From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, p. 127
Birjandī: ʿAbd al‐ʿAlī ibn Muḥammad ibn Ḥusayn al‐Birjandī
Birjandī, a pupil of Manṣūr ibn Muʿīn al‐Dīn al‐Kāshī (who was a staff member of the Samarqand Observatory) and of Sayf al‐Dīn Taftāzānī, was known for his numerous astronomical commentaries and supercommentaries. He wrote several commentaries on the works of Naṣīr al‐Dīn al‐Ṭūsī, including Ṭūsī's al‐Tadhkira fī ʿilm al‐hayʾa, his Taḥrīr al‐Majisṭī (recension of Ptolemy's Almagest), and Ṭūsī's book on astrolabes. In the preface to the last book Birjandī mentions some tables of the positions of stars that he calculated for the year 853 Yazdigird (1484). In addition, Birjandī wrote a commentary on Kāshī's Zīj‐i Khāqānī, which was Kāshī's attempt to correct Ṭūsī's Īlkhānī Zīj. Birjandī was also known for his commentary on the Zīj of Ulugh Beg (the last date provided in it being 929 H = 1523) as well as for his supercommentary (ḥāshiya) on Qāḍīzāde's commentary (sharḥ) to Maḥmūd al‐Jaghmīnī's al‐Mulakhkhaṣ fī ʿilm al‐hayʾa al‐basīṭa.
In addition to these commentaries, Birjandī wrote several independent astronomical works, whose subjects included cosmology, ephemeredes, instruments of observation, as well as a treatise on the distances and sizes of the planets that was dedicated to Ḥabīb Allāh, and another work on the construction of almanacs completed in 1478/1479.
Birjandī completed his Sharḥ al‐Tadhkira (Commentary on the Tadhkira) in 1507/1508. Nayanasukha translated the 11th chapter of the second book of this work into Sanskrit. This is the chapter in which Ṭūsī deals with the device called the “Ṭūsī couple” and its applications, mainly to the lunar theory. From the colophon of the Sanskrit translation we learn that a Persian, Muḥammad Ābida, dictated it (presumably in a vernacular language) to Nayanasukha as he composed it in Sanskrit. Muḥammad Ābida had been at Jai Singh's court since at least 1725.
Birjandī's commentary on the Tadhkira is a good example of the commentary tradition within Islam. In analyzing Ṭūsī's work, Birjandī provides the reader with explanations of meanings, shows variants, provides grammatical explanations, and engages in philosophical discussions. He also provides different interpretations and examines the objections of his predecessors against Ṭūsī. In Book II, Chapter 11, Birjandī cites the following authors and works: Ṭūsī's Risālah‐i muʿīniyya; Ptolemy's Almagest; Ibn al‐Haytham; Euclid's Elements; Quṭb al‐Dīn al‐Shīrāzī's Tuḥfa and Nihāya; Theodosius's Sphaerica; Menelaus; and Autolycus.
In his commentary, Birjandī seems to follow Shīrāzī's opinions and his devices. For example, Birjandī mentions an objection against the application of the Ṭūsī couple to the celestial spheres regarding the necessity of rest between two motions; such a discussion about rest between ascending and descending motions is given by Shīrāzī as well as Shams al‐Dīn al‐Khafrī (Ragep, pp. 432–433). Also when Birjandī discusses an application of the curvilinear or spherical version of the Ṭūsī couple, he mentions that this version produces a slight longitudinal inclination, which had been discussed by Shīrāzī in his Tuḥfa (Kusuba and Pingree, pp. 246–247). Finally we note that Birjandī gives a proof for a device that G. Saliba has called the “ʿUrḍī lemma,” after Muʾayyad al‐Dīn al‐ʿUrḍī, but the proof is similar to that given by Shīrāzī rather than ʿUrḍī's original in his Kitāb al‐Hayʾa.
Kusuba, Takanori and David Pingree (eds. and trans.) (2002). Arabic Astronomy in Sanskrit: Al‐Birjandī on Tadhkira II, Chapter 11 and its Sanskrit Translation. Leiden: E. J. Brill. (The Arabic text and Sanskrit translation of Birjandī's Sharḥ al‐Tadhkira, Book II, Chap. 11; also contains commentary.)
Ragep, F. J. (1993). Naṣīr al‐Dīn al‐Ṭūsī's Memoir on Astronomy (al‐Tadhkira fī ʿilm al‐hayʾa). 2 Vols. New York: Springer‐Verlag.
Rosenfeld, B. A. and Ekmeleddin Ihsanoğlu (2003). Mathematicians, Astronomers, and Other Scholars of Islamic Civilization and Their Works (7th–19th c.). Istanbul: IRCICA, pp. 314–316.
Saliba, George (1979). “The Original Source of Quṭb al‐Dīn al‐Shīrāzī's Planetary Model.” Journal for the History of Arabic Science 3: 3–18.
Sayılı, Aydın (1960). The Observatory in Islam. Ankara: Turkish Historical Society.