Given an equation like where b and d are not zero, one can cross-multiply to get In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.
[4] For an equation of the form where the variable to be evaluated is in the right-hand denominator, the rule of three states that In this context, a is referred to as the extreme of the proportion, and b and c are called the means.
The rule of three gives the answer to this problem directly; whereas in modern arithmetic, we would solve it by introducing a variable x to stand for the cost of 6 yards of cloth, writing down the equation and then using cross-multiplication to calculate x: An anonymous manuscript dated 1570[7] said: "Multiplication is vexation, / Division is as bad; / The Rule of three doth puzzle me, / And Practice drives me mad."
Charles Darwin refers to his use of the rule of three in estimating the number of species in a newly discerned genus.
An example of such a problem might be If 6 builders can build 8 houses in 100 days, how many days would it take 10 builders to build 20 houses at the same rate?, and this can be set up as which, with cross-multiplication twice, gives Lewis Carroll's "The Mad Gardener's Song" includes the lines "He thought he saw a Garden-Door / That opened with a key: / He looked again, and found it was / A double Rule of Three".