quadrature
(ˈkwɒdrətjʊə(r))
[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.) 25 Euery quadrature or syde of the wall hath in it thre principal portes or gates. |
3. Math. a. 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. More widely, the calculation of the area bounded by, or lying under, a curve.
| 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 Marquis of Anglesey Let. 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 R. Routledge Science ii. 36 The attention which the problem of the quadrature of the circle has attracted. 1911 E. B. Wilson Adv. Calculus xi. 313 It is therefore customary to restrict the application of the term ‘area’ to such simple closed curves as have lu = 0, and to say that the quadrature of such curves is possible, but that the quadrature of curves for which lu ≠ 0 is impossible. 1942 H. M. Bacon Differential & Integral Calculus i. 3 The desire was to find a square equal in area to the area bounded by the given curve (in this case, a circle). For this reason the problem has been called the problem of quadrature. Ibid. xiv. 410 The definite integral, which solves the problem of quadrature mentioned in Chap. I, suggests the notation for integrals, the ∫ being a conventionalized form of ‘S’ for ‘sum’. 1968 Fox & Mayers Computing Methods ix. 170 Apart from the rare possibility of being able to perform the quadrature by expressing the indefinite integral in closed form.., we have various general methods and some special methods. |
† 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 tr. 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 Sparry tr. 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]. |
e. Electr. A phase difference of 90 degrees. Usu. attrib. or in phr. in quadrature (with).
| 1889 T. H. Blakesley Alternating Currents of Electr. (ed. 2) xiii. 117 The only induction in the secondary coil is derived from the core, and is, therefore, as regards phase, in quadrature with the magnetization. 1892 S. P. Thompson Dynamo-Electric Machinery (ed. 4) xxii. 628 The waves of self-induced electromotive-force will lag exactly a quarter-period behind those of the current, or will be ‘in quadrature’ with them. 1940 Chambers's Techn. Dict. 691/2 Quadrature transformer, a transformer designed so that the secondary e.m.f. is 90° displaced from the primary e.m.f. Ibid. 705/1 Reactive component, the term now preferred for the component of the vector representing an alternating quantity which is in quadrature (at 90°) with some reference vector... Also called quadrature component. 1944 Electronic Engin. XVII. 58/2 The only unusual section is the reactance modulator or quadrature tube, so called because the anode circuit is back-coupled to the grid..in such a way as to cause a 90-degree phase difference between grid and anode voltages. 1967 Electronics 6 Mar. 120/2 The current in these resistors is in quadrature with the current in A3's input resistor. 1974 Harvey & Bohlman Stereo F.M. Radio Handbk. iv. 65 The normal signal is again divided by 2 to give a 19kHz quadrature signal for feeding back along the phase-lock loop. |
† 5. A division into four parts (? cf. quadrate n.2). Obs. rare—1.
| 1578 Lyte Dodoens vi. lxxix. 759 Foure straight lines running alongst the young shutes or branches, the which do make a quadrature, or a diuision of the said young branches into foure square partes or cliftes. |