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The words "elliptic", "parabolic" (or "like a parable"), "hyperbolic", and "circular" all have meaning in rhetoric. Are these meanings etymologically connected to the conic sections?

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There certainly is an etymological connection (see jwpat7's answer) but, just so people don't get the wrong idea, metaphorically the meanings are not evocative of each other in anyway at all. The mathematical meanings are all 'shaped like an X'. (Except for 'circular', yes, there they are metaphorically similar) –  Mitch Oct 16 '11 at 19:56
I suspect OP is really asking if the meanings in rhetoric derive from the meanings in geometry. I always thought the Greeks were into rhetoric first, so if anything it would be the other way round. But are we discussing the etymology of Greek words, or of English ones? –  FumbleFingers Oct 16 '11 at 21:12
@FumbleFingers: Excellent point. The (first three) mathematical terms are pure loans from Greek. And the rhetorical ones are too? If so, then maybe this would be better for linguistics.SE. –  Mitch Oct 16 '11 at 21:22
See more elaborate answers here: english.stackexchange.com/q/175756/73094 –  Honza Zidek Jun 10 at 6:01
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1 Answer

up vote 7 down vote accepted

Yes, all the mathematical meanings are related to their respective rhetorical meanings, as seen in etymonline entries for stem parts parabol, ellipse, hyperbol, circul, and circle.

It appears that the mathematical meanings follow the non-mathematical ones, in the sense that the conic section names are based on metaphorical usage of pre-existing terms from the Greek. For example, in the ellipse entry mentioned above, we see:

Ellipse, 1753, from Fr. ellipse (17c.), from L. ellipsis "ellipse," also, "a falling short, deficit," from Gk. elleipsis (see ellipsis). 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." First applied by Apollonius of Perga (3c. B.C.E.).

and also

Ellipsis, 1560s, "an ellipse," from L. ellipsis, from Gk. 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.

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