trapeziumn.

Etymology: < modern Latin trapezium, < Greek τραπέζιον , diminutive of τράπεζα table, in geometry used by Euclid in the general sense (see 1 below), by Proclus (ed. Friedlein, p. 414) in sense 1b (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 (c300 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 n. and adj. 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 (French trapèze, German trapez, Dutch trapezium, Italian 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 c1875 this is the prevalent use.