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/
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