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### Parabola

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Date: 06/06/2001 at 11:20:41
Subject: Parabola

Hi! I was wondering about the meaning of the word parabola. I think
it's not Greek.

Thanks,
```

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Date: 06/06/2001 at 16:14:53
From: Doctor Rick
Subject: Re: Parabola

Decent dictionaries include the etymology (origin) of words. Mine
(Random House Webster's College Dictionary) says:

[1570-80; < NL < Gk parabole an application. See PARABLE]

In other words: the first known use of the word in English was in the
1570s. It is a New Latin word derived from the Greek word "parabole,"
meaning "an application."

The etymology under "parable" adds that the Greek word also means
"comparison" (relevant to the meaning of "parable"), and that it comes
from the Greek prefix para-, "beside, alongside, of, by, beyond," plus
the root bole, "a throwing."

I must admit that the connection between "an application" and what we
mean by parabola is not very clear.

At the bottom of the first page of our Dr. Math FAQ

http://mathforum.org/dr.math/faq/

you will find a link to the Web site "Earliest Known Uses of Some of
the Words of Mathematics" by Jeff Miller. There we find information
about the Greek origins of the word:

PARABOLA was probably coined by Apollonius, who, according to
Pappus, had terms for all three conic sections. Michael N. Fried
says there are two known occasions where Archimedes used the terms
"parabola" and "ellipse," but that "these are, most likely, later
interpolations rather than Archimedes' own terminology."

This still doesn't tell us why the word was chosen. We can make some
guesses, though. If you track down the etymologies of the other conic
sections, you'll find that "ellipse" is from a Greek word meaning
"falling short" while "hyperbola" is from a word meaning "excess." If
you consider the conic sections in terms of how they are obtained by
slicing a cone, you see that the plane that produces an ellipse is
less tilted than the side of the cone ("falling short"?); the plane
that produces a hyperbola is more tilted than the side of the cone
("excess"?); and the plane that produces a parabola is parallel to the
side of the cone. Thus, perhaps the idea is that a parabola "runs
alongside" the side of the cone.

That's only my best guess. Many math terms don't have a lot of meaning
in themselves, that is, in their original meaning; mathematicians have
put a very specific meaning into otherwise rather bland terms.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Conic Sections/Circles
High School Definitions
High School Geometry

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