This paper presents an analysis of the systematic astronomical observations performed by Muḥyī al-Dīn al-Maghribī at the Maragha observatory between 1262 and 1274 AD. In a treatise entitled Talkhīṣ al-majisṭī, preserved in a unique copy at Leiden, Universiteitsbibliotheek, 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. (shrink)

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. (shrink)

Ibn al-Zarqālluh (al-Andalus, d. 1100) introduced a new inequality in the longitudinal motion of the Moon into Ptolemy’s lunar model with the amplitude of 24′, which periodically changes in terms of a sine function with the distance in longitude between the mean Moon and the solar apogee as the variable. It can be shown that the discovery had its roots in his examination of the discrepancies between the times of the lunar eclipses he obtained from the data of his eclipse (...) observations over a 37-year period in the latter part of the eleventh century and the predictions made on the basis of the lunar theories in the Mumta $$\textit{\d{h}}$$ an zīj (Baghdad, ca. 830) and al-Battānī’s zīj (Raqqa, d. 929), which were available to him at the time. What Ibn al-Zarqālluh found is, in fact, a special case of the annual equation of the Moon, which is applicable in the oppositions and, thus, in the lunar eclipses. The inequality was discovered independently by Tycho Brahe (d. 1601) and Johannes Kepler (d. 1630). As Ibn Yūnus (d. 1009) reports in his $$\textit{\d{H}}$$ ākimī zīj, Ibn al-Zarqālluh’s medieval Middle Eastern predecessors, the Persian astronomers Māhānī (d. ca. 880) and Nayrīzī (d. 922) as well as ‘Alī b. Amājūr (fl. ca. 920), were already acquainted with the problem of the eclipse timing errors, but it had remained unresolved until Ibn Yūnus provided a provisional, and incorrect, solution by reducing the size of the lunar epicycle. As we argue, the diverse ways to tackle the same problem stem from two different methodologies in astronomical reasoning in the traditions developed separately in the Eastern and Western regions of the medieval Islamic domain. (shrink)