Etymologies of Algebra, Geometry, Trigonometry

Date: 10/22/2001 at 20:51:53
From: Nikki
Subject: Math roots

What are the origins and roots of the words geometry, algebra, and 
trigonometry?

Date: 10/23/2001 at 09:44:38
From: Doctor Sarah
Subject: Re: Math roots

Hi Nikki - thanks for writing to Dr. Math.

A good dictionary will give you this information, but in case you 
don't have one handy, here's what you would find in _The Words of 
Mathematics, An Etymological Dictionary of Mathematical Terms Used in 
English_, by Steven Schwartzman (1994, Mathematical Association of 
America).

(1) algebra: from the title of a work written around 825 by the 
             Arabic mathematician known as al-Khowarizmi, entitled 
            _al-jebr w'al-muqabalah_. 

In Arabic, al- is the definite article "the." The first noun in the 
title is jebr "reunion of broken parts," from the verb jabara "to 
reunite, to consolidate." The second noun is from the verb qabala, 
with meanings that include "to place in front of, to balance, to 
oppose, to set equal." Together the two nouns describe some of the 
manipulations so common in algebra: combining like terms, transposing 
a term to the opposite side of an equation, setting two quantities 
equal, etc. Because the original Arabic title was so long, and because 
it was in Arabic, Europeans soon shortened it. The result was algeber 
or something phonetically similar, which then took on the meanings of 
both nouns and eventually acquired its modern sense...

(2) geometry: from Greek geo- "earth," of unknown prior origin, and 
              metron "a measure.  The Indo-European root is me- 
              "to measure."

As indicated by the etymology, geometry must originally have dealt 
with measuring land. Although geometry gradually grew more abstract, 
people assumed until the beginning of the 19th century that the axioms 
and postulates of geometry naturally corresponded to the physical 
world as they knew it on earth. In modern terms, however, geometry 
need have no physical referent at all. 

(3) trigonometry: the first part of the word is Greek trigon 
                  "triangle," from Greek tri-, from the Indo-European 
                  root trei- "three" and gonia "angle," from the Indo-
                  European root genu- "angle, knee." The second part 
                  of trigonometry is from Greek metron "a measure." 
                  The Indo-European root is probably me- "to measure." 

Trigonometry is literally the measuring (of angles and sides) of 
triangles. Historically speaking, the triangular approach to 
trigonometry is ancient, whereas the circular approach now taught in 
our schools is relatively recent.

For the historical development of these topics, see the MacTutor 
History of Mathematics archive at St. Andrews: History Topics:

Algebra Index
http://www-history.mcs.st-and.ac.uk/history/Indexes/Algebra.html   

Geometry and Topology Index
http://www-history.mcs.st-and.ac.uk/history/Indexes/Geometry_Topology.html   

The trigonometric functions
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Trigonometric_functions.html   

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/