History of Ratio and Proportion

Date: 12/28/2003 at 13:50:08
From: Eric Burgagni
Subject: history of ratios and proportions

I have a math project on ratios and proportions and I have looked on a 
lot of sites but I still can't find out who discovered ratios or when 
they were discovered.  Can you help me out?

Date: 12/28/2003 at 20:03:57
From: Doctor Peterson
Subject: Re: history of ratios and proportions

Hi, Eric.

Ratios are one of those ideas that go too far back to be sure where 
they originated.  The discussion of the topic in D. E. Smith's History 
of Mathematics begins this way:

  It is rather profitless to speculate as to the domain in which the
  concept of ratio first appeared.  The idea that one tribe is twice
  as large as another and the idea that one leather strap is only
  half as long as another both involve the notion of ratio; both are
  such as would develop early in the history of the race, and yet
  one has to do with ratio of numbers and the other with the ratio
  of geometric magnitudes.  Indeed, when we come to the Greek writers
  we find Nicomachus including ratio in his arithmetic, Eudoxus in
  his geometry, and Theon of Smyrna in his chapter on music.

So we can't say who discovered the idea, or what problems first 
suggested it; the best we can say is that the people he lists (and 
probably many others, perhaps before the Greeks) developed the theory 
of ratios beyond the basics.  You can look them up on the Web in
general, or in this site listed in our FAQ:

  MacTutor Math History Archive
    http://www-history.mcs.st-and.ac.uk/ 

If you have any further questions, feel free to write back.

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