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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Bagheri, Mohammad. A Newly Found Letter of al‐Kashi on Scientific Life in Samarkand. Historia Mathematica 24 (1997): 241–56.
‐‐‐. A New Treatise by al‐Kashi on the Depression of the Visible Horizon from China to Paris: 2000 Years Transmission of Mathematical Ideas. Proceedings of a Conference held in Bellagio, Italy, 8–12 May 2000. Stuttgart: Steiner, 2002. 357–68.
Dold‐Samplonius, Yvonne. How al‐Kashi Measures the Muqarnas: A Second Look. Mathematische Probleme im Mittelalter: Der lateinische und arabische Sprachbereich. Ed. Menso Folkerts. Wiesbaden: Harrassowitz, 1996. 57–90.
Ğamšīd, b. Mas˓ūd al‐Kāṣī. Der Lehrbrief über der Kreisum‐fang (ar‐Risāla al‐Muḥīṭiyyaa). Übersetzt und erläutert von P. Luckey. Ed. Herausg von A. Siggel. Berlin: Akademie‐Verlag, 1953.
Jamshīd Ghiyāth al‐Dīn al‐Kāshī. Key of Arithmetics. Treatise on Circumference. Moscow: Gostehizdat, 1956. (Arabic with Russian translations by B. A. Rosenfeld).
Kennedy, Edward S. The Planetary Equatorium of Jamshīd Ghiyāth al‐Dīn al‐Kāshī. Princeton: Princeton University Press, 1960.
Luckey, Paul. Die Rechenkunst bei Ğamšīd b. Mas˓ūd al‐Kāšī mit Rückblicken auf die ältere Geschichte des Rechnens. Abhandlungen für die Kunde des Morgenlandes, Bd. 31. Wiesbaden: F. Steiner, 1951.
Matvievskaya, Galina P. and Boris A. Rosenfeld. Mathematicians and Astronomers of Medieval Islam and Their Works (8–17th centuries) (in Russian). Moscow: Nauka, 1983. 480–6.
Youschkevitch, Adolphe and Boris Rosenfeld. Al‐Kāshī (or al‐Kāshāni). Dictionary of Scientific Biography. Ed. Charles Gillispie. Vol. 7. New York: Scribner, 1973. 255–62.
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Rosenfeld, B. (2008). Al‐Kāshī. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4425-0_9315
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