The Term Power

Date: 10/23/2001 at 13:33:44
From: Toni Delvecchio
Subject: Exponents

One of my students asked how we came to use the term power to express 
the number of times we multiply a number by itself. I searched your 
link provided by Jeff Miller on mathematical terms, but didn't find a 
good explanation of its origin.

Can you give us a good explanation? 

Thank You,
T. DelVecchio
6th gr. teacher
Birch Lane School

Date: 10/23/2001 at 15:00:26
From: Doctor Rob
Subject: Re: Exponents

Thanks for writing to Ask Dr. Math, Toni.

I looked in Smith's _History of Mathematics_, vol. II, pp. 393-394.
Apparently this goes back to the Greek geometric algebra.  They used
the word "dynamis" which translates in English to "power."  (Compare
the English words "dynamic" and "dynamo," from the same root.)  I
don't think anyone knows why the Greeks chose that word, the reasons
being lost in the mists of time.

Perhaps it has something to do with the fact that x^n grows faster
than x^(n-1), as x increases, and so is thought of as more powerful.
This is just a personal guess.

From Pat Ballew's Math Words, and Some Other Words of Interest:

   http://www.geocities.com/Paris/Rue/1861/etyindex.html   

POWER 
The word power comes from the French poeir and perhaps the earlier 
Latin word potere from which we get potent. Both words refer to 
ability or being able. In mathematics, power refers to the number 
arrived at by raising a number to an exponent. In the mathematical 
expression 3^2 = 9, three is the base, two is the exponent, and nine 
is the power. Students often refer to the exponent as the power, but 
this is not historically correct, although it has become so common, 
even among many teachers, that some dictionaries refer to the power as 
the exponent. From Jeff Miller's Web page on the first use of some 
math words I found that "POWER appears in English in 1570 in Sir Henry 
Billingsley's translation of Euclid's Elements: 'The power of a line, 
is the square of the same line.' ."

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