[Formed with TRI- after BINOMIAL, q.v.]
A. adj. 1. Math. Consisting of three terms, as an algebraical expression.
1704. J. Harris, Lex. Techn., I. Trinomial-Root, in Mathematicks, is a Root consisting of three parts connected together by the Sign +; as a + b + c. See Binomial.
1743. Emerson, Fluxions, I. 83. The Fluents of the Trinomial or compound Binomial Fluxions.
c. 1865. Circ. Sc., I. 483/2. The … multiplier will be trinomial.
2. Nat. Hist. Consisting of three terms, the first being that of the genus, the second that of the species, the third that of the subspecies or variety, instead of the two former only; involving or characterized by three terms, as a system of nomenclature. (Cf. BINOMIAL A. 2.)
1865. Darwin, Lett. (1903), I. 474. I have sometimes … speculated on what nomenclature would come to, and concluded that it would be trinomial.
1884. Nature, 10 July, 257/1. More than ten years ago … Dr. Coues, in his ‘Key to the North American Birds,’ first began to adopt the trinomial nomenclature which is now so generally accepted by American ornithologists.
B. sb. 1. Math. An expression consisting of three terms connected by + or –.
1674. Jeake, Arith. (1696), 294. If three Quantities be conjoyned, and but three, they are sometime called Trinomials.
1706. W. Jones, Syn. Palmar. Matheseos, 171. To raise any Trinomial … to any given Power.
c. 1865. Circ. Sc., I. 473/1. The square of a binomial consists of three terms; that is, it is a trinomial.
2. Nat. Hist. The name of a subspecies or variety when composed of three terms (the names of the genus, species, and subspecies or variety).
1884. Proc. Boston Soc. Nat. Hist., 19 March, 166. According to recent lists all names are to be trinomials, either through duplication or addition.
Hence Trinomialism, the trinomial system of nomenclature, or the use of trinomial names (see A. 2); Trinomialist, one who uses or advocates this system; Trinomiality, the quality or character of being trinomial; Trinomially adv., in a trinomial manner; by the use of trinomial names.
1884. Academy, 5 July, 13/3. Dr. Coues … showed how useful *‘trinomialism’ was in describing species which over the vast extent of North America varied to an extent hardly realised in the Old World.
1893. Nature, 30 June, 196/2. Mr. Blanford has not yet brought himself to accept the principle of trinomialism for birds.
1884. Proc. Boston Soc. Nat. Hist., 19 March, 168. Some *trinomialists disclaim responsibility for the repetition or duplication.
1891. Cent. Dict., *Trinomiality.
1884. Nature, 10 July, 257/2. There has been … a consensus of opinion … that they [the Yellow Wagtails] ought to be treated *trinomially.
