# The Best of Arithmetic

## Description

This treatise on the art of arithmetic, completed in the late 1880s, opens a window into the early interaction between traditional and modern mathematical pedagogy in Egypt. The use of French loan words, such as million, along with some modern notation, indicates the author’s familiarity with developments in the teaching of arithmetic at the time. The work has an introduction followed by ten chapters and a conclusion. Following traditional praise for God, the Prophet Muhammad, and virtuous vanguards of learning, the treatise opens by introducing arithmetic as a useful and rigorous science, which underlies mathematics, is the cornerstone of worldly transactions, and is a source of knowledge on which many questions in Islamic law depend. In his introduction, the author offers a descriptive and operational definition of numbers and their classifications. Chapter 1 covers operations (addition, subtraction, multiplication, and division) on whole numbers. Chapter 2 deals with fractions, and their expansion, reduction, and basic operations. Chapter 3 addresses the special case of fractions based on division by 24 parts, each called a qirāt (carat), which are said to have been in wide use by the Egyptian Copts; these he calls Coptic fractions. In Chapter 5, the author turns to decimal fractions, which he introduces as being widely used in Europe. Chapter 6 discusses sexagesimal fractions used in celestial calculations, provides information on a variety of arithmetic transactions used in Egypt at the time, and discusses measurements of length, weights, scales, and exchange rates. Chapter 7 treats the extraction of square roots and cube roots, as well as operations on radicals. Chapter 8 discusses geometric, arithmetic, and musical numbers, along with operations on them. Chapter 9 is on solving equations and contains problems related to calculating zakāt (alms tax) and the division of inheritance. Chapter 10 treats the question of inheritance in more detail. The conclusion of the book introduces algebraic methods.

## Title in Original Language

الأنتخاب فى علم الحساب