Preparation for Astronomy: ‘Alī Qushjī’s Risāla dar ‘Ilm-i Ḥisāb

Alī Qūshjī (d. 879/1474), a fifteenth-century astronomer, mathematician, theologian, and linguist, played a key role in the formation of Ottoman scientific life. This role has been analyzed in the history of science and in the history of thought more broadly. Upon Sultan Mehmed II’s invitation, he contributed to the formation of the Fatih Semâniye and Ayasofya Madrasas by transferring the scholarly accumulation of the Samarkand mathematics- astronomy school to Istanbul, and his works were widely used in Ottoman intellectual circles for centuries. Risāla dar ʻIlm-i Hisāb, which is the first of two mathematical works by Alī Qūshjī, was written in Persian, probably in Samarkand, sometime before 861/1456. This work has a remarkable place in the Islamic mathematical tradition given its numerous copies, its widespread distribution in Iran and Anatolia, and its being used as a textbook for centuries. In this work, an analysis based on several copies of the work will be shared, correcting outdated information in the literature and clarifying the place and value of Risāla dar ‘Ilm-i Hisāb in terms of the history of science. As an example of the work’s content, the method of finding the quadratic root of integers will be examined and the proof of the method will be given.