equal to 5 cubits, the circumference of the greatest of these circles will not be less than 16 2/3 cubits. Thus, 1/16 of it becomes greater than 3 spans [NB: 1 cubit = 3 spans, as also noted by al-‘Urḍī in the description of the mural quadrant; al-‘Urḍī, Fī kayfiyyat al-irṣād, P: f. 3r, N: f. 38v], which contains 22.5° of the circumference of a great circle; each degree becomes larger than one finger, and thus it will be possible to divide it into 60 parts or 30 distinct parts (al-‘Urḍī, Fī kayfiyyat al-iṣād, P: f. 11r, N: f. 43v).” By an outer diameter of 5 cubits + 4 fingers (~ 210.58 cm), the circumference of the ring amounts to ~ 16.23 (≈ 16 1/4) cubits (~ 1079.40 cm), and thus, each 1° corresponds to a length of around 1.1 fingers (~ 3.0 cm) on it; consequently, in al-‘Urḍī’s estimate, a distance of 30 mm can be subdivided to 30 “distinct” parts.
For the figures of it, see Sezgin and Neubauer 2010, Vol. 2, p. 31.
Ibn al-Fuwaṭī, Vol. 4, pp. 413–414; the poem reads:
A tentative translation of it is as follows. “I am a quadrant of the circle of the orb./Good for everyone such as me as an angel!/By me the times are known truly/and securely, without any doubt.”
Noted earlier in Saliba 1985, p. 115.
The solar noon altitudes at Maragha on 7–14 December 1264 were as follows (rounded to 30″):
7: 29;15,30° 9: 29;10,30° 11: 29; 7, 0° 13: 29; 5,30° 8: 29;12,30 10: 28; 8,30 12: 29; 6, 0° 14: 29; 6, 0°
Al-‘Urḍī, Fī Kayfiyyat al-irṣād, P: ff. 15r–17v, N: ff. 45v–47v; Seemann 1929, pp. 72–81. This instrument consisted of the two quadrants pivoted on an iron axis, which could move freely on a circular wall. The altitude was determined by the quadrants and the azimuth was read from a graduated copper ring installed on the top of the wall. The other two instruments could be used to simultaneously measure the horizontal coordinates of the two celestial objects with the diametrically opposed azimuths. The last instrument may only have been used to measure the altitude and azimuth of one object at a given time; of course, al-‘Urḍī does not mention that he constructed it at the Maragha observatory. Al-‘Urḍī, Fī Kayfiyyat al-irṣād, P: ff. 19v–25r, N: ff. 48v–52v; Seemann 1929, pp. 87–88, 92–104. For a reconstruction of these instruments, see Sezgin and Neubauer 2010, Vol. 2, pp. 44, 46–51.
Drawn on the basis of the formula given in Meeus 1998, p. 106.
Al-Jazarī 1973, p. 17.
See Al-Ṣufī 1995, chapters 354–357: pp. 299–302.
Pingree 1973, pp. 3–4. It is highly probable that Babylonians used clepsydras for astronomical purposes, e.g., to determine the times of eclipses (Stephenson 1997, p. 59). On Babylonian clepsydras, see esp. Neugebauer 1947; Michel-Nozières 2000. Indian sources, for example, Súrya Siddhánta XIII.23 ( 1997, p. 264;  1974, p. 91) refer to this type of clepsydra. For more details, see Sarma 1994a, b, pp. 512–514, 2001, p. 54; and especially Sarma 2004; Sharma 2000, pp. 241–243; Ōhashi 2008; Pandey 2011; and other articles cited therein.
See Bīrūnī 1910, Vol. 1, pp. 337–338.
See Cullen 1996, p. 42; Stephenson 1997, chapter 9.
Stephenson 1997, p. 278.
Needham 1981, p. 136; more on Chinese clepsydras can be found in the classic study Needham et al. 1986, chapters 6 and 7. The best example of the compound mechanism of Chinese clepsydras is Su Song’s water-powered mechanical clock implemented with an escapement regulator from about 1088 AD (cf. Yan 2007, pp. 163–198; 2009).
Hill 2008, p. 130. E.g., Pseudo-Archimedes’s On the construction of water clocks is preserved in an Arabic translation (Archimedes 1976; Sezgin and Neubauer 2010, Vol. 3, pp. 94–95), and the names of al-Jazarī’s three clocks (“peacock,” “man,” and “monkey”) are also mentioned in Súrya Siddhánta XIII.21 ( 1997, pp. 263–264;  1974, p. 90). For illustrations of some Islamic clepsydras, see Sezgin and Neubauer 2010, Vol. 3, chapter 4.
al-Khāzinī, Kayfiyyat al-i‘tibār, in Zīj, V: ff. 6r–7r. The other four instruments are the alidade, the triquetrum, the dioptra, and the triangle. See also the following note.
The use of sand instead of water is seen in the automatic celestial globe invented by al-Khāzinī, about one century later, in which a sand reservoir provided the power required for the rotation of the globe (see Lorch 1980). Sand clocks are also mentioned in Súrya Siddhánta XIII.21 and 22 ( 1997, pp. 263–4;  1974, pp. 90–91).
al-Bīrūnī 1967, pp. 155–156 (with a change in the translation: in the first sentence, “care and attention” has replaced “precision,” which may be somewhat misleading).
Toomer  1998, p. 252; Ptolemy, Tetrabiblos  1956, p. 231. The method of measuring the Sun’s apparent diameter using the clepsydra was to count how many times the vessel of clepsydra is filled during the time from one sunrise to the next. The Egyptian value 750, for example, corresponds to the Sun’s angular diameter being equal to 1/750 part of its entire orbit, i.e., 28′ 48″ (see Neugebauer 1975, Vol. 2, pp. 865–868).
al-Jazarī 1973, pp. 17–82.
In mid-latitudes and for mid-altitudes, these measurements might be precise to some 5–6 min (Stephenson 1997, p. 466).
Wābkanawī, Zīj, T: ff. 92r–v, Y: ff. 159r–160r, P: ff. 139r–140r. The passage in question can also be found in the Ghāzānid treatise on observational instruments, written ca. 1294–1305 AD (see Sects. 5.3 and 6). In it, the time-measuring device is called the “time glass” (shīsha-i sā‘at) (see Mozaffari and Zotti 2012, pp. 419–421; 2013, pp. 128–130). Interestingly, in the seventeenth century, European astronomers still preferred to time eclipses by measuring altitudes rather than by relying on mechanical clocks (Stephenson and Said 1991, p. 207, note 26).
See Sivin 2009, chapter 5, esp. pp. 174–176 and Appendixes A and B.
It seems that he introduced the Chinese-Uighur calendar incorporated in Īlkhānī zīj, which is also found in Persian zījes from the Mongol period onwards (see van Dalen et al. 1997).
E.g., see Makovicky 1992.
The basic idea has been taken from Morrall 2009.
Toomer  1998, p. 56.
Wābkanawī, Zīj, T: ff. 92r–v, Y: ff. 159r–v, P: ff. 139r–v. For the measurement of the apparent angular diameter of the Moon and the magnitude of lunar eclipses, Wābkanawī recommends the use of an instrument called dhāt al-misṭaratayn, “having two rulers,” which is also used to measure the angular distance of the two heavenly bodies near their conjunction/occultation (Wābkanawī, Zīj IV.15.7,9: T: ff. 91r–92v, Y: ff. 158r–160r, P: ff. 138r–140r).
See above, note 77.
See Mozaffari 2018, esp. pp. 229, 235.
al-Maghribī, Talkhīṣ, f. 117r, corresponding to Toomer  1998, p. 423: lines 10–13.
Smith 1996, p. 241: “when the star rises to position H [= a point on the meridian], it reaches a point where the visual ray is refracted without any perceptible difference between apparent and true location.”
Al-Maghribī, Talkhīṣ, ff. 94r–v. He does not identify the book on optics he has in mind. The inverse relation between the distance and apparent diameter is discussed, e.g., in Ibn al-Haytham’s Optics II.3 (Vol. 1, pp. 273–295; Smith 2001, Vol. 1, pp. 164–191, Vol. 2, pp. 475–494).
A problem arises from the fact that in Talkhīṣ VII.4 (f. 117r), Muḥyī al-Dīn quotes a passage from Almagest IX referring to the difference in the angular distance of two heavenly objects between the horizon and near the zenith (Toomer  1998, p. 421). In the other parallel passage in Almagest I.3 (Toomer  1998, p. 39), Ptolemy refers to a similar phenomenon, that is, the enlargement of the apparent diameters of the Sun and Moon in the vicinity of the horizon; there he treats the problem as the effect of the atmospheric refraction, but later in Planetary Hypotheses I (Goldstein 1967, pp. 9, 34–35) and Optics III.59 (Smith 1996, p. 151), explains it as merely an optical illusion. This is relevant to the problem mentioned above of the angular separation of two celestial bodies near the horizon (also, see Goldstein 1997, p. 5); if the relation between the enlargement of the Luminaries and the increase in the angular distance between two objects near the horizon was correctly understood, the latter would no longer be referred to as an observational fact. Muḥyī al-Dīn does not seem to have seen any clear relation between them. Interestingly, in his Taḥrīr al-majisṭī, al-Ṭusī does not comment upon either of the passages from the Almagest in question (P1: pp. 5, 284, P2: f. 82v, P3: ff. 18v, 107v).
Lawkarī was a peripatetic philosopher who wrote an encyclopedia entitled Bayān al-ḥaqq bi-ḍimān al-ṣidq, including an epitome of Ptolemy’s Almagest, which was well known to the later Islamic astronomers (e.g., Quṭb al-Dīn al-Shīrāzī referred to it in the prologue on astronomy of his Durrat al-tāj li qurrat al-Dibāj; see al-Shīrāzī 1944, Vol. 2, p. 1); however, the surviving manuscripts and published editions of this work do not contain its astronomical part. A chapter from it, dealing with al-Lawkarī’s invented instrument, has been partially preserved in MS. Utrecht, Universiteitsbibliotheek, 1442, pp. 23–26, titled “On the description of the instrument making unnecessary [the use of] the armillary sphere and of the method (ṭarīqa) by which it becomes possible to attain knowledge of the position of any star investigated without the use of the armillary sphere.” In it, the Book on [astronomical] observations (Kitāb al-irṣād) is attributed to al-Lawkarī, and he also mentions that he had already written a treatise on the instrument in question; neither work is extant today. The detailed description of the instrument is missing from the Utrecht MS, but this text is very likely the source of al-Marrākushī (d. 1262 AD) in his Jāmi‘al-mabādī wa-’l-ghāyāt II.7.7 (I: pp. 116–119, N: ff. 155r–156r, P: ff. 207r–v), in which he describes al-Lawkarī’s instrument in the category of observational instruments: It consists of a single azimuthal ring, an altitudinal quadrant of another ring of the same diameter, both made of copper, and an alidade with two pinnulas with tiny holes. The azimuthal ring is installed on a round, hollow booth (dakka) on a steady flattened horizontal ground. The quadrant is installed in a cross (ṣalīb) which is erected in the center of the circular wall, in such a manner that the cross smoothly rotates in the hollow inside the azimuthal ring and the quadrant steadily and smoothly rotates on its circumference toward any direction. It is worth noting that as he himself clarifies, al-Marrākushī’s source for the description and application of the armillary sphere in Jāmi‘al-mabādī wa-’l-ghāyāt II.7.5,6 (I: pp. 113–116, N: ff. 154r–155r, P: ff. 206r–207r) was also al-Lawkarī’s al-Bayān.
al-Khāzinī, Kayfiyyat al-i‘tibār, in Zīj, V: ff. 4v–5r. This treatise comes as an introduction to his zīj, in which Khāzinī deals with the principal features of observational astronomy and explains the technical experiments for testing and re-measuring the astronomical quantities and parameter values from a methodologically consistent point of view.
al-Khāzinī, Kayfiyyat al-i‘tibār, in Zīj, V: ff. 6r–7r.
al-‘Urḍī, Fī Kayfiyyat al-irṣād, P: f. 15r, N: f. 45v.
al-Maghribī, Talkhīṣ, f. 114v. The declinations of Vega and Capella were, respectively, about +44;51.5° and +38;17.5° at the time, and both thus transited the meridian of Maragha in its northern half. The non-Ptolemaic star table of Īlkhānī zīj includes the ecliptical coordinates of both Vega and Capella.
See Mozaffari 2016a.
Said and Stephenson 1995, pp. 122–123, 125, and 129–130.
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A detailed study of the early Islamic planetary observations recorded in Ibn Yūnus’s Ḥākimī zīj (see above, note 65) is under preparation by the author.
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The author wishes to thank Benno van Dalen (Germany), Julio Samsó Moya (Spain), James Evans, George Saliba, John Steele, and Noel Swerdlow (USA) for their encouragement. This work was financially supported by the Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under research project No. 1/5750–5.
Communicated by Noel M. Swerdlow.
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Mozaffari, S.M. Astronomical observations at the Maragha observatory in the 1260s–1270s. Arch. Hist. Exact Sci. 72, 591–641 (2018). https://doi.org/10.1007/s00407-018-0217-z