ratio

Ratio in Latin means a reckoning, a calculation, an account, a reason, from reri (to reckon, to think, to believe). The word covered both the act of calculating and the faculty of reasoning — for the Romans, these were not separate activities. A ratio of accounts was a financial calculation. The ratio of a decision was its logical basis. The word moved between numbers and thoughts without friction.

The mathematical meaning narrowed in medieval and early modern Europe. Euclid's Greek word for ratio — logos — was translated into Latin as ratio. A ratio became specifically a comparison of two quantities: the ratio 3:4 compares three of something to four of something. The word kept its calculating sense and shed (in mathematical contexts) its reasoning sense. But the two meanings never fully separated — to this day, a 'rational number' is one that can be expressed as a ratio.

The golden ratio (approximately 1.618) has been celebrated since antiquity. Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity. The Greeks called it the 'extreme and mean ratio.' Luca Pacioli called it the 'divine proportion' in 1509. The golden ratio appears in the Fibonacci sequence, in phyllotaxis (leaf arrangement), and allegedly in the Parthenon's proportions — though this last claim is disputed.

In modern English, 'ratio' is standard in mathematics, science, finance, and everyday speech. Debt-to-income ratio. Student-teacher ratio. Aspect ratio. The word compares two quantities and expresses their relationship as a single number. The Latin reckoning has become a universal comparison tool.