This work is an elaboration of the commentary written by the Egyptian mathematician Sibṭ al-Māridīnī—i.e., a commentary on another commentary—on the urjūzah (versified introduction) to the science of algebra, originally composed by the Berber mathematician and man of letters Abū Muḥammad ‘Abd-Allāh al-Ishbīlī al-Marrakushī, also known as Ibn al-Yāsamīn, who died in 1204 (600 AH). Al-Yāsamīn summarized his mathematical knowledge in a versified treatise known as the Yāsamīnīyya (The treatise by al-Yāsamīn). Around the end of the 15th century, al-Yāsamīn’s verses were the object of a prose commentary, Lum‘a al-Mardinīyya fī Šarh al-Yāsamīnīyya (The shimmer of al-Maridinī in the explanation of the treatise by al-Yāsamīn), by Muhammad ibn Muhammad ibn Ahmad Abū ‘Abdallāh Badr al-Dīn, also known as Sibṭ al-Māridīnī. His main contribution was the description of the periodicity of sexagesimal fractions. Interest in this treatise was still alive in the 18th century, when the supercommentary preserved in this manuscript appeared. Its author, Muhammad ibn Sālim al-Hifnī, was born in 1689–90 into a very humble family in the Egyptian province of Ash Sharqīyah. He moved to Cairo in his early teens, where he worked as a copyist of manuscripts, until a benefactor enabled him to devote himself completely to religious and juridical studies. His career as a jurist of the Šāfī‘ī school and as an active member of the Sufi order of the Khalwatiyya led him to one of the most prestigious intellectual positions in the Islamic world. He was appointed head of Al-Azhar University in Cairo in 1757 and continued in this role until his death in 1767–68. A page at the beginning of this copy gives information about those who have owned it, states that it is meant to be a bequest, and says that it once belonged to Musa ibn al-Sayyid Qasim Hajjaj, “the Maliki in school of thought, the Hasani in linage, the Ash’arite in belief, the Andalusian in origin.”