Guide to Operations on Irrational Radicals for Neophytes


This mathematical treatise by Muḥammad b. Abi al-Fatḥ Muḥammad b. al-Sharafī Abi al-Rūḥ ‘Īsā b. Aḥmad al-Ṣūfī al-Shāfi‘ī al-Muqrī, was written in 1491-92 (897 AH). It begins with a "General Introduction," followed by two main parts, with a concluding section on the study of cubes and cube roots. Part I, "Operations on Simple Irrational Radicals," is divided into four chapters. Chapter 1 covers simplification of radicals. Chapters 2, 3, and 4 deal respectively with the multiplication, addition and subtraction, and division of radicals. Part II, on "Operations with Compound Radicals," begins with an introduction followed by five chapters. The introduction presents various forms of compound radicals and ends with a useful summary in tabular form. The first four chapters systematically go through basic algebraic operations on compound radicals, while the fifth chapter deals with the question of testing and verifying obtained numerical values for radicals. The concluding section of the treatise has an introduction and four chapters, and deals with operations with cubes and cube roots. Extraction of cube roots, and their multiplication, division, addition, and subtraction, are methodically discussed.

Last updated: September 29, 2014