paraboloid, n. (a.) Geom.
(pəˈræbəlɔɪd)
Also 7 -oeides, -oeid, 8–9 -oide.
[In form, ad. Gr. παραβολοειδής a. (in a different sense), whence in 17th c. use paraboloeides: see parabola and -oid, and cf. F. paraboloïde.]
† 1. A parabola of a higher degree: = parabola b.
| 1656 Hobbes Six Lessons Wks. 1845 VII. 315 The parabola is 2/3, and the cubical paraboloeides 3/4 of their parallelograms respectively. 1697 Evelyn Numism. viii. 281 The Equated Isocrone Motion..in a Paraboloeid. 1706 W. Jones Syn. Palmar. Matheseos 245 Those of the Third..Order will be the Cubic Paraboloid. 1710 J. Harris Lex. Techn. II. s.v., Suppose the Parameter multiply'd into the Square of the Abscissa to be equal to the Cube of the Ordinate; that is, pxx = y3. Then the Curve is called a Semicubical Paraboloid. |
2. A solid or surface of the second degree, some of whose plane sections are parabolas; formerly restricted to that of circular section, generated by the revolution of a parabola about its axis, now called paraboloid of revolution.
elliptic paraboloid: a paraboloid of elliptic section. hyperbolic paraboloid: a curved surface of which every plane section is either a parabola or a hyperbola, the curvature being concave in one direction and convex in another (as in a saddle concave towards front and back, and convex towards each side).
| 1702 Ralphson Math. Dict., Paraboloid, is a Solid formed by the Circumvolution of a Parabola about its Ax. This is otherwise called a Parabolick Conoid. 1807 Hutton Course Math. II. 127 The Solid Content of a Paraboloid (or Solid generated by the Rotation of a Parabola about its Axis), is equal to Half its Circumscribing Cylinder. 1829 Nat. Philos. I. Optics vii. 22 (U.K.S.) The specula, or mirrors, of all reflecting telescopes are ground into the shape of a paraboloid. 1840 Penny Cycl. XVII. 222/2 Paraboloid. The simplest form of this surface is the paraboloid of revolution. 1842 Ibid. XXIII. 304/2 For the elliptic paraboloid, let a parabola revolve about its principal axis, and let the circular sections become ellipses. Ibid., Let two parabolas have a common vertex, and let their planes be at right angles to one another, being turned contrary ways. Let the one parabola then move over the other, always continuing parallel to its first position, and having its vertex constantly on the other: its arc will then trace out an hyperbolic paraboloid. |
B. adj. = paraboloidal. rare.
| 1857 in Mayne Expos. Lex. 1901 19th Cent. Oct. 586 The voice aided by a paraboloid megaphone. |