Sharḥ al-Lumaʻ fī ʻilm al-ḥisāb

The system of fara'iḍ (shares) for inheritances is considered to be one of the most advanced innovations introduced by Muslim conquerors in Middle Eastern and North African societies. The exact calculation of shares of inheritance is a complex chapter in Islamic law, and it is not surprising that Muslim intellectuals and scientists developed a system of mathematical tools in order to master "the science of the shares" ('ilm al-fara'iḍ). An important contribution to this field can be found in the work of Aḥmad ibn Muḥammad Ibn al-Hāʼim, who dealt with the mathematical implications of the reckoning of inheritance shares in his late-14th-century treatise Al-Luma' al-yasīra fī 'ilm al-ḥisāb (The little sparkles on the science of calculation). The present manuscript testifies to the relevance of this treatise over the centuries, as it preserves a 16th-century commentary on Ibn al-Hāʼim's work by the Egyptian mathematician known as Sibṭ al-Māridīnī, who was active as a muwaqqit (timekeeper) at the Al-Azhar Mosque in Cairo. The subject of Ibn al-Hāʼim's work, and hence of the present commentary, is not limited to problems of inheritance. Also included are extensive passages on numerals and a thorough discussion of the operations of multiplication and division. World Digital Library. The text is a commentary on al-Lumʻah al-yasīrah fī ʻilm al-ḥisāb by Aḥmad ibn Muḥammad Ibn al-Hāʼim.