2
$\begingroup$

This is more of an etymology question I believe.

I am curious to know how did the word 'mantissa' came to be used in mathematics, who used it first and from what other word or what other language did it originate?

Also, is the person who first used this word still known?

How did this term became to mean two different things, namely the significand of a number written in scientific form and the fractional part of the common logarithm.

$\endgroup$
3
$\begingroup$

Quoting from Earliest Known Uses of Some of the Words of Mathematics:

MANTISSA is a late Latin term of Etruscan origin, originally meaning an addition, a makeweight, or something of minor value, and was written mantisa. In the 16th century it came to be written mantissa and to mean appendix (Smith vol. 2, page 514).

Numerous sources, including Smith (vol. 2, page 524), Boyer (page 345), the Century Dictionary (1889–97), and Webster’s New International Dictionary (1909), claim that mantissa was introduced by Henry Briggs (1561–1631) in 1624 in Arithmetica logarithmica. However, this information apparently is incorrect. Johannes Tropfke in his “Geschichte der Elementar-Mathematik”, vol. 2, 3rd edition 1933, says “Das Fachwort Mantisse hatte Briggs noch nicht” (p. 252). [Christoph J. Scriba]

According to Cajori (1919, page 152), the word mantissa was first used by John Wallis in 1693:

Ejusque partes decimales abscissas, appendicem voco, sive mantissam.

The citation above is from “Opera mathematica”, vol. 2, Oxoniae, 1693 (De Algebra tractatus), page 41. This is in the Latin edition, and not in the original edition of 1685, in which Wallis uses the English word “appendage.” According to Julio González Cabillón, this is the first use of the term to mean “the decimal part of any number.”

Mantissa was also used by Leonhard Euler in 1748:

Constat ergo logarithmus quisque ex numero integro et fractione decimali et ille numerus integer vocari solet characteristica, fractio decimalis autem mantissa. (The logarithm consists of an integral part, called the characteristic, and a decimal fraction, called the mantissa.)

The citation above is from Euler’s Introductio in analysin infinitorum, vol. 1, page 83 (Lausannae 1748). According to Julio González Cabillón, this is the first use of the term to mean “the decimal part of a logarithm.” According to Smith (vol. 2, page 514), the word was not commonly used until its adoption by Euler.

Gauss suggested using the word for the fractional part of all decimals: “Si fractio communis in decimalem convertitur, seriem figurarum decimalium… fractionis mantissam vocamus…" (Smith vol. 2, page 514).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.