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came upon the word trapezoid today, and when looking it up on m-w, it became apparent that trapeze and trapezoid share the same origins. Helen brought this up oh so many years ago amidst another thread but it was never really dealt with. they come from(well, trapezoid does, anyway) trapeza meaning table. how does trapeze fit in with table? trapezoid I can see, but trapeze? just out looking for fun on a Friday night... 
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Dear etaoin: My handy-dandy ten buck CD dictionary says roots are "four" and "feet". So a table has four legs, a trapezoid has four sides (two parallel), and trapezius muscles that attach scapular to back are four sided. I guess the "trapeze" circus performers use is four sided also, two rope sides, bar to hang on, ropes at top hitched to a fourth "side" of some sort. trapezium n., pl. 3zi[ums or 3zi[a 73!8 5LL < Gr trapezion, trapezium, lit., small table, dim. of trapeza, table, lit., four-footed bench < tra3, for tetra, FOUR + peza, foot; akin to pous, FOOT6 1 a plane figure with four sides, no two of which are parallel: see QUADRILATERAL, illus. 2 Brit., etc. (exc. Cdn.) var. of TRAPEZOID (sense 1)
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Good question, eta. Atomica (AHD 2000) give this: [Late Latin trapezium, trapezoid, from Greek trapezion, diminutive of trapeza, table : tra-, four + peza, foot.] That got me thinking: four feet, four feet...because you have to use all four "feet" to get up TO the high wire? Because you have to use all four to keep your balance once you're on it? Dr. Bill's surmise may be the correct one; I truly can't guess.
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probably nothing whatever to do with feet, but rather visualizing the figure formed..
Prob. orig. applied to a kind in which the ropes formed a trapezium (in sense 1b) with the roof and cross-bar.
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Trap also is used by the dutch to mean a kind of steps or stairs (in the sense of 'tabled' surfaces to climb up-- and the same 'trap' is used to describe much of NY/NJ palisades-- (a basalt that has been turned amost to right angles--(it was laid down horizontal, and is now just 6º to 17º off vertical) as the basalt crystalized at it cooled, and the layers now, break off in "shelves" making a giant 'stair cases' -- and the rock -- is called 'trap rock' (it was mined up until the 1920's, until the robber barron of NY stopped it by buying up all the land..) the dutch first called it trap rock, and the name stuck.. (it is used in the northeast US-- as far north as boston (this old house has used the term) but i don't think it is used in all of US...trap rock is the basalt pulverized to make coarse gravel for road beds and construction. (the crystiline structure makes it easy to pulverize)
the same type of high platteau's in the west are called mesa's-- the spanish for table..
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"He flies through the air with the greatest of ease That daring young man on the flying trapeze...." I had a site about trapeze artists, but I couldn't Edit,Copy the URL, dammit. It was about Alfredo Codona and Lillian Lietzel. I remember at ten years old being humiliated to learn that Lietzel could chin herself ninety times ONE HANDED, when I had struggle to do it ten times with both hands.
Still can't copy URL. If interested, search for "circus trapeze Lietzel".
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heh. I realized my original subject title referred to the tightrope, as opposed to the trapeze...  I guess I see the trapezoid reference to the bar/ropes, but it doesn't seem quite enough. anybody got any historical info indicating when the word trapeze was first used for circus/acrobatics? that might give us a hint? 
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And here I always thought the Trapeze lived in Trapland. 
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the Trapeze lived in Trapland.
It's in the Alps, somewhere, I believe. Remember the von Trapp family?
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It's in the Alps, somewherenah. Vermont. 
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