quadraticadj.n.

Brit.

/kwɒˈdratɪk/,

/kwəˈdratɪk/, U.S.

/kwɑˈdrædɪk/

Forms: 1600s–1700s quadratick, 1600s– quadratic.

Origin: Formed within English, by derivation. Etymons: quadrate n.¹, -ic suffix.

Etymology: < quadrate n.¹ + -ic suffix. Compare post-classical Latin quadraticus of a square (1686 in a British source; 1657 in a British source in radix quadratica square root, numerus quadraticus square number). Compare slightly earlier quadrato-quadratic adj. at quadrato- comb. form 1.In sense A. 1b after German quadratisch (1868 in the passage translated in quot. 1875 at sense A. 1b).

A. adj.

a. Square; approximately square; having square corners, quadrangular; square in cross-section.

ΘΚΠ

the world > space > shape > angularity > specific angular shape > [adjective] > quadrilateral > square or rectangular > square

quarryc1300

four-squarea1400

squarec1400

four-squared1513

quadrant1517

squadrant1599

quadran1605

quadratic1656

quadrantal1690

quadriform1856

1656 T. Stanley Hist. Philos. II. vii. 13 A pyramid of quadratick base.

1738 J. Barber Tom K—g's i. 14 A hollow Cylinder, in which confin'd Two Cubes quadratick each in Durance bind; With various Dots each Iv'ry Side is grac'd.

1871 H. E. Roscoe Lessons Elem. Chem. (new ed.) xix. 215 On boiling this solution the salt NH₄H₂PO₄ is formed, and may be crystallized in quadratic prisms.

1884 F. O. Bower & D. H. Scott tr. H. A. de Bary Compar. Anat. Phanerogams & Ferns 107 One epidermal cell which appears in surface view rounded and quadratic.

1907 E. Blackwelder in Res. in China I. ii. xvi. 411 The numerous quadratic crystal grains suggest an isometric mineral.

1962 Science 24 Aug. 580/1 For a cube of any size, σ = 6, but for a quadratic prism which is three times as high as it is wide, σ = 7.

1989 Trans. Amer. Microsc. Soc. 108 250 The anteriormost lumen of a fully everted mouth cone appears more or less quadratic in transverse section.

b. Crystallography. = tetragonal adj. 5. rare.

ΘΚΠ

the world > matter > chemistry > crystallography (general) > crystal (general) > crystal systems > [adjective] > tetragonal

tetragonal1868

quadratic1875

1875 A. W. Bennett & W. T. T. Dyer tr. J. von Sachs Text-bk. Bot. i. 66 The calcium oxalate..crystallises in the quadratic system [Ger. im quadratischen System].

1997 Jrnl. Appl. Physics 81 1121/1 In a cubic or quadratic crystal symmetry, the directions in the real space and in the reciprocal space are parallels.

2. Mathematics. Of the second degree; involving the second power (square) and no higher power of an unknown quantity or of a variable. Esp. in quadratic equation n. at Compounds. Also of a property, substance, etc.: described by a quadratic equation. Cf. quadrate adj. 1b.

ΘΚΠ

the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to equations > involving terms of specific highest power

quadratic1668

quadrato-quadratical1668

quadraticala1690

biordinal1853

octavic1854

quartic1856

nonic1910

1668 Bp. J. Wilkins Ess. Real Char. ii. vii. 181 Those Algebraical notions of Absolute, Lineary, Quadratic, Cubic.

1709 J. Kersey Elem. Math. Art ix. 209 When two Rational Quantities..are multiplied into two unequal Surd Roots of the same kind, or into one common Surd above the quadratic kind, [etc.].

1798 N. Vilant Elem. Math. Anal. 43 The root of any cubic binomial, involving a quadratic surd quantity, may be determined by the resolution of a commensurate cubic equation, wanting the second term.

1885 H. W. Watson & S. H. Burbury Math. Theory 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.

1938 in Statist. Res. Mem. 1 91 (title) On the best unbiased quadratic estimate of the variance.

1985 S. Musikant Optical Materials xi. 223 Some materials have a quadratic rather than linear electro-optic effect.

1990 Glasgow Math. Jrnl. 32 309 It has only been for certain cubic polynomials that results have been produced that are comparable in power with those for quadratic polynomials.

B. n.

Mathematics. A quadratic equation.In quot. 1674: a curve of the second degree.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > branch or subset of

quadratic1674

tactic1861

linear algebra1870

group theory1888

subalgebra1903

Clifford algebra1907

the world > relative properties > number > algebra > [noun] > expression > equation > named according to highest power

quadratic equation1647

biquadratic1661

quadratic1674

linear1684

cubic equation1728

linear equation1816

biordinal1876

1674 J. Wallis Let. 14 Feb. in H. Oldenburg Corr. (1975) X. 475 Ellipses, Conchoeids, & many others, (amongst which are all ye Paraboloeids) he accounts Geometrical: But not, Cycloeids, Spirals, Quadraticks, & the like: though some of these may have their points Geometrically designed.

1684 T. Baker Geom. Key (title page) Of linears, qvadratics, cubics, biqvadratics; And the finding of all their Roots.

1728 E. Chambers Cycl. (at cited word) Adfected Quadratics..have some intermediate Power of the unknown Number.

1798 Philos. Trans. (Royal Soc.) 88 376 This biquadratic may be resolved into two quadratics.

a1839 W. M. Praed Poems (1864) II. 41 By turns, as Thought or Pleasure wills, Quadratics struggle with quadrilles.

1870 I. Todhunter Algebra for Schools xx. 169 Quadratic equations which contain the first power of the unknown quantity as well as the square are called adfected quadratics.

1972 M. Kline Math. Thought vi. 141 Diophantus..also treats the case of simultaneous quadratics.

2003 Amer. Econ. Rev. 93 442 Additional controls for all equations include quadratics in age for both husband and wife.

Compounds

(Mathematics, in sense A. 2.)

quadratic equation n. an equation of the second degree; spec. an equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is unknown.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > equation > named according to highest power

quadratic equation1647

biquadratic1661

quadratic1674

linear1684

cubic equation1728

linear equation1816

biordinal1876

1647 J. Pell Let. 4 Nov. in J. Pell Corr. with C. Cavendish (2005) 518 Not so high as a quadratic equation.

1668 J. Wallis Let. 30 Mar. in H. Oldenburg Corr. (1967) IV. 290 He tells us, that in these two forms of Quadratick Equations, aa−ca+dd = 0, and aa+ca+dd = 0; the Roots are both Affirmative.

1706 W. Jones Synopsis Palmariorum Matheseos 128 All Quadratic Equations are reducible to one of these Forms.

1806 C. Hutton Course Math. (ed. 5) I. 247 A simple quadratic equation, is that which involves the square of the unknown quantity only.

1972 M. Kline Math. Thought ix. 186 The Hindus recognized that quadratic equations have two roots.

quadratic form n. a homogeneous polynomial of the second degree in two or more variables.

ΚΠ

1801 Philos. Trans. (Royal Soc.) 91 96 To know what operations are to be performed with the symbol √−1, it is necessary to recur to the quadratic forms from which it is arbitrarily derived.

1859 G. Salmon Lessons Mod. Higher Algebra xii. 88 A quadratic form can be reduced in an infinity of ways to a sum of squares, yet the number of positive and negative squares in this sum is fixed.

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.

2002 Social Forces 80 1322 Changes in respondent's work values over this period of time was best captured by quadratic-form growth models.

quadratic programming n. a technique analogous to linear programming but dealing with a quadratic rather than a linear objective function.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > method of calculation or analysis

extrapolation1872

functional analysis1876

inversion1880

Fourier analysis1929

formalism1940

linear programming1949

quadratic programming1951

simplex method1951

convex programming1963

deconvolution1967

1951 R. Dorfman Applic. Linear Programming to Theory of Ferm iii. 69 The limitations within which the monopolist must work are the same as those of the competitor,..but the function which he wishes to maximize is a quadratic rather than a linear function of the process levels. For this reason we refer to this problem as quadratic programming.

1974 P. R. Adby & M. A. H. Dempster Introd. Optimization Methods v. 153 Although this is an effective strategy for quadratic programming, it can multiply unnecessary function evaluations for general f.

1991 A. Noble in C. Bondi New Applic. Math. x. 239 If the objective function is quadratic and the constraints are linear, an optimum solution can be obtained under certain circumstances by quadratic programming.

Categories »

quadratic residue n. see residue n. 3b.

This entry has been updated (OED Third Edition, December 2007; most recently modified version published online June 2022).

单词	quadratic
释义	quadraticadj.n. Brit. /kwɒˈdratɪk/, /kwəˈdratɪk/, U.S. /kwɑˈdrædɪk/ Forms: 1600s–1700s quadratick, 1600s– quadratic. Origin: Formed within English, by derivation. Etymons: quadrate n.¹, -ic suffix. Etymology: < quadrate n.¹ + -ic suffix. Compare post-classical Latin quadraticus of a square (1686 in a British source; 1657 in a British source in radix quadratica square root, numerus quadraticus square number). Compare slightly earlier quadrato-quadratic adj. at quadrato- comb. form 1.In sense A. 1b after German quadratisch (1868 in the passage translated in quot. 1875 at sense A. 1b). A. adj. 1. a. Square; approximately square; having square corners, quadrangular; square in cross-section. ΘΚΠ the world > space > shape > angularity > specific angular shape > [adjective] > quadrilateral > square or rectangular > square quarryc1300 four-squarea1400 squarec1400 four-squared1513 quadrant1517 squadrant1599 quadran1605 quadratic1656 quadrantal1690 quadriform1856 1656 T. Stanley Hist. Philos. II. vii. 13 A pyramid of quadratick base. 1738 J. Barber Tom K—g's i. 14 A hollow Cylinder, in which confin'd Two Cubes quadratick each in Durance bind; With various Dots each Iv'ry Side is grac'd. 1871 H. E. Roscoe Lessons Elem. Chem. (new ed.) xix. 215 On boiling this solution the salt NH₄H₂PO₄ is formed, and may be crystallized in quadratic prisms. 1884 F. O. Bower & D. H. Scott tr. H. A. de Bary Compar. Anat. Phanerogams & Ferns 107 One epidermal cell which appears in surface view rounded and quadratic. 1907 E. Blackwelder in Res. in China I. ii. xvi. 411 The numerous quadratic crystal grains suggest an isometric mineral. 1962 Science 24 Aug. 580/1 For a cube of any size, σ = 6, but for a quadratic prism which is three times as high as it is wide, σ = 7. 1989 Trans. Amer. Microsc. Soc. 108 250 The anteriormost lumen of a fully everted mouth cone appears more or less quadratic in transverse section. b. Crystallography. = tetragonal adj. 5. rare. ΘΚΠ the world > matter > chemistry > crystallography (general) > crystal (general) > crystal systems > [adjective] > tetragonal tetragonal1868 quadratic1875 1875 A. W. Bennett & W. T. T. Dyer tr. J. von Sachs Text-bk. Bot. i. 66 The calcium oxalate..crystallises in the quadratic system [Ger. im quadratischen System]. 1997 Jrnl. Appl. Physics 81 1121/1 In a cubic or quadratic crystal symmetry, the directions in the real space and in the reciprocal space are parallels. 2. Mathematics. Of the second degree; involving the second power (square) and no higher power of an unknown quantity or of a variable. Esp. in quadratic equation n. at Compounds. Also of a property, substance, etc.: described by a quadratic equation. Cf. quadrate adj. 1b. ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to equations > involving terms of specific highest power quadratic1668 quadrato-quadratical1668 quadraticala1690 biordinal1853 octavic1854 quartic1856 nonic1910 1668 Bp. J. Wilkins Ess. Real Char. ii. vii. 181 Those Algebraical notions of Absolute, Lineary, Quadratic, Cubic. 1709 J. Kersey Elem. Math. Art ix. 209 When two Rational Quantities..are multiplied into two unequal Surd Roots of the same kind, or into one common Surd above the quadratic kind, [etc.]. 1798 N. Vilant Elem. Math. Anal. 43 The root of any cubic binomial, involving a quadratic surd quantity, may be determined by the resolution of a commensurate cubic equation, wanting the second term. 1885 H. W. Watson & S. H. Burbury Math. Theory 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. 1938 in Statist. Res. Mem. 1 91 (title) On the best unbiased quadratic estimate of the variance. 1985 S. Musikant Optical Materials xi. 223 Some materials have a quadratic rather than linear electro-optic effect. 1990 Glasgow Math. Jrnl. 32 309 It has only been for certain cubic polynomials that results have been produced that are comparable in power with those for quadratic polynomials. B. n. Mathematics. A quadratic equation.In quot. 1674: a curve of the second degree. ΘΚΠ the world > relative properties > number > algebra > [noun] > branch or subset of quadratic1674 tactic1861 linear algebra1870 group theory1888 subalgebra1903 Clifford algebra1907 the world > relative properties > number > algebra > [noun] > expression > equation > named according to highest power quadratic equation1647 biquadratic1661 quadratic1674 linear1684 cubic equation1728 linear equation1816 biordinal1876 1674 J. Wallis Let. 14 Feb. in H. Oldenburg Corr. (1975) X. 475 Ellipses, Conchoeids, & many others, (amongst which are all ye Paraboloeids) he accounts Geometrical: But not, Cycloeids, Spirals, Quadraticks, & the like: though some of these may have their points Geometrically designed. 1684 T. Baker Geom. Key (title page) Of linears, qvadratics, cubics, biqvadratics; And the finding of all their Roots. 1728 E. Chambers Cycl. (at cited word) Adfected Quadratics..have some intermediate Power of the unknown Number. 1798 Philos. Trans. (Royal Soc.) 88 376 This biquadratic may be resolved into two quadratics. a1839 W. M. Praed Poems (1864) II. 41 By turns, as Thought or Pleasure wills, Quadratics struggle with quadrilles. 1870 I. Todhunter Algebra for Schools xx. 169 Quadratic equations which contain the first power of the unknown quantity as well as the square are called adfected quadratics. 1972 M. Kline Math. Thought vi. 141 Diophantus..also treats the case of simultaneous quadratics. 2003 Amer. Econ. Rev. 93 442 Additional controls for all equations include quadratics in age for both husband and wife. Compounds (Mathematics, in sense A. 2.) quadratic equation n. an equation of the second degree; spec. an equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is unknown. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > equation > named according to highest power quadratic equation1647 biquadratic1661 quadratic1674 linear1684 cubic equation1728 linear equation1816 biordinal1876 1647 J. Pell Let. 4 Nov. in J. Pell Corr. with C. Cavendish (2005) 518 Not so high as a quadratic equation. 1668 J. Wallis Let. 30 Mar. in H. Oldenburg Corr. (1967) IV. 290 He tells us, that in these two forms of Quadratick Equations, aa−ca+dd = 0, and aa+ca+dd = 0; the Roots are both Affirmative. 1706 W. Jones Synopsis Palmariorum Matheseos 128 All Quadratic Equations are reducible to one of these Forms. 1806 C. Hutton Course Math. (ed. 5) I. 247 A simple quadratic equation, is that which involves the square of the unknown quantity only. 1972 M. Kline Math. Thought ix. 186 The Hindus recognized that quadratic equations have two roots. quadratic form n. a homogeneous polynomial of the second degree in two or more variables. ΚΠ 1801 Philos. Trans. (Royal Soc.) 91 96 To know what operations are to be performed with the symbol √−1, it is necessary to recur to the quadratic forms from which it is arbitrarily derived. 1859 G. Salmon Lessons Mod. Higher Algebra xii. 88 A quadratic form can be reduced in an infinity of ways to a sum of squares, yet the number of positive and negative squares in this sum is fixed. 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. 2002 Social Forces 80 1322 Changes in respondent's work values over this period of time was best captured by quadratic-form growth models. quadratic programming n. a technique analogous to linear programming but dealing with a quadratic rather than a linear objective function. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > method of calculation or analysis extrapolation1872 functional analysis1876 inversion1880 Fourier analysis1929 formalism1940 linear programming1949 quadratic programming1951 simplex method1951 convex programming1963 deconvolution1967 1951 R. Dorfman Applic. Linear Programming to Theory of Ferm iii. 69 The limitations within which the monopolist must work are the same as those of the competitor,..but the function which he wishes to maximize is a quadratic rather than a linear function of the process levels. For this reason we refer to this problem as quadratic programming. 1974 P. R. Adby & M. A. H. Dempster Introd. Optimization Methods v. 153 Although this is an effective strategy for quadratic programming, it can multiply unnecessary function evaluations for general f. 1991 A. Noble in C. Bondi New Applic. Math. x. 239 If the objective function is quadratic and the constraints are linear, an optimum solution can be obtained under certain circumstances by quadratic programming. Categories » quadratic residue n. see residue n. 3b. This entry has been updated (OED Third Edition, December 2007; most recently modified version published online June 2022). < adj.n.1647
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