Papers by Seyyed Mohammad Mozaffari
Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation, 2015
This paper deals with an optical aid named barbakh that Abū al-Ray¬ān al-Bīrūnī (973–1048 AD) pro... more This paper deals with an optical aid named barbakh that Abū al-Ray¬ān al-Bīrūnī (973–1048 AD) proposes for facilitating the observation of the lunar crescent in his al-Qānūn al-Mas‘ūdī VIII.14. The device consists of a long tube mounted on a shaft erected at the centre of the Indian circle, and can rotate around itself and also move in the vertical plane. The main function of this sighting tube is to provide an observer with a darkened environment in order to strengthen his eyesight and give him more focus for finding the narrow crescent near the western horizon about the beginning of a lunar month. We first briefly review the history of altitude-azimuthal observational instruments, and then present a translation of Bīrūnī’s account, visualize the instrument in question by a 3D virtual reconstruction, and comment upon its structure and applicability.
Journal of the British Astronomical Association, 2013
Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation, 2016
The table of 24 stars in one of the two extant manuscripts of the Mumtaḥan zīj is the earliest no... more The table of 24 stars in one of the two extant manuscripts of the Mumtaḥan zīj is the earliest non-Ptolemaic star table in medieval Middle Eastern astronomy. Dated to 829 AD, it is a fruit of the two systematic observational programs carried out by a group of astronomers in Baghdad and Damascus in the early ninth century. In this study, the accuracy of this table is examined, showing the existence of an obvious systematic negative error in the longitude values. The manuscripts also contain another table of 18 stars, all of which also appear in the first table, in which the longitudes are updated for 1011 AD. This table is further updated for 1231 AD in the Īlkhānī zīj, the official product of the observational programs in the Maragha observatory, northwestern Iran, in the 1260s, where it is ascribed to Ibn al-A‘lam (d. 985 AD). In this paper, some verifiable and convincing proofs are provided for the hypothesis that the second Mumtaḥan star table is quite probably a refinement of th...
Journal for the History of Astronomy, 2020
The observatory of Ulugh Beg, erected in Samarqand in the 1420s, represents the culmination in th... more The observatory of Ulugh Beg, erected in Samarqand in the 1420s, represents the culmination in the development of astronomical observatories in the Islamic world. After its rediscovery and excavation in the early twentieth century there have been several attempts to reconstruct its appearance and explain how it worked in detail, based on archaeological finds and the analysis of relevant manuscripts. A new look at illustrated copies of an important manuscript provides new, hitherto unmentioned details to the understanding of this instrument. Based on previous reports, we have created a virtual reconstruction of the observatory and the new version of the instrument, from which we have gained new insights.
Archive for History of Exact Sciences, 2019
Farīd al-Dīn Abu al-Ḣ asan 'Alī b. al-Fahhād's astronomical tradition as represented in the prole... more Farīd al-Dīn Abu al-Ḣ asan '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.
Archive for History of Exact Sciences, 2018
This paper presents an analysis of the systematic astronomical observations performed by Muh. yī ... more This paper presents an analysis of the systematic astronomical observations performed by Muh. yī 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 Talkhīs. al-majist .ī (Compendium of the Almagest), preserved in a unique copy at Leiden, Universiteitsbibliotheek (Or. 110), Muh. yī 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 Muh. yī 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. 3 Muh. yī al-Dīn al-Maghribī Little is known about Muh. yī al-Dīn except that, according to Ibn al-Fuwat .ī , the librarian of the Maragha observatory, his full name was Muh. yī al-Dīn Abu al-Shukr Yah. yā b. Muh. ammad b. Abī al-Shukr b. H. amīd al-Tūnisī (of Tunis) al-Maghribī (of the Maghrib). Muh. yī al-Dīn had learned Islamic jurisprudence (fiqh), according to the Mālikī school, in his native city. He spent some years in the service of al-Sult .ā n al-Malik al-Nās. ir Yūsuf b. al-'Azīz b. Ghāzī b. al-Malik al-Nās .
Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation, 2019
Muḥyī al-Dīn al-Maghribī (d. 1283 AD) carried out a systematic observational programme at the Mar... more Muḥyī al-Dīn al-Maghribī (d. 1283 AD) carried out a systematic observational programme at the Maragha observatory in northwestern Iran in order to provide new measurements of solar, lunar, and planetary parameters, as he explains in his treatise Talkhīṣ al-majisṭī (Compendium of the Almagest). His project produces a new and consistent set of parameters. On the basis of his four documented observations of Mars, carried out in 1264, 1266, 1270, and 1271 AD, he measured the unprecedented values for the radius of the epicycle, the longitude of the apogee, and the mean motion in longitude of the planet and also confirmed that Ptolemy's value for its eccentricity was correct for his time. This paper presents a detailed, critical account of Muḥyī al-Dīn's measurements. Using a criterion described below, we compare the accuracy of his values for the structural parameters of Mars with that of other historically important values known for these parameters from medieval Middle Eastern astronomy from the early eighth to the late fifteenth century. Muḥyī al-Dīn attained a higher degree of precision in his theory of Mars established at Maragha than the majority of his predecessors; the results were also more accurate than those established in his earlier zīj written in Damascus in 1258 AD and used in the official astronomical tables produced at the Maragha observatory, the Īlkhānī zīj.
Journal for the History of Astronomy, 2019
The orbital elements of each planet are the eccentricity and the direction of the apsidal line of... more The orbital elements of each planet are the eccentricity and the direction of the apsidal line of its orbit defined by the ecliptic longitude of either of its apses, i.e., the two points on its orbit where the planet is either furthest from or closest to the Earth, which are called the planet’s apogee and perigee. In the geocentric view of the solar system, the eccentricity of Venus is a bit less than half of the solar one, and its apogee is located behind that of the Sun. Ptolemy correctly found that the apogee of Venus is behind that of the Sun, but determined the eccentricity of Venus to be exactly half the solar one. In the Indian Midnight System of Āryabhaṭa (b. ad 476), the eccentricity of Venus is assumed to be half the solar one, and also the longitudes of their apogees are assumed to be the same. This hypothesis became prevalent in early medieval Middle Eastern astronomy (ad 800–1000), where its adoption resulted in large errors of more than 10° in the values for the longit...
Archive for History of Exact Sciences, 2018
From Antiquity through the early modern period, the apparent motion of the Sun in longitude was s... more From Antiquity through the early modern period, the apparent motion of the Sun in longitude was simulated by the eccentric model set forth in Ptolemy's Almagest III, with the fundamental parameters including the two orbital elements, the eccentricity e and the longitude of the apogee λ A , the mean motion ω, and the radix of the mean longitudeλ 0. In this article we investigate the accuracy of 11 solar theories established across the Middle East from 800 to 1600 as well as Ptolemy's and Tycho Brahe's, with respect to the precision of the parameter values and of the solar longitudes λ that they produce. The theoretical deviation due to the mismatch between the eccentric model with uniform motion and the elliptical model with Keplerian motion is taken into account in order to determine the precision of e and λ A in the theories whose observational basis is available. The smallest errors in the eccentricity are found in these theories: the Mumtah. an (830):
Journal for the History of Astronomy, 2013
(ProQuest: ... denotes formulae omitted.)In the Ptolemaic models for the superior planets and Ven... more (ProQuest: ... denotes formulae omitted.)In the Ptolemaic models for the superior planets and Venus, the centre of the epicycle is located on a circle (the so-called deferent), the centre of which is displaced from that of the Earth by an eccentricity e, but its motion is uniform with respect to the so-called equant point, removed from the Earth by an eccentricity 2e from the Earth on the side of the centre of the deferent. The derivation of the planet's orbital elements (eccentricity and direction of the apsidal line) requires observations of three oppositions of the planet to the mean sun, when the planet points to the centre of epicycle. A difficulty arises since the angles of mean motion of the planet between two successive mean oppositions are known with respect to the equant point while the angles of the true motions between two consecutive mean oppositions are measured with respect to the Earth, the centre of the deferent being located exactly between the two. Ptolemy, in the Almagest (X.7, XI. 1 , XL5), explains an iterative algorithmic solution for finding the two parameters.1N. M. Swerdlow, in 1987, published a detailed analysis of another method proposed by Jabir b. Aflah of Seville (fl. the first quarter of the twelfth century), based on the Latin translation of his Islah al-majisfi (Improvement of the Almagest), made by Gerard of Cremona in 1 175. The method is a theoretical alternative to Ptolemy's method, but, as Swerdlow shows, it is practically inapplicable.2 1 will here call it the "four-point method", because it makes use of four oppositions of the planet with the mean sun. Hitherto it has remained unnoticed that this method is already found in al-Qanun al-mas'udi of Abu al-Rayhan al-Biruni (973-1 048), 3 composed about one century earlier (apparently, during the reign of Mas 'Ud I, the ninth ruler of the Ghaznavid dynasty of Iran, 1030-41). What follows is a complete description of the method as explained by Biruni supplied with some mathematical explanations.Biruni states that Ptolemy was able to determine the eccentricity and the direction of the apsidal Une of a superior planet by seeking out four oppositions of the planet with the mean sun satisfying the condition below. Figure 1, as drawn in the edited text of al-Qanun with the original lettering (except those bearing primes) transcribed according to the standard proposed by E. S. Kennedy,4 shows the deferent ABCGK of the planet about the centre D; E represents the Earth and T, the centre of uniform motion, the equant [point]. TE is then the eccentricity of the equant [point] and DE, that of the deferent; in the Ptolemaic context, TE = 2DE = 2e. In the four mean oppositions, the planet and thus the centre of the epicycle are located, respectively, at the points A, B, G, and K. Our author first explains the essential condition in the application of the method: the difference between the true longitudes of the planet in each pair of oppositions (A-B and G-K) should be identical: angle AEB = angle GEK. The trajectories travelled by the epicycle's centre on the deferent in each pair of oppositions should also be identical (arc AB = arc GK) so that the mean motions of the planet in each pair of oppositions are equal: angle ATB = angle KTG. These conditions may be formulated as follows: in the two pairs of oppositions, the planet's centre of the epicycle describes the equal arcs, AB and GK, in equal periods of time. Biruni adds that "what we mentioned is the property of the two arcs on the deferent equidistant from the diameter of the deferent passing through the apogee and perigee". Then the point C that marks one of the two apses (here, the apogee) is at the middle of the arc BG between the two arcs AB and GK (the point O, diametrically opposed to C, is then the perigee). Our author had already proved (al-Qanun VL8)5 the two particular theorems treating of the relation between the true motion in longitude and the corresponding equation of centrum in the solar eccentric orbit. …
Journal for the History of Astronomy, 2016
The Īlkhānī zīj compiled by Naṣīr al-Dīn al-Ṭūsī and his colleagues in the first period of the as... more The Īlkhānī zīj compiled by Naṣīr al-Dīn al-Ṭūsī and his colleagues in the first period of the astronomical activities (the 1260s and early 1270s) in the Maragha observatory includes a star table collecting important observations of Islamic astronomers from the early ninth century through the third quarter of the thirteenth century, including the Mumtaḥan astronomers, Ibn al-A‘lam, Ibn Yūnus, as well as the Maragha astronomers themselves. This table gives the ecliptical coordinates of 18 bright stars in comparison with Ptolemy’s corresponding values. This medieval bright star table is especially interesting for two reasons: first, it provides reliable evidence for the examination of the accuracy of the observations made and the instruments employed (notably, an armillary sphere) in the Maragha observatory. Second, it facilitates a comparative study of the accuracy of stellar observations in medieval Middle Eastern astronomy in the period in question. We have obtained the result that...
Archive for History of Exact Sciences, 2016
Some variants in the materials related to the planetary latitudes, including computational proced... more Some variants in the materials related to the planetary latitudes, including computational procedures, underlying parameters, numerical tables, and so on, may be addressed in the corpus of the astronomical tables preserved from the medieval Islamic period (zīj literature), which have already been classified comprehensively by Van Dalen (Current perspectives in the history of science in East Asia. Seoul National University Press, Seoul, pp 316–329, 1999). Of these, the new values obtained for the planetary inclinations and the longitude of their ascending nodes might have something to do with actual observations in the period in question, which are the main concern of this paper. The paper is in the following sections. In the first section, Ptolemy’s latitude models and their reception in Islamic astronomy are briefly reviewed. In the next section, the medieval non-Ptolemaic values for the inclinations and the longitudes of the nodal lines are introduced. The paper ends with the discussion and some concluding remarks. The derivation of the underlying inclination values from the medieval planetary latitude tables and determining the accuracy of the tables are postponed to “Appendix” in the end of the paper.
Archive For History of Exact Sciences, 2014
Archive for History of Exact Sciences, 2015
This paper analyses a kinematic model for the solar motion by Quṭb al-Dīn al-Shīrāzī, a thirteent... more This paper analyses a kinematic model for the solar motion by Quṭb al-Dīn al-Shīrāzī, a thirteenth-century Iranian astronomer at the Marāgha observatory in northwestern Iran. The purpose of this model is to account for the continuous decrease of the obliquity of the ecliptic and the solar eccentricity since the time of Ptolemy. Shīrāzī puts forward different versions of the model in his three major cosmographical works. In the final version, in his Tuḥfa, the mean ecliptic is defined by an eccentric of fixed mean eccentricity and a mean obliquity fixed with respect to the celestial equator, and the center of the epicycle, which is inclined to the eccentric, moves on the eccentric with an annual period. By an additional slow motion of the sun on the epicycle, the true eccentricity of the solar deferent, defined by the annual motion of the sun, and the sun’s extreme declination from the equator change, accounting for the reduction of the eccentricity and the obliquity of the ecliptic since the time of Ptolemy.
Astrophysics and Space Science Proceedings, 2014
This study deals with considerations on the angular diameters of the Sun and Moon in ancient and ... more This study deals with considerations on the angular diameters of the Sun and Moon in ancient and medieval astronomy and focuses on their role in predicting the existence of annular eclipses. Historical reports of annular eclipses probably date back to the ancient Greeks. From that period there are some documented theoretical considerations about the angular diameters of the Sun and Moon, implying the possible existence of annular eclipses. Nevertheless, according to the Ptolemaic context, since the minimum angular diameters of the Sun and Moon were considered to be equal, there was no justifiable basis for annular eclipses. During the medieval Islamic period, some observational evidence, including annular eclipses in AD 873 and 1283, and a total solar eclipse in AD 876 in which the Sun was completely covered for an unusually long interval, led to attempts by the astronomers of the time to revise Ptolemaic ideas, and come up with acceptable alternatives. Accordingly, non-Ptolemaic ideas concerning the angular diameters of the Sun and Moon were adopted from Indian astronomy, inserted into the Ptolemaic model, and eventually transferred to European astronomy. Finally, by the late medieval period a ‘bright ring eclipse’ had become an accepted term for one of the three types of solar eclipses––the others being total and partial. With the progress of astronomy, the discussion of annular eclipses was back on the agenda whenever the idea of homocentric models arose, and were used to reveal their glaring deficiencies.
Trames. Journal of the Humanities and Social Sciences, 2012
This paper is based on the assumption that the 'egocentric perspective' of the human mind acted a... more This paper is based on the assumption that the 'egocentric perspective' of the human mind acted as an efficient psychological factor for evolving the astrological doctrines. We adopt a psychological approach to studying the relation between historicalsocial events and the astrological doctrines in the medieval period. In its focus, this study deals with the two celestial phenomena observed in the Middle East from the beginning of the 14th century to that of the 15th one, where astrological interpretations or the prognostications had political, social and historical effects. The examples have been selected from the primary historical sources. They are Comet 1402 D1 and the unordinary conjunctions between Mars and Saturn. Considering them in various contexts, it is shown how those phenomena were 'the cause of anthropocentric historical events' such as wars, or identified as 'the justifier of social or natural accidents' like epidemics. The explanation of the role astrology played in such events, in particular, and its impact upon societies, in general, must be sought in the psychical effect caused by the astrological ideas on the human mind and its relation with the physical world. We conclude that as the human egocentric mind was a main cause of the formation of astrology, astrology itself penetrated into the consciousness of the human mind and objectively appeared in the physical world, and therefore conducted history in a specific direction. It is shown that this effect was so extended to give birth to the astrological history. In addition, having classified the four ways of interpreting the celestial phenomena in the ancient-medieval period (meteorological/weather prognostication, natural philosophical, meteorological/atmopheric, astrological), we briefly noticed the situation of the astrological dogma in Islam and the methodological distinction between astrology and astronomy by Avicenna in that period.
This paper deals with the analysis of data obtained from observations of two sets of three lunar ... more This paper deals with the analysis of data obtained from observations of two sets of three lunar eclipses in the Late Medieval Islamic Period. The first trio consists of the lunar eclipses of 7 March 1262, 7 April 1270 and 24 January 1274, observed by Muḥyī al-Dīn al-Maghribī from the Maragha Observatory (in northwestern Iran), and the second includes those of 2 June and 26 November 1406, and 22 May 1407, observed by Jamshīd Ghiyāth al-Dīn al-Kāshī from Kāshān (in central Iran). The results are that al-Maghribī"s values for the magnitudes of these eclipses agree excellently with modern data, and his values for the times when the maximum phases occurred agree to within five minutes with modern values. Al-Kāshī"s values for the times of the maximum phases show a rather larger divergence from modern data, varying from about ten minutes to about one hour. The errors in all six values both astronomers computed from their own solar parameters for the longitude of the Sun at the instant of the opposition of the Moon to the Sun in these eclipses remain below ten minutes of arc. The motivation for doing these observations was to measure the lunar epicycle radius r in the Ptolemaic model. Al-Maghribī achieved r = 5;12 and al-Kāshī r ≈ 5;17, 1 in terms of the radius of an orbit of R = 60 arbitrary units. It is argued that comparing with modern theory, neither of these two medieval values can be considered an improvement on Ptolemy"s value of r = 5;15.
Journal for the History of Astronomy, 2014
Ptolemy's complete lunar model in Almagest V produces a large variation of distance of the ce... more Ptolemy's complete lunar model in Almagest V produces a large variation of distance of the centre of the epicycle, between its maximum at mean conjunction and opposition to the mean position of the Sun and its minimum at mean quadrature, so that the resulting path of the centre of the epicycle about the Earth is an oval figure. In Figure 1, with the Earth at T, the centre of the epicycle L moves uniformly about T on an eccentric of radius R with centre E and apogee A, through the mean elongation from the mean position of the Sun S in the direction of increasing longitude, while the apsidal line of the eccentric rotates in the opposite direction through the same mean elongation. Consequently, L reaches the apogee A and perigee B of the eccentric twice in each mean synodic month, which produces the oval path, farthest from the Earth at mean conjunction and opposition, closest at mean quadrature. The Moon M moves on the epicycle of radius r in the direction opposite to the motion of L through the mean anomaly, completed in an anomalistic month, uniformly with respect to the mean apogee F, which has an 'inclination' (pmsneusis) toward a point P, opposite to the direction of F from the Earth and with the same eccentricity, e = PT = TE.1 The true apogee G lies on the line TEG from the Earth. Our concern here is the path described by the variable distance of the lunar epicycle from the Earth p = TL. At mean conjunction and opposition, p = EA + ET=R + e and at mean quadrature p = EA - ET = R - e. The figure has been drawn using historical values due to Muhyi al-Din al-Maghrib! (d. 1283) of the Maragha Observatory in north-western Iran, where R + e = 60, R = 51,e = 9, and r = 5;12.2 Thus at conjunction and opposition p = R + e = 60 and at quadrature p = R - e = 42.Ptolemy, as Pedersen remarks, "always conceives the motion of the lunar epicycle centre as a circular motion around the moving centre of the deferent. He never asks for the orbit described by the lunar epicycle centre relative to the centre of the Earth."3 Abu al-Rayhan al-Biruni (973-1048) in his al-Qanun al-mas'udi VII.7.14 considers this problem in the form of question and answer. The translation of the relevant passage is as follows:Q: What [shape] does its [i.e., the Moon's] epicycle centre describe by this motion [i.e., according to Ptolemy's model of a movable eccentric]?A: If it is assumed that the Sun is at rest and if the lunar epicycle centre is at its orb's apogee in its [mean] conjunction or opposition [to the Sun] and is at the perigee in its [mean] quadrature, it will describe a rounded rectangular shape by its motion. It might be thought that it [i.e., the path of the epicycle centre] is an ellipse of the [right circular] conic or cylindrical sections. [But,] it is not so.Take the Moon's orb
Historia Mathematica, 2013
The paper presents a critical review of the iterative process used by Shams al-Dīn Muh. ammad al-... more The paper presents a critical review of the iterative process used by Shams al-Dīn Muh. ammad al-Wābkanawī (Iran, Maragha, ca. 1270-1320) in order to compute the annular solar eclipse of 30 January 1283 from the solar and lunar parameter values obtained by Muh. yī al-Dīn al-Maghribī (Maragha, 1260-1274). The position of this prediction in medieval astronomy will also be discussed. Wābkanawī uses an observation as evidence for the correctness of his prediction, and his results agree to a remarkable extent with modern astronomical computations of the same eclipse.
Journal for the History of Astronomy, 2013
The present paper deals with the methods proposed and the values achieved for the eccentricity an... more The present paper deals with the methods proposed and the values achieved for the eccentricity and the longitude of apogee of the (apparent) orbit of the Sun in the Ptolemaic context in the Middle East during the medieval period. The main goals of this research are as follows: first, to determine the accuracy of the historical values in relation to the theoretical accuracy and/or the intrinsic limitations of the methods used; second, to investigate whether medieval astronomers were aware of the limitations, and if so, which alternative methods (assumed to have a higher accuracy) were then proposed; and finally, to see what was the fruit of the substitution in the sense of improving the accuracy of the values achieved. In Section 1, the Ptolemaic eccentric orbit of the Sun and its parameters are introduced. Then, its relation to the Keplerian elliptical orbit of the Earth, which will be used as a criterion for comparing the historical values, is briefly explained. In Section 2, three standard methods of measurement of the solar orbital elements in the medieval period found in the primary sources are reviewed. In Section 3, more than twenty values for the solar eccentricity and longitude of apogee from the medieval period will be classified, provided with historical comments. Discussion and conclusions will appear in Section 4 (in Part 2), followed there by two discussions of the medieval astronomers' considerations of the motion of the solar apogee and their diverse interpretations of the variation in the values achieved for the solar eccentricity.
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Papers by Seyyed Mohammad Mozaffari