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History of the Word "Polynomial"

Date: 10/18/2006 at 23:21:39
From: Aheli
Subject: what is the meaning of "mials" in polynomials

My teacher asked me to find the meaning of "mials" in the word 
polynomials.  I know "poly" means "many" but what is the meaning of 
"mials" or "nomials"?  And from which language did it come? 

I can not find it in any dictionary.  I think probably it means number
or portion.



Date: 10/19/2006 at 08:55:12
From: Doctor Rick
Subject: Re: what is the meaning of 

Hi, Aheli.

The correct division of the word is poly-nomial.  Did you try looking 
up the entire word "polynomial" in a dictionary?  Good dictionaries 
have etymologies (word origins), and that should tell you what the
-nom- part comes from.  (It's Greek, as is the prefix poly-.)

Having said that, I looked in my own Random House Webster's College 
Dictionary and it doesn't have an etymology for polynomial!  That's 
odd.  What do I do now?  I look up the suffix -nomial, but I don't 
expect to find it there.  What I find is -nomy, as in astronomy; that 
comes from Greek nomos, meaning law.  But I'm not at all confident 
that polynomial comes from this same word, because then polynomial 
would mean "many laws", and that doesn't make a lot of sense.

So I try another dictionary!  Webster's New World Dictionary 
says: "[POLY- + [BI)NOMIAL]", which sends me to look up the word 
binomial.  This says, indeed, "[< LL binomius < bi- + Gr. nomos, law 
+ -AL]".  It is defined as "a mathematical expression consisting of 
two terms connected by a plus or minus sign."  Hmm... maybe each term 
was considered to be a "law" or rule, and a binomial tells you to 
follow both rules, then add the results together.

I know one good Web source that may be able to clear up the matter:

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

Let's look up "polynomial" and "binomial" there.  Maybe it will help. 
Here is what I find:

POLYNOMIAL was used by François Viéta (1540-1603) (Cajori 1919, page 
139). 

The word is found in English in 1674 in Arithmetic by Samuel Jeake 
(1623-1690): "Those knit together by both Signs are called...by some 
Multinomials, or Polynomials, that is, many named" (OED2). 
[According to An Etymological Dictionary of the English Language 
(1879-1882), by Rev. Walter Skeat, polynomial is "an ill-formed 
word, due to the use of binomial. It should rather have been 
polynominal, and even then would be a hybrid word."] 

That confuses things, rather than clearing up the matter!  When it 
says "many named", it is implying (I think) that the -nomial part 
comes from the Latin word nomen, "name", rather than from Greek 
nomos, "law".  The same is suggested by the critique of the word as 
ill-formed and hybrid, that is, a mix of Greek and Latin.

So it looks like there is confusion about where the -nomial part comes 
from, because the word polynomial was created in a messy manner--like 
many new words today that are just formed by sticking two words 
together, or taking parts of words, without considering where those 
words came from.  The New World Dictionary and the Skeat quote above 
both suggest that "polynomial" was formed on the pattern of 
"binomial", rather than being constructed directly from Greek (or 
Latin) roots; and "binomial" itself appears to be a hybrid Latin-
Greek word.

The best answer to your question may be that -nomial may derive from 
Greek nomos, "law", influenced by Latin nomen, "name", or perhaps 
the other way around, but we don't know for sure.

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



Date: 10/19/2006 at 23:10:26
From: Aheli
Subject: Thank you (what is the meaning of "mials" in polynomials)

Dear Doctor Rick,

Thank you very much.  Now I have found the meaning but with 
different possibilities.  And that is why it is interesting, too.
Thanks again.

Aheli



Date: 10/20/2006 at 08:03:41
From: Doctor Rick
Subject: Re: Thank you (what is the meaning of 

Hi, Aheli.

You're welcome!  May I add a few more finds?  The American Heritage 
Dictionary online traces "binomial" to "nomen" through the French, 
nom, which I haven't seen elsewhere:

    http://www.bartelby.com/61/86/B0258600.html 

The Merriam-Webster dictionary online traces it to "New Latin 
binomium, from Medieval Latin, neuter of binomius having two names, 
alteration of Latin binominis, from bi- + nomin-, nomen name" :

    http://www.m-w.com/cgi-bin/dictionary?va=binomial 

Both say that "polynomial" was formed from poly- + -nomial (as in 
binomial).  Dictionaries are consistent on this point, at least.  The 
weight of professional opinion seems to lean toward the nomen origin 
rather than the nomos origin; the divergence in views concerns how 
the n got dropped.  This just goes to show that we know less about 
where things came from than you might expect!  Our language grows in 
mysterious ways, rarely well documented.

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

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