Journal Article

The Tradition of Large Integers in Historical Arithmetical Textbooks

Stilinovic, Vladimir, Bruckler, Franka Miriam

2024

Overview

After the Hindu-Arabic decimal positional system was introduced in Europe, through-out many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe - the Latin translations of al-Khwarizmi's treatise on decimal arithmetic, and Leonardo's Liber Abaci, containing examples of reading a 16-digit and a 15-digit number respectively. Throughout the centuries, the order of magnitude of these introductory numbers increased, in general up to some 30 digits, but in some cases to over 60 digits. In this paper we examine the development and extent of this characteristic of introductory arithmetic textbooks from the period 13th-19th century, and the conditions which lead to this, now extinct, practice.

• Publisher: University of Montana, ScholarWorks; c/o Bharath Sriraman
• Subject: 12th century / 13th century / 19th century / 6th century / Addition & subtraction / Arithmetic / Digits / Education reform / Integers / Mathematics education / Middle Ages / Names / Number Concepts / Number systems / Primary Education / Reading / Subtraction / Teaching / Textbooks / Translations