Do ellipsis, parable, and hyperbole from rhetoric have anything in common with the geometric curves ellipse, parabola, and hyperbola used in mathematics?
There are three geometric curves known as conic sections:
Ellipse: a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve.
Parabola: a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram.
Hyperbola: has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
There are also three terms in linguistics with analogous names (in many languages with the same names, actually):
Ellipsis: the omission from a clause of one or more words that are nevertheless understood in the context of the remaining elements.
Parable: a succinct, didactic story, in prose or verse, which illustrates one or more instructive lessons or principles.
Hyperbole: is the use of exaggeration as a rhetorical device or figure of speech.
Do they have anything in common? Is there any etymological or other reason connecting each pair together? Does the ellipsis remind the ellipse in any way, etc.? Is there any analogy between them?