[ad. L. curvātūra bending, f. curvāre, curvāt- to bend: see -URE.]
1. The action of curving or bending; the fact, quality or manner of being curved; curved form; (with pl.) a particular instance of this.
In Pathol. esp. of the spine, of which there are two sorts, angular or Pott’s curvature, and lateral curvature.
1665. Hooke, Microgr., 236. Attributed to the Curvature of the visual Ray … through so differingly Dense a Medium.
1753. Hogarth, Anal. Beauty, 2. A line … of that peculiar curvature.
1800. Med. Jrnl., IV. 271. Pains are not even perceived … in curvatures of the back-bone.
1840. R. Liston, Elem. Surg. (ed. 2), II. 547. When curvature commences there is very generally more or less weakness of the limbs.
1875. Bennett & Dyer, trans. Sachs’ Bot., III. iv. 706. Sudden curvature of growing shoots from a blow or concussion. Ibid., 707. The permanent curvature which remains … or the Curvature of Concussion, is the result of a lengthening of the convex and a simultaneous contraction of the concave side.
b. Geom. The amount or rate of deviation (of a curve) from a straight line, or (of a curved surface) from a plane.
Circle of curvature: the circle which osculates a curve at any point, and serves to measure the curvature of the curve at that point. Centre of c., radius of c.: the center and radius of the circle of curvature. Chord of c. (see quot. 1875). Double curvature: that of a curve which twists so as not to lie in one plane, e.g., the curve of a screw.
1710. J. Harris, Lex. Techn., Curvature of a Line, is the peculiar manner of its bending or Flexure, whereby it becomes a Curve of such peculiar Properties…. The Curvatures of different Circles are to one another Reciprocally as their Radii.
1796. Hutton, Math. Dict., Curve of a Double Curvature, is such a curve as has not all its parts in the same plane. Ibid. (1807), Course Math., II. 320. The radius of a circle which has the same curvature with the curve at any given point, is the radius of curvature at that point.
1866. Chamb. Jrnl., 28 April, 271/2. The axles of the locomotive are directed towards the centre of curvature of the railway.
1875. Todhunter, Diff. Calc., xxiv. § 320. If a straight line be drawn from any point of a curve in any direction, the portion of this straight line which is intercepted by the circle of curvature at the assumed point is called the chord of curvature.
1879. Thomson & Tait, Nat. Phil., I. I. § 5. The direction of motion changes from point to point, and the rate of this change, per unit of length of the curve … is called the curvature.
2. concr. A curved portion of anything; a curve.
1603. Holland, Plutarch’s Mor., 1312. The said Sistrum being in the upper part round, the curvature and Absis thereof comprehendeth foure things.
1686. Goad, Celest. Bodies, III. ii. 409. [It] makes the Lofty Curvature of the Celestial Arch to ring.
1800. Med. Jrnl., III. 168. The second curvature of the duodenum was partly torn.
1881. J. Russell, Haigs, 3. A magnificent curvature of the river Tweed.
Hence Curvature v. intr., to curve, bend. Curvatured a., having curvature, curved (rare).
a. 1810. Tannahill, Poems (1846), 28. Our tiny hero … Ascends the hair’s curvatur’d side.
1812. J. J. Henry, Camp. agst. Quebec, 175. We came to the main passage, which curvatured down the hill.
