Published online by Cambridge University Press: 12 April 2016
A commentary, on the spherical astronomy in the Zīj-i Īlkhanī[1], written by the famous Naṣīr ad-Dīn aṭ-Ṭusī (c. 1270) would be an important contribution to the history of medieval astronomy. But we postpone this and attempt here to describe the contents of the third and fourth sections of Treatise III of this zīj. We hope that it will serve to elucidate a small part of this work, which has remained unexploited. I have made a preliminary English translation of the entire Zīj-i Īlkhanī, which awaits final revision and preparation for publication.
The rules explained verbally and without proof by Naṣīr ad-Dīn in the sections under consideration are similar to the ones described by Kāshi in his Zīj-i khāqānī and analysed by E. S. Kennedy in [2]. Therefore, we do not present our proofs of the rules, but refer the reader to [2].