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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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: