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Mathematical Treasure: Al-Amili's Quintessence of Calculation

Frank J. Swetz (The Pennsylvania State University)

The Quintessence of Calculation was written by Bahā' al-dīn Al-‘Āmilī (1547-1621), a leading Persian intellectual of the late 16th and early 17th centuries. The book is a ten-chapter compendium of arithmetic and algebraic operations. Information on astronomical calculations is also included.

Figure 1. The first page of the text contains much marginalia indicating it was heavily studied.


Figure 2. Al-‘Āmilī used charts and diagrams to illustrate some of his instruction.


Figure 3. A page upon which a reader carried out two addition computations.


Figure 4. The Explanation of the Abridgment on Calculus was written by the Persian scholar Ramaḍān ibn Abī Hurayrah Al-Jazarī (fl. 1665-1681). It is a commentary on a work of Al-‘Āmilī. The page shown above provides an example of the content and format of this book.

Index to Mathematical Treasures


Quintessence of Calculation, World Digital Library:

Explanation of the Abridgment on Calculus, World Digital Library:


The images above were obtained through the courtesy of the World Digital Library (WDL) and the assistance of the digital imaging staff at the United States Library of Congress. All items can be viewed in full at the WDL website.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Al-Amili's Quintessence of Calculation," Convergence (January 2014)