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trapezium|trəˈpiːzɪəm|
Pl. trapezia, -iums.
[a. mod.L. trapezium, ad. Gr. τραπέζιον, dim. of τράπεζα table, in geometry used by Euclid in the general sense (see 1 below), by Proclus (ed. Friedlein, p. 414) in sense 1 b. (The early Latin editions of Euclid 1482–1516 have not trapezium, but the Arabic helmariphe; trapezium is in the Basle ed. of 1546.)
With Euclid (c 300 b.c.) τραπέζιον included all quadrilateral figures except the square, rectangle, rhombus, and rhomboid; into the varieties of trapezia he did not enter. But Proclus, who wrote Commentaries on the First Book of Euclid's Elements a.d. 450, retained the name τραπέζιον only for quadrilaterals having two sides parallel, subdividing these into the τραπέζιον ἰσοσκελές, isosceles trapezium, having the two non-parallel sides (and the angles at their bases) equal, and σκαληνὸν τραπέζιον, scalene trapezium, in which these sides and angles are unequal. For quadrilaterals having no sides parallel, Proclus introduced the name τραπεζοειδές trapezoid. This nomenclature is retained in all the continental languages, and was universal in England till late in the 18th century, when the application of the terms was transposed, so that the figure which Proclus and modern geometers of other nations call specifically a trapezium (F. trapèze, Ger. trapez, Du. trapezium, It. trapezio) became with most English writers a trapezoid, and the trapezoid of Proclus and other nations a trapezium. This changed sense of trapezoid is given in Hutton's Mathematical Dictionary, 1795, as ‘sometimes’ used—he does not say by whom; but he himself unfortunately adopted and used it, and his Dictionary was doubtless the chief agent in its diffusion. Some geometers however continued to use the terms in their original senses, and since c 1875 this is the prevalent use.]
1. Geom.
a. Any four-sided plane rectilineal figure that is not a parallelogram; any irregular quadrilateral. (The Euclidean sense.)
[1551Recorde Pathw. Knowl. B iv, The fift sorte doth containe all other fashions of foure cornered figurs, and ar called of the Grekes trapezia.] 1570Billingsley Euclid i. Def. 34. 6 All other figures of foure sides besides these, are called trapezia, or tables. Ibid. 52 A trapesium hauing two sides parallels hath of necessitie the one of them longer then the other. 1660Barrow Euclid i. Def. 33 All other quadrilateral figures besides these are called Trapezia or Tables. 1846Potts Euclid 5. 1862 Todhunter Euclid 5. 1906 Hamilton & Kettle 2nd Geometry Bk. 39 Some terms for quadrilaterals are variously used by different writers. Here trapezium is used for all quadrilaterals that are not parallelograms.
b. spec. A quadrilateral having only one pair of its opposite sides parallel. (The specific sense to which the term was restricted by Proclus.)
The specific sense in Eng. in 17th and 18th c., and again the prevalent one in recent use.
[1570: see a.] 1698Fryer Acc. E. India & P. 289 Geometrical Figures, like the Trapezium, or Square, in which the opposite sides are parallel. 1706Phillips (ed. Kersey), Trapezium (in Geom.) a Quadrilateral, or Square Figure, whose four Sides and Angles are not equal, but two of its Sides are parallel. 1721Bailey, Trapezium,..a Quadrilateral Figure in Geometry, whose opposite Sides are parallel to one another. 1788[see trapezoid n. 1 a]. 1840Lardner Geom. 72 If the angles at the base of a trapezium be equal, its sides will be equal. 1862Todhunter Euclid 5 Some writers propose to restrict the word trapezium to a quadrilateral which has two of its sides parallel, and it would be certainly convenient if this restriction were universally adopted. 1882Casey Euclid 45 A quadrilateral which has one pair of opposite sides parallel is called a trapezium. 1903Hall & Stevens School Geom. 56. 1903 Baker & Bourne Elem. Geom. 81. 1908 ― Elem. Mensuration 48. 1909 Godfrey & Siddons Geom. for Beginners 77 A quadrilateral which has only one pair of sides parallel is called a trapezium. A trapezium in which the sides that are not parallel are equal is called an isosceles trapezium.
c. An irregular quadrilateral having neither pair of opposite sides parallel. (The usual sense in England from c 1800 to c 1875. Now rare. This sense is the one that is standard in the U.S., but in practice quadrilateral is used rather than trapezium.)
This is the trapezoid (τραπεζοειδές) of Proclus: see trapezoid A. 1 a.
1795Hutton Math. Dict. II. 610/1 Trapezium,.. a plane figure contained under four right lines, of which both the opposite pairs are not parallel. When this figure has two of its sides parallel to each other, it is sometimes called a trapezoid. 1807― Course Math. II. 78 Lines are drawn in the fields on the plan, so as to divide them into trapeziums and triangles, the bases and perpendiculars of which are measured on the plan by means of the scale from which it was drawn. 1831Brewster Optics xxv. 214 The solid called the icositetrahedron..is bounded by twenty-four equal and similar trapezia. 1901T. F. Holgate Elem. Geom. i. 74 If only two sides of a quadrilateral are parallel, the figure is called a trapezoid. If no two sides of a quadrilateral are parallel, the figure is called a trapezium. 1959G. & R. C. James Math. Dict. 400/2 Trapezium, a quadrilateral, none of whose sides are parallel.
2. Anat.
a. A bone of the wrist, articulating with the metacarpal bone of the thumb (so called from its shape); also, the corresponding bone in the lower animals; the first of the distal row of carpal bones. Also trapezium bone; Fr. os trapèze.
1840E. Wilson Anat. Vade M. (1842) 70 The trapezium is too irregular in form to be compared to any known object. Ibid. (1851) 238 Groove in the scaphoid and trapezium bones. 1881Mivart Cat 97 The trapezium is the smallest carpal and the most radial of the distal series.
b. (In full, trapezium cerebri.) A band of nerve-fibres in the pons Varolii of the brain.
1890Billings Nat. Med. Dict., Trapezium (cerebri), in the pons Varolii a set of transverse fibres situated dorsally from the pyramids. In many animals..these fibres appear on the surface as an irregular quadrilateral area; hence the name.
3. Astron. A configuration of stars in the form of a trapezium; esp. that in the great nebula of Orion.
1851Nichol Archit. Heav. 143 All about the trapezium is a mass of stars. 1868Lockyer Elem. Astron. §354 The constellation Hercules is easily recognised by..the trapezium formed by four of its stars. 1883Knowledge 15 June 357/2 The famous trapezium [in the great nebula in Orion], consisting of four bright stars and two smaller ones.
4. = trapeze 1. rare.
1856Encycl. Brit. (ed. 8) XI. 169/2 The triangle and trapezium are two of the most amusing instruments in modern gymnasiums. 1862A. Maclaren Milit. Syst. Gymnastic Exerc. 92 The trapezium consists of a turned ash bar..suspended by a rope at each end. Ibid. 93 The evolutions on the trapezium. |