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Why are coefficients called "coefficients"?

For example I learned that squaring a number is called "squaring" because it actually refers to "making a square". That's how it was developed.

|<----+-----+---->|   3 

      squared


+-----+-----+-----+ 
|     |     |     |
|     |     |     |
|     |     |     |
+-----+-----+-----+ 
|     |     |     |
|     |     |     |
|     |     |     |
+-----+-----+-----+ 
|     |     |     |
|     |     |     |
|     |     |     |
+-----+-----+-----+ 

So what is efficient about a coefficient and why is it a "co" like a "coworker" or "coauthor" or a "coeditor"? I feel like if I understood it's history I might remember what it refers to.

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closed as off-topic by Najib Idrissi, Claude Leibovici, Jean-Claude Arbaut, Jyrki Lahtonen, drhab Aug 24 '14 at 11:56

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – Najib Idrissi, Claude Leibovici, Jean-Claude Arbaut, Jyrki Lahtonen, drhab
If this question can be reworded to fit the rules in the help center, please edit the question.

1  
see prntscr.com/4fskyd –  rsadhvika Aug 23 '14 at 22:44
4  
How is this not on topic. It's fully fits "History and development of mathematics". The history of the term describes why it's called "coefficient" in the same way the history and development of "squaring" describes why it's called the "square" of a number. I edited it to make that clearer –  gman Aug 24 '14 at 12:48
1  
This is what happens with idle people who don't know how to contribute constructively but want to desperately indulge in some activity for timepass. They had put my first question on hold for a similar stupid reason. I love this site very much but really hate these mindless moderators >.< –  rsadhvika Aug 24 '14 at 12:56
2  
I have voted to re-open, math.stackexchange.com seems quite resilient enough to support questions of math-history, which is after all an existing tag. –  Lee Mosher Aug 24 '14 at 13:39

2 Answers 2

up vote 7 down vote accepted

com- from modern Latin meaning together.

efficient- also from modern Latin meaning accomplishing.

So it means to cooperate to produce a result.

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really? That's it? That description fits every part of the an equation –  gman Aug 23 '14 at 22:46
7  
There are manifold meanings of mathematical terminology, in variable contexts. –  Lee Mosher Aug 23 '14 at 22:47
3  
@gman the word conjugate literally means yoked together which could also be applied to any part of an equation. But it's not... –  lemon Aug 23 '14 at 22:48
1  
The word coefficient is used not only in the context of an equation, but whenever a "fixed" or predetermined quantity (the coefficient) is multiplied by a "variable" or not-yet determined quantity. –  hardmath Aug 23 '14 at 22:49

The Oxford English Dictionary says:

According to Hutton, Vieta, who died in 1603, and wrote in Latin, introduced coefficiens in this sense.

and general meaning of the word around that time seems to have been

Cooperating to produce a result.

So perhaps the meaning is that the coefficient on $5 x$, namely the numeral $5$, cooperates with the value of $x$ to produce the result.

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