[ad. L. quadrātūra a square, the act of squaring: see QUADRATE v. and -URE. Cf. F. quadrature (1529).]
† 1. Square shape, squareness. Obs.
1563. Foxe, A. & M. (1596), 1670. The maruellous quadrature of the same, I take to signifie the vniuersal agreement in the same.
1600. Holland, Livy, XXV. xxiii. 565. One of the Romans … counted the stones … and made estimate to himselfe of their quadrature and proportion.
1653. R. Sanders, Physiogn., 60. When the Quadrangle is broad, and well-proportioned in its quadrature.
1667. Milton, P. L., X. 380. Parted by th’ Empyreal bounds, His Quadrature, from thy Orbicular World.
† 2. One side of a square. Obs. rare–1.
1553. Eden, Treat. Newe Ind. (Arb.), 29. Euery quadrature or syde of the wall hath in it thre principal portes or gates.
3. Math. The action or process of squaring; spec. the expression of an area bounded by a curve, esp. a circle, by means of an equivalent square.
1596. Nashe, Saffron Walden, 22. As much time … as a man might haue found out the quadrature of the circle in.
1652. Benlowes, Theoph., XI. xxxvii. As hard to find thy cure As circles puzling Quadrature.
1664. Phil. Trans., I. 15. A method for the Quadrature of Parabola’s of all degrees.
1743. Emerson, Fluxions, p. iii. Drawing Tangents to Curves, finding their Curvatures, their Lengths, and Quadratures.
1829. Mrq. Anglesea, Lett., 28 Feb., in Lady Morgan’s Mem. (1862), II. 278. I am as incapable of making a rhyme as of effecting the quadrature of the circle.
1881. Routledge, Science, ii. 36. The attention which the problem of the quadrature of the circle has attracted.
† b. (See quot.) Obs.
1727–41. Chambers, Cycl., Quadrature-lines, or lines of Quadrature, are two lines frequently placed on Gunter’s sector. [Description follows.]
4. Astron. † a. One of the four cardinal points. Obs. rare–1. (See note on QUADRATE a. 2.)
1601. Holland, Pliny, I. 37. When this concurrence [of the planets with the sun] is about the quadratures of the heaven. [L. circa quadrata mundi.]
b. One of the two points (in space or time) at which the moon is 90° distant from the sun, or midway between the points of conjunction and opposition.
1685. Boyle, Enq. Notion Nat., vii. 256. When the Moon is in Opposition to the Sun … that Part of Her Body which respects the Earth, is more Enlightned than at the New Moon, or at either of the Quadratures.
1726. trans. Gregory’s Astron., I. 126. The Passage of the Body L from the Quadratures to the Syzygies.
1774. Goldsm., Nat. Hist. (1862), I. 91. The tides are greatest in the syzigies, and least in the quadratures.
1867–77. G. F. Chambers, Astron., I. ii. (ed. 3), 39. After starting from conjunction with the Sun it successively reaches its Eastern quadrature [etc.].
c. The position of one heavenly body relative to another when they are 90° apart, esp. of the moon to the sun when at the quadratures (see prec.). † Also Quadrature aspect.
1591. F. Sparry, trans. Cattan’s Geomancie (1599), 185. The Quadrature Aspect is from the first to the fourth, or from the first to the tenth.
1797. Encycl. Brit. (ed. 3), II. 508/2. Thus the sun and moon,… or any two planets, may be in conjunction, opposition, or quadrature.
1812. Woodhouse, Astron., vii. 44. The Sun is said to be in quadrature with a star, or planet, when the difference of their longitudes is 90° or 270°.
1854. Brewster, More Worlds, xvi. 236. The rays reflected from them when the planets are in quadrature.
† d. Her. In quadrature, at intervals of a quarter-circle. Obs.
1766. Porny, Heraldry (1787), 188. A circular Wreath, Pearl and Diamond [= Argent and Sable] with four Hawk’s Bells joined thereto in quadrature Topaz [= Or].
† 5. A division into four parts (? cf. QUADRATE sb.2). Obs. rare–1.
1578. Lyte, Dodoens, VI. lxxix. 759. Foure straight lines running alongst the young shutes or branches, the whiche do make a quadrature, or a diuision of the said young branches into foure square partes or cliftes.
