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I had cause to investigate the word trapeza in Greek and I was intrigued as to how it had evolved into the meaning of 'trapeze' as we use it in modern English.

How did this happen ?

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    That was an interesting read; thank you for posting (+1). With the Q&A nature of the site, though, you might be better off splitting the post into two parts, posting just the question in the question box, with perhaps a hint of the oddity in translation, and the developed answer as your own answer below. You can even mark the answer as accepted. – Lawrence Jul 8 at 15:42
  • 'Parallelograms' are classed as a subset of trapeziums in maths; the corresponding defininition for trapezium is 'a quadrilateral with at least one pair of [opposite] sides parallel'. And of course 'a four sided figure with two sets of parallel sides' does not have to be a rectangle. – Edwin Ashworth Jul 8 at 15:42
  • @EdwinAshworth Thank you. Edited, as above. – Nigel J Aug 18 at 10:46
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    As Lawrence says, this should be split up into a question part and an answer part to fit the format properly. It shouldn’t be difficult to do this, just copy-paste most of it into the answer box and tweak the question itself a little to be formed as an actual question. (Also note that it is now fairly generally accepted that τράπεζα in fact comes from *tr̥-ped-ih₂ ‘three-legs’, rather than *kʷtu̯r̥-ped-ih₂ ‘four-legs’, but that doesn’t really change much in terms of the resulting shape. The specific ‘counter’ mean is only Modern Greek, though; in Ancient Greek it was just any table.) – Janus Bahs Jacquet Aug 18 at 11:09
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    As advised by Lawrence and @JanusBahsJacquet, I have re-posted a brief question and answered it myself. – Nigel J Aug 18 at 12:57
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From tetra, four, and peza, 'foot' (in the sense of extremity) comes the Greek word trapeza meaning 'table' which can be precisely translated 'counter' in English as the noun is always used in Greek as a service table for serving food or as a surface upon which to handle coinage in banking.

Greek mathematicians (led by Euclid) then used the 'four-legged' sense in geometry to denote four-sided figures, such that we, in English, refer to one which has no parallels as a 'trapezoid' and to a four-sided figure which has one set of parallels as a 'trapezium'.

(A four sided figure with two sets of parallels is a parallelogram, which, if the angles are right angles, will be a rectangle.)

Since a 'table' or a 'counter' does not necessarily have to be square on top (the servant's side is actually better to be shorter than the customer's side) the word trapeza denotes, in Greek, any four sided figure.

1570 H. Billingsley tr. Euclid Elements Geom. i. f. 5v All other figures of foure sides besides these, are called trapezia, or tables.

When a wooden handle is suspended from a sloping ceiling (in a hall or a circus marquee) then the arrangement forms a trapezium (one set of parallel sides) - as seen in the inset of the picture below - and this arrangement is called a trapeze .

1830 Encycl. Brit. XI. 350/2 The trapeze consists of a horizontal bar suspended by ropes at a height of 4 or 5 feet from the floor.

But there is also another arrangement when a sailor on board a small yacht or dinghy leans out from the side, suspended by a 'trapeze' in order to lean the vessel into the wind - as in the main picture below. Strictly speaking the figure displayed here (by the deck, the sailor's body, the line to the mast and the mast itself) is a trapezoid since there are no parallels and it is completely irregular.

1961 F. H. Burgess Dict. Sailing 211 Trapeze, in sailing dinghies, a sliding support used by the crew for outboard balancing when they lay up to windward.

enter image description here

  • 'Trapeze' means most canonically to me the circus act. I was expecting that to be the point of discussion, the 'modern' meaning. Where does that fit in? – Mitch Aug 18 at 15:06

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