paraboloidn.adj.

Brit.

/pəˈrabəlɔɪd/,

/pəˈrabl̩ɔɪd/, U.S.

/pəˈræbəˌlɔɪd/

Inflections: Plural paraboloeides, paraboloids.

Forms: 1600s paraboloeid, 1700s–1800s paraboloide, 1700s– paraboloid.

Origin: Formed within English, by derivation. Etymons: parabola n., -oid suffix.

Etymology: < parabola n. + -oid suffix. Compare post-classical Latin parabolois (1686 in a British source), French paraboloïde (1660 as adjective, 1691 as noun).

Mathematics.

A. n.

†1. = parabola n. 1b. Obsolete.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > conic section > parabola > resembling

parabolaster1656

paraboloid1656

parabola1664

1656 T. Hobbes Six Lessons v. 49 in Elements Philos. The Parabola is ²/ ₃, and the Cubical Paraboloeides ³/ ₄ of their Parallelograms respectively.

1697 J. Evelyn Numismata viii. 281 The Equated Isocrone Motion..in a Paraboloeid.

1706 W. Jones Synopsis Palmariorum Matheseos 245 Those of the Third..Order will be the Cubic Paraboloid.

1728 E. Chambers Cycl. at Parabola Parabola's of the higher Kinds are Algebraic Curves, defined by a^{m − 1}x = y^m... Some call these Paraboloides.

2. A solid or surface whose cross sections in two mutually perpendicular directions are parabolas and those in the third are either ellipses (including circles as a special case) or hyperbolas; spec. (more fully paraboloid of revolution) one with circular cross sections, generated by the rotation of a parabola about its axis of symmetry.elliptic paraboloid: see elliptic adj. Compounds 1. hyperbolic paraboloid n. a paraboloid having hyperbolic cross sections, being concave in one direction and convex in another (like a saddle).

ΘΚΠ

the world > space > shape > curvature > curved three-dimensional shape or body > [noun] > solid of revolution having conic section

conoida1664

paraboloid1677

the world > relative properties > number > geometry > shape or figure > [noun] > three-dimensional > solid of revolution > formed from curve

conoida1664

paraboloid1677

parabolic conoid1702

spindle1706

hyperboloid1743

1677 R. Boyle in Philos. Trans. 1676 (Royal Soc.) 11 800 It may suffice for me to refer the Fluids..to such of the more known Figures as they seemed to be the least remote from, without troubling you or my self with..Spheroids, Conoids, Paraboloids, and other hard words.

1702 J. Raphson Math. Dict. Paraboloid, is a Solid formed by the Circumvolution of a Parabola about its Ax.

1807 C. Hutton Course Math. (ed. 5) II. 127 The Solid Content of a Paraboloid..is equal to Half its Circumscribing Cylinder.

a1831 Encycl. Metrop. (1845) I. 730/2 A parabola is x² = 2pz. Then the equation of a paraboloid of revolution is x² + y² = 2pz.

1842 Penny Cycl. XXIII. 304/2 For the elliptic paraboloid, let a parabola revolve about its principal axis, and let the circular sections become ellipses.

1842 Penny Cycl. XXIII. 304/2 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.

1883 Analyst 10 47 The volume of a paraboloid is one-half the volume of its circumscribing cylinder.

1935 A. H. G. Palmer & K. S. Snell Mechanics xiii. 266 A homogeneous solid, in the form of a paraboloid of revolution cut off by a plane perpendicular to its axis, is balanced vertex downwards on the top of a fixed rough sphere.

1972 M. Kline Math. Thought xxiii. 547 The hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces, that is, each can be generated in two different ways by the motion of a line or each surface is formed by two systems of lines.

1993 Discover Feb. 18/1 To convert a hunk of glass into a perfect paraboloid—the right shape for collecting and focusing light into a point—requires painstaking grinding and polishing.

1993 College Math. Jrnl. 24 244 The graph..of this function is an elliptic paraboloid opening upward.

B. adj.

= paraboloidal adj.

ΘΚΠ

the world > space > shape > curvature > curved three-dimensional shape or body > [adjective] > solid of revolution having conic section

conoidal1571

paraboloidal1825

paraboloid1831

1831 J. H. Curtis Treat. Ear (ed. 5) v. 164 A perforated plate..collects sound into a paraboloid vase.

1901 19th Cent. Oct. 586 The voice aided by a paraboloid megaphone.

1927 Q. Rev. Biol. 2 89/1 The relations between position and length of fruiting branches of sea-island cotton..suggest a paraboloid curve.

1975 I. Asimov Eyes on Universe x. 193 The resin, whirling with it, assumed a paraboloid shape and set, permanently, in that shape.

1996 B. Sterling Holy Fire 193 Dust motes floated in the glare of a few paraboloid overheads.

This entry has been updated (OED Third Edition, June 2005; most recently modified version published online March 2022).

单词	paraboloid
释义	paraboloidn.adj. Brit. /pəˈrabəlɔɪd/, /pəˈrabl̩ɔɪd/, U.S. /pəˈræbəˌlɔɪd/ Inflections: Plural paraboloeides, paraboloids. Forms: 1600s paraboloeid, 1700s–1800s paraboloide, 1700s– paraboloid. Origin: Formed within English, by derivation. Etymons: parabola n., -oid suffix. Etymology: < parabola n. + -oid suffix. Compare post-classical Latin parabolois (1686 in a British source), French paraboloïde (1660 as adjective, 1691 as noun). Mathematics. A. n. †1. = parabola n. 1b. Obsolete. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > conic section > parabola > resembling parabolaster1656 paraboloid1656 parabola1664 1656 T. Hobbes Six Lessons v. 49 in Elements Philos. The Parabola is ²/ ₃, and the Cubical Paraboloeides ³/ ₄ of their Parallelograms respectively. 1697 J. Evelyn Numismata viii. 281 The Equated Isocrone Motion..in a Paraboloeid. 1706 W. Jones Synopsis Palmariorum Matheseos 245 Those of the Third..Order will be the Cubic Paraboloid. 1728 E. Chambers Cycl. at Parabola Parabola's of the higher Kinds are Algebraic Curves, defined by a^{m − 1}x = y^m... Some call these Paraboloides. 2. A solid or surface whose cross sections in two mutually perpendicular directions are parabolas and those in the third are either ellipses (including circles as a special case) or hyperbolas; spec. (more fully paraboloid of revolution) one with circular cross sections, generated by the rotation of a parabola about its axis of symmetry.elliptic paraboloid: see elliptic adj. Compounds 1. hyperbolic paraboloid n. a paraboloid having hyperbolic cross sections, being concave in one direction and convex in another (like a saddle). ΘΚΠ the world > space > shape > curvature > curved three-dimensional shape or body > [noun] > solid of revolution having conic section conoida1664 paraboloid1677 the world > relative properties > number > geometry > shape or figure > [noun] > three-dimensional > solid of revolution > formed from curve conoida1664 paraboloid1677 parabolic conoid1702 spindle1706 hyperboloid1743 1677 R. Boyle in Philos. Trans. 1676 (Royal Soc.) 11 800 It may suffice for me to refer the Fluids..to such of the more known Figures as they seemed to be the least remote from, without troubling you or my self with..Spheroids, Conoids, Paraboloids, and other hard words. 1702 J. Raphson Math. Dict. Paraboloid, is a Solid formed by the Circumvolution of a Parabola about its Ax. 1807 C. Hutton Course Math. (ed. 5) II. 127 The Solid Content of a Paraboloid..is equal to Half its Circumscribing Cylinder. a1831 Encycl. Metrop. (1845) I. 730/2 A parabola is x² = 2pz. Then the equation of a paraboloid of revolution is x² + y² = 2pz. 1842 Penny Cycl. XXIII. 304/2 For the elliptic paraboloid, let a parabola revolve about its principal axis, and let the circular sections become ellipses. 1842 Penny Cycl. XXIII. 304/2 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. 1883 Analyst 10 47 The volume of a paraboloid is one-half the volume of its circumscribing cylinder. 1935 A. H. G. Palmer & K. S. Snell Mechanics xiii. 266 A homogeneous solid, in the form of a paraboloid of revolution cut off by a plane perpendicular to its axis, is balanced vertex downwards on the top of a fixed rough sphere. 1972 M. Kline Math. Thought xxiii. 547 The hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces, that is, each can be generated in two different ways by the motion of a line or each surface is formed by two systems of lines. 1993 Discover Feb. 18/1 To convert a hunk of glass into a perfect paraboloid—the right shape for collecting and focusing light into a point—requires painstaking grinding and polishing. 1993 College Math. Jrnl. 24 244 The graph..of this function is an elliptic paraboloid opening upward. B. adj. = paraboloidal adj. ΘΚΠ the world > space > shape > curvature > curved three-dimensional shape or body > [adjective] > solid of revolution having conic section conoidal1571 paraboloidal1825 paraboloid1831 1831 J. H. Curtis Treat. Ear (ed. 5) v. 164 A perforated plate..collects sound into a paraboloid vase. 1901 19th Cent. Oct. 586 The voice aided by a paraboloid megaphone. 1927 Q. Rev. Biol. 2 89/1 The relations between position and length of fruiting branches of sea-island cotton..suggest a paraboloid curve. 1975 I. Asimov Eyes on Universe x. 193 The resin, whirling with it, assumed a paraboloid shape and set, permanently, in that shape. 1996 B. Sterling Holy Fire 193 Dust motes floated in the glare of a few paraboloid overheads. This entry has been updated (OED Third Edition, June 2005; most recently modified version published online March 2022). < n.adj.1656
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