Yet another Yank/Brit difference I never knew about. It suddenly occurred to me to wonder why a cross-bar suspended by ropes for acrobatic purposes was called a trapeze. I went to the OED, which said “Prob. orig. applied to a kind in which the ropes formed a trapezium (in sense 1b) with the roof and cross-bar.” So I went to trapezium and found:
1. Geom. a. Any four-sided plane rectilineal figure that is not a parallelogram; any irregular quadrilateral. (The Euclidean sense.)
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.
c. An irregular quadrilateral having neither pair of opposite sides parallel. (The usual sense in England from c1800 to c1875. 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. 1a.
What a mess! The etymology, after explaining that the Greek etymon trapezion is a diminutive of the word for ‘table,’ trapeza, has a long small-type paragraph that describes the shift in meaning from Euclid’s (a above) to Proclus’s (b) and then adds:
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.
I’d sure like to know what Hutton was up to. Was he mischievous, or just dyslexic? The only saving grace is that we don’t have much occasion to talk about trapezoids and trapezia, so not too much confusion results. Still, what a mess.