A proportion is an equation stating that two ratios are equal: a/b = c/d.
In a proportion, the cross-products are equal: ad = bc. If a/b = c/d, we say a, b, c, d are in proportion. Direct proportion: y = kx, where k is a constant (y increases as x increases). Inverse proportion: y = k/x (y decreases as x increases). Proportions are used in scale drawings, unit conversion, recipes, map reading, and solving percentage problems.
The theory of proportions was developed by Eudoxus of Cnidus (400-350 BCE) and is presented in Book V of Euclid's "Elements." The concept was crucial for Greek mathematics, allowing them to work with irrational numbers through geometric means. The Rule of Three (solving proportions) was taught in medieval schools and used in commerce.