Means and Extremes

Date: 06/20/2001 at 07:38:14
From: Jill Ilyes
Subject: Means and extremes in proportions

My class is currently learning about proportions, and has asked the 
question, "Why are certain parts of the proportion called the means 
and the other parts called the extremes?"

Can you assist us in clarifying why these particular terms are used 
and how they apply to the ratios in a proportion?

Thanks,
Jill

Date: 06/20/2001 at 12:20:06
From: Doctor Peterson
Subject: Re: Means and extremes in proportions

Hi, Jill.

As you know, the "means" are the inside terms, b and c, and the 
"extremes" are the outside terms, a and d, in the proportion we might 
write in any of these ways:

    a : b :: c : d

    a : b = c : d

    a/b = c/d

     a     c
    --- = ---
     b     d

Whichever way we write it, except the last, b and c are on the inside, 
and a and d are on the outside.

The word "mean" comes through French from Latin "medius," meaing 
"middle." (It is used in several ways in math, all related to the 
middle.)

The word "extreme" comes from Latin "extremus," the superlative form 
of "exterus," meaning "outside"; so it means "outermost."

Now it should make sense!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/