quadratic, a. and n.
(kwəˈdrætɪk)
[ad. L. type *quadrātic-us: see quadrate n.1 and -ic, and cf. F. quadratique.]
A. adj.
1. a. Square. rare.
| 1656 in Blount Glossogr. 1876 tr. Wagner's Gen. Pathol. 115 They first assume the quadratic form at a distance of one metre behind the head. 1884 Bower & Scott De Bary's Phaner. 107 One epidermal cell which appears in surface view rounded and quadratic. |
b. Cryst. Of square section through the lateral or secondary axes; characterized by this form.
| 1871 Roscoe Elem. Chem. 215 On boiling this solution the salt is formed, and may be crystallized in quadratic prisms. 1875 Bennett & Dyer tr. Sachs' Bot. 66 The calcium oxalate..crystallises in the quadratic system. |
2. Math. Involving the second and no higher power of an unknown quantity or of a variable; esp. in quadratic equation: see equation 6. Also quadratic form (see form n. 5 d); quadratic programming, a technique analogous to linear programming but dealing with a quadratic rather than a linear objective function.
| 1668 Wilkins Real Char. ii. vii. 181 Those Algebraical notions of Absolute, Lineary, Quadratic, Cubic. 1690 Leybourn Curs. Math. 337 All Quadratick Aequations of this kind..have two Roots. 1706 W. Jones Syn. Palmar. Matheseos 128 All Quadratic Equations are reducible to one of these Forms. 1806 Hutton Course Math. I. 247 A simple quadratic equation, is that which involves the square of the unknown quantity only. 1859 [see form n. 5 d]. 1885 Watson & Burbury Math. The. Electr. & Magn. I. 169 If we express every e in terms of the potentials by means of equations..E will be a quadratic function of the potentials. 1896 Bull. Amer. Math. Soc. III. 100 The general theory of quadratic forms is not taken up. 1965 C. H. Springer et al. Adv. Methods & Models viii. 232 Quadratic Programing—a name given to a problem which looks much like a linear program, except the objective function is of second degree, i.e., contains squared terms in it. 1968 E. T. Copson Metric Spaces ix. 141 This space was first studied by David Hilbert in his work on quadratic forms in infinitely many variables. 1974 Adby & Dempster Introd. Optimization Methods v. 153 Although this is an effective strategy for quadratic programming, it can multiply unnecessary function evaluations for general f. |
B. n. a. A quadratic equation. b. pl. The branch of algebra dealing with quadratic equations.
| 1684 Baker Geometr. Key Title-p., Of linears, qvadratics, cubics [etc.]. 1690 Leybourn Curs. Math. 337 The three sorts of Mixed Aequations above expressed, are all that can happen in Quadraticks. 1727–41 Chambers Cycl. s.v., There are several methods of extracting the roots of adfected quadratics. 1827 Hutton Course Math. I. 256 note, Cubic equations, when occurring in pairs, may usually be reduced to quadratics, by extermination. a 1839 Praed Poems (1864) II. 41 By turns, as Thought or Pleasure wills, Quadratics struggle with quadrilles. 1870 [see adfected]. |