Risālah al-watar waʾl-jaib

work by al-Kāshī

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July 16, 2026

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The Risālah al-watar wa’l-jayb (Treatise on the Chord and Sine) is a work by the Persian mathematician and astronomer Ghiyāth al-Dīn Jamshīd al-Kāshī. Written around 1427, this treatise is known for its precise calculation of the sine of 1 degree to ten sexagesimal places. This level of accuracy was crucial for the astronomical tables being compiled by Ulugh Beg, a Timurid ruler and astronomer. Al-Kāshī was a leading scholar at Ulugh Beg's observatory in Samarkand, contributing significantly to mathematics and astronomy during the Islamic Golden Age.12

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al-Kāshī
Life in Samarkand
In his third masterpiece, Risālah al-watar waʾl-jayb (“Treatise on the Chord and Sine”), he calculates the sine of 1° correct to 10 sexagesimal places. This precision was essential for the accuracy of Ulūgh Beg’s Astronomical Tables. It is unclear, however, whether al-Kāshī completed the treatise himself or whether it…
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In his third masterpiece, Risālah al-watar waʾl-jayb (“Treatise on the Chord and Sine”), he calculates the sine of 1° correct to 10 sexagesimal places. This precision was essential for the accuracy of Ulūgh Beg’s Astronomical Tables. It is unclear, however, whether al-Kāshī completed the treatise himself or whether it…
Read More