a. and sb. [f. late L. binōmi-us (see BINOMY) + -AL 1; cf. F. binôme.]
A. adj.
1. Math. Consisting of two terms; see B. Binomial theorem: the general algebraic formula, discovered by Newton, by which any power of a binomial quantity may be found without performing the progressive multiplications.
1570. Billingsley, Euclid, X. xxxvi. 258. If two rationall lines commensurable in power onely be added together: the whole line is irrationall, and is called a binomium, or a binomiall line.
1706. Phillips, s.v., A binomial Quantity or Root, i. e. a Quantity or Root that consists of two Names or Parts joyn’d together by the Sign + as a + b, or 3 + 2.
1725. J. Kersey, Algebra (1741), 137. I shall first shew the Genesis or Production of Powers from Roots Binomial, Trinomial, &c.
1870. Bowen, Logic, xii. 410. The Binomial Theorem … is a true Law of Nature according to our definition.
2. Having or characterized by two names; = BINOMINAL.
1656. in Blount, Glossogr.
1850. Gard. Chron., 404. The binomial system adopted in every department of science since the days of Linnæus.
1880. Huxley, Crayfish, 16. The terms of this binomial nomenclature.
B. sb. An algebraic expression consisting of two terms joined by the sign + or –: formerly only when connected by +. (Cf. binomium, BINOMY.)
1557. Recorde, Whetst., Pp iv a. The nombers that be compounde with + be called Bimedialles…. If their partes be of 2 denominations, then are thei named Binomialles properly. Howbeit many vse to call Binomialles all compounde nombers that haue +.
1720. Raphson, Arith., 223. The Binomial a – q/3a, or a + b.
1806. Hutton, Course Math., I. 214. To extract any Root of a Binomial.
