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/
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