proportion, in mathematics, the equality of two ratios. Two pairs of quantities a,b and c,d are in proportion if their ratios a/b and c/d are equal, i.e., if the equation a/b=c/d is true. For example, the lengths of two sides of any triangle and the lengths of the corresponding two sides of any similar (same-shaped) triangle are in proportion, for the ratio of the two sides of the first can be proved to be the same as the ratio of the two sides of the second. The proportion a/b=c/d was formerly written a:b::c:d and is read as “a is to b as c is to d.” In this form it is customary to call b and c the means and a and d the extremes. These terms are used in the statement of the rule—the product of the means equals the product of the extremes. When the proportion is written in equation form, however, this rule is seen to be simply the result of a familiar algebraic operation. Similarly all the other rules stated for proportions become obvious when the proportion is written as an equation and the usual rules of algebra are applied. The special proportion a/b=b/(a+b) is known as the Divine Proportion, or Golden Section.
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