Etymology From Middle English quadrat, quadrate, from Latin quadrātus (“square”), past participle of quadrō (“to make four-cornered, square, put in order, intransitive be square”), from quadra (“a square”), later quadrus (“square”), from quattuor (“four”).
1
Having four equal sides, the opposite sides parallel, and four right angles; square.
[…]figures some rounde, some triangle, some quadrate,[…]1563 March 30 (Gregorian calendar), John Foxe, “The examination of William Liuing, and of hys wyfe, before Darbyshere Chauncellor of London”, in Actes and Monuments of These Latter and Perillous Dayes, […], London: […] Iohn Day, […], →OCLC, book V, page 1673 [1754], column 2:
2
Produced by multiplying a number by itself; square.
The number of Ten hath been as highly extolled, as containing even, odd, long, plain, quadrate and cubical numbers.1646-72, Sir Thomas Browne, Pseudodoxia Epidemica, book 4, ch. 12
The Moraliſt tells us that a quadrat ſolid wiſe man, ſhould[…]be ſtill the same,[…]2026 August 2 (Gregorian calendar), James Howell, “To Sir Ed. Sa. Knight”, in [Epistolæ Ho-Elianæ.], 3rd edition, volume I, London: […] Humphrey Mos[e]ley, […], published 1655, section VI, page 306:
Etymology From Middle English quadrat, quadrate, from Latin quadrātum. Doublet of quadrat; compare also quadrant (“square or quadrangle”).
1
Geometry, Mathematics, Sciences A plane surface with four equal sides and four right angles; a square; hence, figuratively, anything having the outline of a square.
At which command, the powers militant That stood for heav'n, in mighty quadrate joyn'd.1667, John Milton, “Book V”, in Paradise Lost. […], London: […] [Samuel Simmons], and are to be sold by Peter Parker […]; [a]nd by Robert Boulter […]; [a]nd Matthias Walker, […], →OCLC; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873, →OCLC, lines 61-62:
2
Astrology, Human sciences, Mysticism, Philosophy, Sciences An aspect of the heavenly bodies in which they are distant from each other 90°, or the quarter of a circle; quartile.
Archaic To square; to agree; to suit; to correspond (with).
not quadrating with American ideas of right, justice and reason
The objections of these speculatists, if its forces do not quadrate with their theories, are as valid against such an old and beneficent government as against the most violent tyranny or the greenest usurpation.1790 November, Edmund Burke, Reflections on the Revolution in France, and on the Proceedings in Certain Societies in London Relative to that Event. […], London: […] J[ames] Dodsley, […], →OCLC:
1 more example
In short I am resolved, from this instance, never to give way to the weakness of human nature more, nor to think anything virtue which doth not exactly quadrate with the unerring rule of right.1749, Henry Fielding, The History of Tom Jones, a Foundling, volume (please specify |volume=I to VI), London: A[ndrew] Millar, […], →OCLC: