Ellipse

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Klear
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Ellipse

Postby Klear » Tue Mar 04, 2014 12:19 pm UTC

So, as it often happens, a word popped into my mind and I simply had to read its etymology. Surprisingly, I didn't forget about it before I got the the computer, but sadly I couldn't find much.

I'm talking about ellipse in geometry. The Online Etymology Dictionary explains ellipsis (...) pretty well:

1560s, "an ellipse," from Latin ellipsis, from Greek elleipsis "a falling short, defect, ellipse," from elleipein "to fall short, leave out," from en- "in" + leipein "to leave" (see relinquish). Grammatical sense first recorded 1610s.


It only notes that ellipse is derived from that, but doesn't explain the leap in meaning. I've been trying to think of any property of an ellipse that has to do with leaving out something but I can't think of any. The best I've came up is that it's through the meaning "defect", as it can be thought of as an imperfect circle, but I'm not entirely convinced, so I wonder if any of you have some better ideas, or better yet, better sources.

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Re: Ellipse

Postby eSOANEM » Tue Mar 04, 2014 1:11 pm UTC

Etymonline tells me "So called because the conic section of the cutting plane makes a smaller angle with the base than does the side of the cone, hence, a 'falling short.'"

This seems a bit off to me although given how much the ancients loved conic sections something based on that seems possible.

My hunch would have been that it falls short of a circle (in terms of enclosed area for instance or simply as a curve).
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Klear
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Re: Ellipse

Postby Klear » Tue Mar 04, 2014 1:44 pm UTC

Bummer. I was hoping for something eye-opening. Also, I have no idea how I failed to read that part of Etymonline entry. I've seen it at least three times while researching it =/

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Re: Ellipse

Postby Envelope Generator » Tue Mar 04, 2014 6:49 pm UTC

How certain is that etymology? I would have been tempted to assume an etymological connection between ellipsis and elision.
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Re: Ellipse

Postby Valdeut » Tue Mar 04, 2014 9:33 pm UTC

I'm not a mathematician, but I think the name should be seen in relation to the other two types of conic section: the hyperbola and the parabola. Hyperbola comes from ὐπερβάλλω meaning "to go beyond, to exceed" while parabola comes from παραβάλλω meaning "to lay beside". The ellipse, then, comes from ἐλλείπω meaning "to leave behind" or "to fall short". The name actually makes sense if seen as part of a pattern: exceeding, laying beside and falling short.

Other dictionaries also has very similar explanations to Etymonline.
The OED gives the following explanation.
"In the case of the ellipse regarded as a conic section the inclination of the cutting plane to the base ‘comes short of’, as in the case of the hyperbola it exceeds, the inclination of the side of the cone."

The Scott–Liddell Ancient Greek Dictionary give the following explanation for how ἔλλειψις
"so called because the square on the ordinate is equal to a rectangle with height equal to the abscissa and applied to the parameter, but falling short of it"
They actually cite Apollonius of Perga who studied conic sections and who may have been the first to use the word in this sense.

Envelope Generator wrote:How certain is that etymology? I would have been tempted to assume an etymological connection between ellipsis and elision.
Very certain, I would say. There is almost certainly no etymological connection between ellipsis and elision. Of course, the former is from Greek and the latter from Latin, but the words are not cognates either. The first ē in the latin word actually means "out of" (the allomorph ex– is more well known) while the greek ἔλ– is an assimilated form of ἐν meaning "in" or "into". The greek verb λείπω (meaning "to leave") and the latin verb laedō (meaning "to strike") are not related. The greek verb actually comes from one of the best attested indo-european verb roots, while the latin verb has a more uncertain etymology.

I do think that the si– part of the two words may actually be related (as a suffix forming abstract nouns relating to an action) but that's about it.

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Re: Ellipse

Postby gmalivuk » Tue Mar 04, 2014 11:51 pm UTC

Valdeut wrote:I'm not a mathematician, but I think the name should be seen in relation to the other two types of conic section: the hyperbola and the parabola. Hyperbola comes from ὐπερβάλλω meaning "to go beyond, to exceed" while parabola comes from παραβάλλω meaning "to lay beside". The ellipse, then, comes from ἐλλείπω meaning "to leave behind" or "to fall short". The name actually makes sense if seen as part of a pattern: exceeding, laying beside and falling short.
Yeah, I was just about to point out this same thing. It seems perfectly reasonable that the conic section sense gave rise to the name, what with the conic section sense being how ellipses were first studied.
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