Polynomial, a general term for algebraic terms joined by plus or minus signs, also uses the "poly" root for many. The word is a hybrid of Greek and Latin roots. Polynomial means "many names" and is an extension of binomial, literally two names, and monomial which means "one name". Nomen is a Latin root related to "name" and is also found in nominate (to name a candidate) , misnomer (wrongly named), nomenclature (the names of things in a discipline or science) and of course, the French nom de Plume or pen name.
In Florian Cajori's Hisotry of Mathematics he says that Francois Vieta coined the term, and the OED credits the first use in English to the Arithmetic of Samuel Jeake in 1674.
Binomial is, according to the Miriam Webster 0n-line dictionary, from "New Latin binomium, from Medieval Latin, neuter of binomius having two names, alteration of Latin binominis, from bi- + nomin-, nomen name ". Jeff Miller's web site on the first use of mathematical terms says the first English use of the term was in The Whetstone of Witte in 1577 by Robert Recorde. He quotes from the OED "The nombers that be compound with + be called Bimedialles... If their partes be of 2 denominations, then thei named Binomialles properly. Howbeit many vse to call Binomialles all compounde nombers that have +". Miller credits the first English use of monomial to "a 1706 dictionary".
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