English: JAMSHID BIN MAS'UD BIN MAHMUD AL-TABIB AL-KASHI KNOWN AS GHIYATH (D. 1429 AD): MIFTAH AL-HISAB

SIGNED IBN MUHAMMAD MU'MIN TAJ AL-DIN AL-SHIRAZI, IRAN, DATED 7 SHA'BAN AH 1066/31 MAY 1656 AD

Al-Kashi's important astronomical treatise dedicated to the Timurid ruler Ulugh Beg's library, Arabic manuscript on paper, 151ff. plus seven flyleaves, each folio with 18ll. of black naskh, titles and important words in red, text within gold, black and blue rules, numerous tables and diagrams in gold, black and red, with catchwords, opening bifolio with floral illumination, colophon signed and dated, occasional marginal notes, later ownership inscription and rubbed seal impression on final folio, in tooled red morocco Text panel 4 5/8 x 2 ¼in. (11.8 x 5.6cm.); folio 7 ½ x 4 ¾in. (19 x 12.1cm.)

This important treatise by Al-Kashi was composed in 1427 AD and dedicated to Ulugh Beg's library. In the prologue of the manual, Al-Kashi gives a list of some of his works. The treatise deals with arithmetics and subjects such as Tartaglia's or Pascal's triangle, the demonstration of the proof by 9, the absolute sexagesimal system and decimal fractions. It also deals with trigonometry and algebra. Al-Kashi died in Samarqand in 1429 (art. 'al-Kashi', in Brill, 1986-2000, vol.IV, pp.702-703).