Origin of the word Quadratic

Date: 04/07/98 at 23:34:28
From: Paul Wilson
Subject: Why call it "quad"ratic? it has Two terms!

Dr. Math,

I am in the middle of a unit on quadratic equations with my algebra I 
students. We discussed monomials, binominals, trinomials, and so 
on. The problem started with a discussion about the different types 
of equations: mono means one, bi means two, tri means three, but 
when we started "quad"ratic eqautions, the big question was asked:  

     If the degree of the equation is two why isn't it a
     "biadic" equation?

I thought quad means four, but your highest power is two and at most 
you have three terms. I don't get it. The question I have for 
you:

     Why is it called "quadratic"?

I tried dictionaries, searches, archives, etc. It was my guess, that 
the word is derived from Latin, but I haven't found someone to verify 
this. Can you help?

Thanks for any help you can lend in this endeavor.

P. Wilson

Date: 04/08/98 at 09:53:43
From: Doctor Sonya
Subject: Re: Why call it "quad"ratic? it has Two terms!

Well, here's what I was able to find out. Jeff Miller's History of 
Mathematics pages say that the word "quadratic" was first used in 
English in 1668 by John Wilkins (1614-1672) in an essay towards a real 
character, and a philosophical language [London: Printed for Sa. 
Gellibrand, and for John Martyn, 1668]. He wrote: "Those Algebraical 
notions of Absolute, Lineary, Quadratic, Cubic" (OED2). They don't say 
why he chose that word, though.

We use the word quadratic because "quadra" refers to a square, and the 
leading term in a quadratic equation is "squared." This is consistent 
with calling a degree three polynomial a "cubic" for the leading term 
represents a cube. The word for an equation with a leading term of x^4 
is "quartic."

See also "Quadratic Equations" in our archives:

  http://mathforum.org/library/drmath/view/58332.html   

-Doctor Sonya,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/   

Date: 04/08/98 at 15:21:15
From: Sleprock01
Subject: Re: Why call it "quad"ratic? it has Two terms!

Thank you.  I will relay the info to my kids. That was my guess, but
I just didn't find "quadra" to mean square!