Abū Rayḥān al-Bīrūnī (d. after 442/1050) is one of the greatest scholars in the history of Islam. A native of Kāth, capital of Khwārazm, he wrote on subjects ranging from mathematics, geography, astronomy and natural science to history, linguistics and ethnography. He was a student of, among others, the astronomer-mathematicians Kushyār b. Labbān (fl. 390/1000) and Abū Maḥmūd al-Khujandī (d. 390/1000). He also met and corresponded with Avicenna (d. 428/1037). As was common for a scholar of his rank in those days, he spent his life in the entourage of powerful rulers, in Khwārazm, Khurāsān, and Sidjistān. It was at the court of Maḥmūd b. Sebüktigin (d. 421/1030) and his sucessors in Ghazna that he accompanied Maḥmūd on his campaigns to north-west India. It is there that he got acquainted with Indian methods in the arithmetic of proportions and ratios, the subject of this book. Arabic text with a Persian translation by the editor.
Abu ʼl-Ḥasan Nasawī
Edited by Muḥammad Mahdī Kāva Yazdī and Riḍā Afkhamī ʿAqdā
Abu ʼl-Ḥasan Nasawī was a mathematician and geometer of the 5th/11th century. He was a contemporary of Bīrūnī (d. 440/1048) and a student of Avicenna (d. 428/1037). Naṣīr al-Dīn Ṭūsī (d. 672/1274) mentions him in his works and so do others. Nasawī became known in the west through the publications of Franz Woepcke in the nineteenth century. Born in Rayy, Nasawī worked for the Buyid ruler Majd al-Dawla (d. 420/1029) and later for Sharaf al-Dawla, vizier to the Buyid ruler of Baghdad, Jalāl al-Dawla (d. 435/1044). In Nasawī’s time, there were three types of arithmetic: finger-counting as used in business, a sexagesimal sytem with numbers denoted by letters of the Arabic alphabet, and an Indian system of numerals and fractions with decimal notation. The present work is about the Indian system and treats of four classes of numbers in four separate sections. This is Nasawī’s own Arabic reworking of the Persian original, now lost.