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History of the Word 'Exponent'

Date: 11/26/2003 at 11:15:52
From: Brittany
Subject: who came up with the name exponent

Who came up with the name "exponent"?



Date: 11/26/2003 at 12:33:06
From: Doctor Peterson
Subject: Re: who came up with the name exponent

Hi Brittany -

A full answer to your question may be more than you want, but I'd like 
to go into some detail!

If you go to our FAQ you will find this link:

  Earliest uses of mathematical words
    http://jeff560.tripod.com/mathword.html 

Look up "exponent," and you will find this:

  The term EXPONENT was introduced by Michael Stifel (1487-1567) in
  1544 in Arithmetica integra.  He wrote, "Est autem 3 exponens
  ipsius octonarij, & 5 est exponens 32 & 8 est exponens numeri
  256" (Smith vol. 2, page 521). 

The Latin translates roughly as

  But 3 is the exponent of that same eight, and 5 is the exponent
  of 32, and 8 is the exponent of the number 256.

(There are some grammatical twists here that I don't quite get!)

Looking up the context of this sentence in Smith, I find that it 
follows a table of powers of 2:

  0   1   2   3   4   5   6   7   8
  1   2   4   8  16  32  64 128 256

He says (in Latin), "Just as, by addition, (in the upper row) 3 
[added] to 5 makes 8, so (in the bottom row), by multiplication, 8 
[multiplied] by 32 makes 256".  Then he continues with the sentence 
above.  So the words "exponent" refers to the number in the top row 
corresponding to a given number in the bottom row; this is the number 
of 2's multiplied to make the given number--what we today would 
call its base-2 logarithm, or the exponent of 2 that gives the number.

Another source is

  Math Words
    http://www.pballew.net/etyindex.html 

which says

  Exponent is the union of the Latin roots exo(out of) + ponere
  (place).  The literal interpretation is to make something visible
  or obvious.  That seems to be what happens when the index is
  raised "out of" the line.  The English word expound, from the same
  source, means to make clear.  An exponent is also used in English
  to describe a person who explains or interprets.  Exponent, as a
  math term, was introduced by Michael Stifel (1487-1567) in his
  book, Arithmetica Integra, in 1544.

I'm not convinced by the idea that "exponent" refers to the raising 
of the number above the line ("out of place", or "placed out of 
line") because a raised exponent notation, though used by Chuquet 
in the 1400's, was not popularized until the 1600's.  Stifel did not 
use such a notation, but a complicated set of symbols for different 
powers.  Literally, Stifel's "exponens" would be "setting out": "3 is 
the setting out of 8" might mean "3 is the number of times you write 
2 as a factor, in order to get 8 by multiplying".  Other authors of 
that period would call 2 the "index" of 8, meaning its place in the 
list of powers, as "indicated" by the top row of numbers.  That word 
is still used, especially in England, for what we call the exponent.

In any case, that is what "exponent" means, and the meaning is more 
important than the details of its origin.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Definitions
High School Exponents
High School History/Biography
Middle School Definitions
Middle School Exponents
Middle School History/Biography

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