• Boris Rosenfeld
Reference work entry

Al‐Kāshī, or al‐Kāshānī (Ghiyāth al‐Dīn Jamshīd ibn Mas˓ūd al‐Kāshī (al‐Kāshānī)), was a Persian mathematician and astronomer. He was born in Kāshān in northern Iran, and worked at first in Herat (now in Afghanistan) at the court of khāqān (“khān of khāns” Shāhrukh, the son of Tīmur). In 1417 he was invited by Ulugh Beg, the son of Shāhrukh, the ruler of Samarqand (now in Uzbekistan) to become the director of his astronomical observatory. His scientific treatises were mostly written in Arabic, and partly in Persian. Al‐Kāshī died in Samarqand in about 1430.

Al‐Kāshī's main mathematical work is Miftāḥ al‐ḥisāb (Key of Arithmetic). This work, written in the tradition of Arabic mathematical texts, contains five books (1) Arithmetic of integers, (2) Arithmetic of fractions, (3) Arithmetic of astronomers, (4) Geometry, and (5) Algebra.

In book 1, al‐Kāshī considers duplication (multiplication by 2), mediation (division into 2), addition, subtraction, multiplication, and division. As Naṣīr...

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  • Boris Rosenfeld

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