quadratic

Etymology

The revised OED takes it as formed from English quadrate + -ic, comparing post-classical Latin quadrāticus (“of a square”), recorded in British sources from 1657.^[2][3][4][5] The Shorter Oxford, Hoad and the Oxford Dictionary of English instead derive it from French quadratique or New Latin quadrāticus.^[6][7][8] Quadrate goes back to Latin quadrātum (“a square”), the noun use of quadrātus (“square, squared”), past participle of quadrō (“to square, make square; put in order”), which is related to quadrus (“a square”) and quattuor (“four”), from Proto-Indo-European *kwetwer- (“four”).^[3] The crystallographic sense follows German quadratisch.^[2]

Earliest recorded meaning

Square, roughly square, or square in cross-section: 1656, in Thomas Stanley's History of Philosophy.^[2][9] Etymonline also dates the word to the 1650s.^[3]

Semantic evolution

The mathematical sense, "of the second degree", involving the square and no higher power of an unknown quantity or variable, followed in 1668, in Bishop John Wilkins's Essay Towards a Real Character;^[2] Etymonline dates mathematical use to the 1660s and quadratic equations, so named because they involve the square and no higher power of x, to the 1680s.^[3] The noun, a quadratic equation, appears in 1674 in a letter of John Wallis.^[2] In 1875 a translation of Sachs used quadratic in crystallography for tetragonal, after the German word.^[2] The plural quadratics names the branch of algebra that deals with quadratic equations.^[9]

Timeline

• 1656 – square, roughly square.^[2][9]
• 1668 – in mathematics, of the second degree.^[2]
• 1674 – noun, a quadratic equation.^[2]
• 1875 – in crystallography, tetragonal (rare).^[2]

Meanings

Adjective

1. In mathematics, involving terms of the second degree at most, that is, a square but no higher power of the unknown or variable: a quadratic function.^[9][10][2]
2. Of or like a square; square.^[9][2][6]
3. (crystallography, rare) Tetragonal.^[9][2]

Noun

1. A quadratic polynomial or equation: Every quadratic has at most two real roots.^[9][10][2]
2. quadratics: the branch of algebra that deals with quadratic equations.^[9]

Word family

• quadratically
• biquadratic
• quadratic equation
• quadratic form
• quadratic formula
• quadratic residue

Related words

• quadrate
• quadrature

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
5. ^ Gove, Philip Babcock, ed. (1961), Webster's Third New International Dictionary of the English Language, Unabridged, Springfield, Mass.: G. & C. Merriam
6. ^ a b Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
7. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
8. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
9. ^ a b c d e f g h Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
10. ^ a b Collins English Dictionary (2023), Glasgow: HarperCollins