Parables, hyperbole, and ellipsis

[RadicalPi]

These three terms describe, more or less, rhetorical devices. Crudely, a parable is a fable without animals; hyperbole is overstatement; ellipsis is a kind of stylistic omission.

But, as far as I can tell, these terms are also related to three types of conic section, the parabola, the hyperbola, and the ellipse. The thing is that I have no idea, and have not been able to find, what the link between them is.

So, my question is: Is each rhetorical term related its respective mathematical one, and if so, how? How did the term for a flattened circle get linked to the idea of not repeating certain things? or was it vice versa? and what of the other two? It seems that there might be some interesting etymology behind this.

[Nametag]

From Wikipedia:

The word “hyperbola” derives from the Greek ὑπερβολή, meaning “over-thrown” or “excessive”, from which the English term hyperbole also derives. The term hyperbola is believed to have been coined by Apollonius of Perga (ca. 262 BC–ca. 190 BC) in his definitive work on the conic sections, the Conics. For comparison, the other two general conic sections, the ellipse and the parabola, derive from the corresponding Greek words for “deficient” and “comparable”; these terms may refer to the eccentricity of these curves, which is greater than one (hyperbola), less than one (ellipse) and exactly one (parabola), respectively.

The Greek word “ballo,” I’ve been led to believe, means something like “to place next to; to compare”; thus, hyperbole goes “beyond comparison.” A parable implies that the thing in the story is comparable to another thing; and ellipsis cuts things out.

[dzero]

In the case of ellipse and parabola, it seems that the original meanings related to rhetoric rather than math. This is an assumption on my part based on the etymologies.

For example the etymology of ellipse states

late 17th century: via French from Latin ellipsis (seeellipsis)

It therefore refers you to the etymology of ellipsis, which dates to the 16th century.

mid 16th century: via Latin from Greek elleipsis, from elleipein ‘leave out’

It seems that the original Greek meaning also related first to rhetoric, but that is just a guess. Based on the dates of the etymologies, it would seem that the rhetorical meaning was definitely first in English usage.

A similar pattern is followed with parable and parabola. We are given a 16th century date for parabola but parable dates from Middle English - which is generally regarded as covering the period from 1150AD to 1500AD.

For parabola we have:

late 16th century: modern Latin, from Greek parabolē ‘placing side by side, application’, from para- ‘beside’ + bolē ‘a throw’ (from the verb ballein)

While for parable we have:

Middle English: from Old French parabole, from an ecclesiastical Latin sense ‘discourse, allegory’ of Latin parabola ‘comparison’, from Greek parabolē (seeparabola)

[Nametag]

Did you even look up Apollonius of Perga?

[Dog80]

@Nametag

From Wikipedia:

The Greek word “ballo,” I’ve been led to believe, means something like “to place next to; to compare”; thus, hyperbole goes “beyond comparison.” A parable implies that the thing in the story is comparable to another thing; and ellipsis cuts things out.

Ballo (βάλλω) literally means “to shoot” or “to throw”. βάλλω - Wiktionary, the free dictionary

You use this word in English too, eg. ballistics. Another meaning of the word is “to put” (this is used in modern Greek too) so your interpretation of “to place next to” is very close.

Literally hyperbole means “overshooting” and parable “shooting close to”.

[dzero]

@Nametag

Did you even look up Apollonius of Perga?

no. I said it was a guess based on the dating of the etymologies. If you can prove that the greek words were originally used to describe mathematical concepts and were co-opted by English to describe rhetorical constructs, by all means, enlighten us.

But if the best you can do is a snarky comment . . .

[Lubricious_Integument]

In math a circular argument is logically incorrect since it begs the question. I had a math professor back in the day who joked that the other conic sections are used to describe logically incorrect arguments…

Elliptical argument: has details omitted
Parabolic argument: relies on parable rather than logic
Hyperbolic argument: exaggerates its claims

[danceswithvowels]

What you have is the parallel universes of Math and English:
Conic Sections: Ellipse, Parabola, Hyperbola
Laconic Sections: Ellipsis, Parable, Hyperbole

[biqu]

As it turns out, I happened to bring home this weekend a textbook with a passage relevant to the OP’s question.

The conic sections proper are the intersections of the cone with planes not passing through the origin. Such a plane can meet the cone in three different ways, and the corresponding curves of intersection are called the hyperbola, ellipse, and parabola, from the Greek meaning roughly “too much”, “too little”, and “just right”. Other English words with the same origin are “hyperbole” (something exaggerated or excessive), “ellipsis” (something cut short), and “parable” (something that runs alongside).

The same broad classification “too much”, “too little”, and “just right” occurs elsewhere in mathematics. For example, geometries and differential equations are both divided into hyperbolic, elliptic, and parabolic types. The parabolic case is always the exceptional, transitional case between hyperbolic and elliptic.

– John Stillwell, Numbers and Geometry. New York: Springer-Verlag, 1998.

[RadicalPi]

@biqu

As it turns out, I happened to bring home this weekend a textbook with a passage relevant to the OP’s question.

Thanks for remembering this thread. Very interesting information.