Two Sumerian Words of Fractions in Babylonian Mathematics: igi-n-g\'al and igi-te-en

TL;DR

This paper explores the origins and meanings of two Sumerian words related to fractions in Babylonian mathematics, providing interpretations and etymological insights based on analysis of mathematical terminology.

Contribution

It offers the first probable interpretation of 'igi-n-gal' and a definitive etymology for 'igi-te-en', clarifying their literal meanings and origins.

Findings

'igi-n-gal' interpreted as 'reciprocal of n'

'igi-te-en' explained as 'proportion' or 'ratio'

Etymological origins clarified for both terms

Abstract

In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-g\'al "the reciprocal of (the number) n", which is often abbreviated to igi-n, and igi-te-en whose meaning is somewhat abstract, that is, "a proportion (of something)" or "the ratio (of something to another)"(1). Thus the mathematical meanings of the two terms are quite clear, but we have not been able to clarify their literal meanings or their origins so far. In the present paper I shall offer a most probable interpretation of the early term, igi-n-g\'al, and a definite solution to the etymology of the later term, igi-te-en, both of which are based on my analysis of several mathematical terms that concern multiplication or division.