information:highlighting, linguistic:paraphrasing
Etymology and trapezium versus trapezoid

The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (trapezia literally 'table', itself from τετράς (tetrás) 'four' + πέζα (péza) 'foot; end, border, edge').

Two types of trapezia were introduced by Proclus (AD 412 to 485) in his commentary on the first book of Euclid's Elements:

All European languages follow Proclus's structure as did English until the late 18th century, until an influential mathematical dictionary published by Charles Hutton in 1795 supported without explanation a transposition of the terms. This was reversed in British English in about 1875, but it has been retained in American English to the present.

The following table compares usages, with the most specific definitions at the top to the most general at the bottom.