Origins
Your bank balance owes its name to a Roman dinner plate.βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ Latin lanx meant 'a large flat dish' β a serving platter. When such dishes were repurposed as the pans of a weighing device, the compound bilanx ('two plates') was born. Through Late Latin bilancia and Old French balance, it became the English word for equilibrium.
The weighing metaphor proved extraordinarily fertile. A balanced argument has equal weight on both sides. A balanced diet distributes nutrients evenly. A balanced person maintains emotional stability β as though their temperament sits level on a scale.
Development
The financial meaning appeared in the 15th century. Double-entry bookkeeping, developed in medieval Italy, required debits and credits to balance β to weigh equally, like items on a bilancia. The 'balance' of an account is what remains when the two sides are compared.
The zodiac sign Libra ('scales') represents the same concept in Latin. The constellation was associated with justice β the balanced weighing of evidence. The symbol of justice, a blindfolded figure holding scales, echoes the same imagery that gave English the word balance.