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/
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