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
. 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.