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The rule of three

Abraham Lincoln wrote a letter in 1859 to Jesse W. Fell of Springfield, Illinois, giving a little autobiography of himself. In it, he explained his education as a boy:

There were some schools, so called; but no qualification was ever required of a teacher, beyond readin’, writin’, and cipherin’, to the Rule of Three. If a straggler supposed to understand latin, happened to so-journ in the neighborhood, he was looked upon as a wizzard. There was absolutely nothing to excite ambition for education. 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; but that was all.1

Hmmmmm… “the Rule of Three”…

That phrase came up again at the Association of Professional Genealogists’ Professional Management Conference in Salt Lake City last week, where The Legal Genealogist used an apprenticeship record where the master of a boy being bound to him was required to ensure that the boy learned to “read, write and cypher to the rule of three.”2

And afterwards one of the attendees came up and asked where he could find a definition of the rule of three.

Here’s a hint: you’re not going to find it in Black’s Law Dictionary.

That’s because it’s not a legal term. It’s a mathematical term. And yeah, actually, I had to go look it up too.

Start first with the dictionary definition. It’s “a method of finding a number in the same ratio to a given number as exists between two other given numbers”3 or, more precisely, “a mathematical rule asserting that the value of one unknown quantity in a proportion is found by multiplying the denominator of each ratio by the numerator of the other.”4

That seems easy enough. So how was it described in the school books our ancestors might have used?

Well, in the 17th century a man named Edward Cocker wrote a book called Cocker’s Arithmetick : being a plain and familiar Method suitable to the meanest Capacity for the full understanding of that Incomparable Art, as it is now taught by the ablest School-Masters in City and Country. There’s a 1702 edition available on Google Books. And there, the method explained for folks like me, of the “meanest Capacity” for math, is this:

The Rule of Three (not undeservedly call’d the Golden Rule) is, that by which we find out a fourth number, in proportion unto three given Numbers, so as this fourth Number sought may bear the same Rate, Reason, or Proportion to the third (given) number, as this second doth to the first, from whence it is also called the Rule of Proportion.5


Okay, let’s try Ask Dr. Math. There’s it’s explained this way:

The Rule of Three is an ancient mechanical method for solving proportions, which we can do fairly easily (and with more understanding) using algebra. Briefly, it says that if you know three numbers a, b, and c, and want to find d such that

a/b = c/d (that is, a:b::c:d)


d = cb/a6

And Wikipedia explains it best to this non-mathematical mind in this graphic:7

Whew. Now back to the easy stuff like scire facias and entries ad terminum qui praeteriit and…


  1. A. Lincoln, Letter to Jesse Fell, December 1859, in Roy P. Basler, ed., Collected Works of Abraham Lincoln, Vol. III (New Brunswick : Rutgers University Press, 1953), 511; digital edition, Abraham Lincoln Association, University of Michigan Digital Library ( : accessed 26 Mar 2013).
  2. Minute Book, Burke County, North Carolina, Court of Common Pleas and Quarter Sessions, January 1804 – April 1807, Part II, July 1806 session; call no. C.R.014.301.4; North Carolina State Archives, Raleigh.
  3. Oxford Dictionaries Online ( : accessed 26 Mar 2013), “rule of three.”
  4. The Free Dictionary ( : accessed 26 Mar 2013), “rule of three.”
  5. Edward Cocker, Cocker’s Arithmetick : being a plain and familiar Method suitable to the meanest Capacity for the full understanding of that Incomparable Art, as it is now taught by the ablest School-Masters in City and Country (London : John Hawkins, 1702), 102; digital images, Google Books ( : accessed 26 Mar 2013).
  6. Rule of Three,” Ask Dr. Math: Questions and Answers from our Archives, Math Forum, Drezel University ( : accessed 26 Mar 2013).
  7. Wikipedia (, “Cross-Multiplication: Rule of Three,” rev. 15 Mar 2013.
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