al-Tuḥfa al-shāhiyya (The imperial gift), dedicated to the vizier Amīr Shāh ibn Tāj al-Dīn Mu`tazz ibn Ṭāhir in Siwās in July or August 1285; E. S. Kennedy noted a number of innovative astronomical models in the Nihāya and the Tuḥfa, but G. Saliba showed that many of these models were due to `Urḍī. Shīrāzī should still be credited with new models for the Moon and Mercury (both in the Tuḥfa). He creatively uses what are now known as the `Urḍī lemma and the Ṭūsī couple to achieve combinations of uniform, circular motions (as required by ancient physics for motions in the heavens) that resolve the irregular motions resulting from Ptolemy’s equant for Mercury and from his choice of the center of the universe as the reference point of motion for the Moon’s eccentric orb. [Ragep] Note that the Shīrāzī also dedicated to this vizier his Tarjamah-i taḥrīr-i uṣūl-i Uqlīdis, a translation from Arabic into Persian of Naṣīr al-Dīn al-Ṭūsī’s 15-part “Recension” of Euclid’s Elements. [FJR, New Dictionary of Scientific Biography]