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Topic: Quadratic Equations
Replies: 6   Last Post: Apr 10, 1996 11:09 AM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Quadratic Equations
Posted: Apr 10, 1996 11:09 AM
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On Wed, 10 Apr 1996 wrote:

> From: Jeffrey Darrow <>
> Date: Tue, 9 Apr 1996 17:40:14 -0400
> To:
> Subject: Quadratic Equations
> Today I had a student in my college algebra class ask me why
> "Quadratic Equations" are so named. If we have a polynomial of
> degree 3 set equal to zero, we call it a cubic equation and that
> makes sense to these students. However, this particular student is
> curious because she sees "Q-U-A-D" in quadratic and thinks of four,
> yet the polynomial in such an equation is only of degree 2. I've
> never encountered this question before and I was at a loss for an
> explanation. Does anyone know the origin of the term "quadratic
> equation"? I would be very grateful to receive an answer.
> Thank you in advance.
> Jeff Darrow
> Idaho State University
> Jeff,
> Look in Chapter V of "The Great Art or Rules of Algebra' by Girolamo
> Cardano, translated and edited bt T. Richard Witmer, MIT 1968. When he
> says to complete the square, he really means to complete a geometric
> square. Cardano gives the proper credit to Euclid in II, 4 of the
> elements. Euclid solved quadratic equations geometrically and x^2
> ( x square ) really was a square evan though we use a 2.
> Peace,
> Don Cook

I think people may be given a misleading impression by being referred
to particular works (I know you didn't intend this, Don!).

It's not that any particular person decided to use the term "quadratic"
(or its Latin equivalent) in a particular technical way, but just that
it's (or was in Latin) the adjective referring to squareness. Most
mathematicians before about 1800 wrote in Latin, so of course they used
the Latin word for "square" when they talked about square numbers.

Jeff would have had no trouble answering his own question if our
mathematical language had developed so that we talked of "squareful"
equations. The word "quadratic" is just as transparent in Latin.

John Conway

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