Facts on the Calculation of Degrees and Minutes


This manuscript by Badr al-Dīn Muhammad ibn Muhammad ibn Ahmad ibn Muhammad ibn al-Ġazal (1423–1506) contains a commentary on, and abridgement of, the astrological treatise on the calculation of the movement of stars and planets, Kašf al-haqā’iq fī hisāb al-daraj wa-al-daqā’iq (The uncovering of the facts regarding the calculation of degrees and minutes), by the Egyptian astronomer and mathematician Ahmad ibn Rağab ibn al-Mağdī (1366–1447). Ibn al-Mağdī was a disciple of the famous ‘Abdallāh al-Māridīnī (or al-Mārdīnī), who was the grandfather of the author of this work and who derived his own nickname, Sibt al-Māridīnī, from his famous maternal ancestor. Sibt al-Māridīnī means “the son of al-Māridīnī’s daughter.” While working as a muwaqqit (timekeeper) at Al-Azhar Mosque in Cairo, Sibt al-Māridīnī produced an impressive number of works on various subjects, including the use of astronomical instruments, arithmetic, algebra, and the division of inheritances. He compiled astronomical tables for the latitude of Cairo and wrote several commentaries on earlier works, including a mathematical poem by 12th-century Moroccan or Andalusian scientist Ibn al-Yasamin. This work offers a very detailed treatment of sexagesimal mathematics and includes what appears to be the first mention of the periodicity of sexagesimal fractions. Chapter titles are highlighted in red ink.

Date Created

Subject Date


Title in Original Language

رقائق الحقائق في حساب الدرج والدقائق

Type of Item

Physical Description

22 leaves (23 lines), bound : paper ; 23 x 16 centimeters


  • Paper:yellowed cream, with watermarks, in good condition, though upper part of leaves stained with black ink. Black and red ink in text, catchwords on rectos. Binding: modern cardboard covered with cloth, leather spine. Naskhi script.


Last updated: August 29, 2017