Abraham Lincoln and the Rule of Three

Date: 04/13/2003 at 19:53:33
From: Alex W.
Subject: Mathematics

In the biography of Abraham Lincoln he states that he learned to 
"read, write, and cipher to the rule of 3."  Can you please explain 
the phrase "cipher to the rule of 3"?

Date: 04/14/2003 at 10:50:27
From: Doctor Rick
Subject: Re: Mathematics

Hi, Alex.

It appears that "read, write, and cipher to [or, as far as] the Rule 
of Three" was something of a standard phrase in the nineteenth 
century. On the Internet I found this problem, said to come from 
the National Council of Teachers of Mathematics:

In his 1859 autobiography, Abraham Lincoln wrote, "Of course when I 
came of age I did not know much. Still somehow, I could read, write, 
and cipher to the Rule of Three." The rule of three was a historical 
form of a proportion. To cipher to the rule of three for 3, 9, and 2 
is to complete the phrase "3 is to 9 as 2 is to ___," with the answer 
being the quantity 6. In other words, ciphering to the rule of three 
is to solve a proportion such as 3/9 = 2/x, where x=6. Cipher the 
rule of three for 4, 6, and 3. Cipher the rule of three for a, b, 
and c.

Lincoln was saying that his math education ("ciphering" means 
basically "working with numbers") went as far as learning to solve 
problems with proportions.

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

Date: 04/14/2003 at 11:21:16
From: Doctor Peterson
Subject: Re: Mathematics

Hi, Alex.

If you are interested in the details of this method, you can search 
our archives for the phrase "rule of three". Here is one explanation:

   Rule of Three
   http://mathforum.org/library/drmath/view/60822.html 

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

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