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The authors analyse in more detail and more systematically than any earlier scholars the use of the terms jabr, muqābala, and some others in the solutions of a large number of algebraical problems in a range of medieval mathematical texts. They find that the terms stand for the immediate goals of particular steps in the resolutions, rather than for specific operations, as has been thought before. They thus also find that the phrase al-jabr wa’l-muqābala, which became to stand for the whole fi...

This article presents an edition and translation of a useful chapter of the Jāmi‘ Zīj (ca. AD 1025), the Arabic astronomical handbook with tables by the Persian astronomer Kūsyār ibn Labbān (see also review 304). This chapter, number 31 of Book III in the Zīj, but also distributed separately, contains a glossary of 131 numbered astronomical terms with definitions or descriptions. There is only a small number of other zīj-es with listings of technical terms, the Ḫāqānī Zīj by al-Kāsī (ca. AD 1...

The Sustaka Zīj by Ḥusayn ibn Mūsā al-Hurmūzī, which, judging from a number of sample calculations, was compiled in the early 11th century, is of a very different nature from the Arabic and Persian astronomical handbooks with tables that are usually called “zīj”. In fact, the Sustaka Zīj (possibly meaning “Sexagesimal Zīj” or “Pocket Zīj”) consists of only fourteen brief chapters, explaining for each of the seven planets, how to calculate its position from that of a certain period of time ago...

The zīj prepared around 1120 by Abū Manṣūr ‘Abd al-Raḥmān al-Ḫāzinī for the Seljuk ruler Sanjar ibn Maliksāh (reigned 1118-1157) in Marw is one of the most extensive Islamic astronomical handbooks with tables that are extant. It is partially based on newly made observations, contains important innovations with respect to earlier works, and an abridged version of the Sanjarī Zīj was translated into Byzantine Greek. No detailed study of the original Arabic work has been finished yet. The presen...

What is Seen of Sky and Sea (edited and translated by Rashed in Arabic Sciences and Philosophy, 11 (2001), pp. 157-204) is one of only very few treatises by the 10th century geometer Abū Sahl al-Kūhī that deals with topics outside of mathematics proper, namely the area of the surface of the sea and the part of an altitude circle that can be seen by an observer at the top of a tower on an island. Al-Kūhī's method is criticized by the 12th century physician Ibn Yaḥyā al-Samaw'al al-Maghribī, wh...

Abū ‘Abdallāh Muḥammad ibn ‘Īsā ibn Aḥmad al-Māhānī (fl. 865) was the author of one of the earliest Arabic commentaries on the treatment of ratio and proportionality in Book V of Euclid's Elements. In this commentary, extant in nine manuscripts, he provides an alternative, equivalent definition of ratio by means of anthyphairesis, a process similar to the Euclidean algorithm for finding the greatest common divisor of two numbers. In this article al-Māhānī's definition is explained and some po...

This article gives an update of some of the information in E. S. Kennedy’s “A Survey of Islamic Astronomical Tables”, Philadelphia, American Philosophical Society, 1956, of which a Persian translation by Moḥammad Bāqerī appeared in Tehran in 1995. In particular, the article adds some references to secondary literature and supplies information on 42 zījs not yet listed by Kennedy, mostly on the basis of Aḥmad Monzavī’s Fihristvāra-yi kitāb-hā-yi fārsī.

In this talk we will discuss some aspects of the exchange of astronomical knowledge that took place between the Muslim world and China in the thirteenth and fourteenth century. In that period both the eastern part of the Muslim world, consisting of Persia and surrounding countries, and China, ruled by the Yuan Dynasty, were part of the Mongol world empire. In particular in the period between 1260 and 1280, astronomers as well as astronomical books and instruments were exchanged between Persia and China. As a result, extensive descriptions of a Chinese luni-solar calendar can be found in Arabic and Persian astronomical works from the Mongol period, whereas a Chinese text entitled Huihui li (“Islamic Calendar”) can be seen to be a translation of a typical Islamic astronomical handbook with tables and explanatory text, in Arabic and Persian called zij. Islamic astronomy had a good name in China because of its accurate prediction of eclipses, and the Huihui li was used parallel with the official Chinese calendar for almost 300 years.