The Explanation of the Abridgment on Calculus


The present manuscript preserves an extensive commentary on the 17th-century mathematical treatise Al-Ḫulāṣa fī al-Ḥisāb (The abridgment on calculus), which was composed by Bahā' al-Dīn Al-‘Amilī (1547–1621), one of the leading intellectuals of 17th century Safavid Persia (present-day Iran). Born in the city of Baalbek (present-day Lebanon), Al-‘Amilī was an important figure in many different fields of knowledge, including theology, mysticism, poetry, astronomy, mathematics, and architecture. His main contribution to mathematics, the Al-Ḫulāṣa fī al-Ḥisāb, was well known and is the subject of the commentary by Ramaḍān ibn Abī Hurayrah Al-Jazarī (flourished 1665–81) preserved in this manuscript. Al-Jazarī's work, while following the general structure of the Al-Ḫulāṣa, expands considerably on its arguments and provides numerous examples of the described operations. The present copy of the Šarḥ al-Ḫulāṣa fī al-Ḥisāb clearly shows the high level of internal organization of the commentary. After an extensive introduction with a dedication to the Safavid ruling class and some remarks on grammatical and lexicographical issues, the treatise is divided into ten chapters, which in their turn are opened by one or more introductory notes and are made up of ten or more paragraphs each. The manuscript is embellished with mathematical tables and rubricated headings of the divisions of the treatise. A later hand copied a Persian poem on the opening page and added marginal notes as an explanation to Al-Jazarī's commentary.

Date Created

Subject Date

Title in Original Language

شرح الخلاصة في الحساب

Type of Item

Physical Description

62 leaves (25 lines), bound : paper ; 21 x 15 centimeters


  • Tables and figures in margins of pages 68-75.


Last updated: August 29, 2017