ESHS/HSS Annual Meeting

Qushji’s Commentary on Ulugh Beg’s Zij as a Key to Understanding Islamicate Zij

• In Event: Tabular Practices and the Cross-cultural Exchange of Knowledge in Ancient in Medieval Astronomy 1

English Abstract

In astronomy during the Islamicate era, two traditions developed: theoretical astronomy (hayʾa), which focused on geometric planetary orbs, and practical astronomy (zīj), concerned with producing numerical tables for planetary positions. Although zījes often appear mathematically independent of detailed geometric models, medieval astronomers consistently sought to align observational data with theoretical models. This tension lies at the center of this study.
The Samarqand observatory produced one of the most influential astronomical tables of the Islamicate world, the Zīj-i Ulugh Beg. The present research asks how theoretical models shaped the structure of this zīj. The common assumption that zīj-makers relied on a single, fixed computational equation is challenged by recent studies. Notably, Alī Qushjī, in his commentary on the Zīj-i Ulugh Beg, explicitly states that the planetary latitude tables were constructed using a method different from Ptolemy’s. This suggests this zīj could employ its own set of computational choices rather than following a uniform procedure.
I argue that commentaries on zījes—often overlooked—serve as a relation between hayʾa and numerical table-making, offering the equations principles underlying each set of tables. While modern scholarship has typically treated zījes as “black boxes” to be decoded mathematically, the existence of such commentaries invites a historically grounded alternative.
Qushjī’s commentary provides a clear example: he describes a new technique for computing planetary latitudes taken from a specific form of Thales’ theorem. This construction requires the planet’s apogee and its maximum observed latitude and enables the simultaneous computation of both latitudes of planets with a single operation. This study analyzes Qushjī’s method and compares it to Ptolemy’s solution, and shows the interplay between theoretical models and table construction in the Samarqand tradition.

Author

• Mostafa Yavari, University of Tehran, Institute for the History of Science