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balance (n.)

early 13c., "scales, apparatus for weighing by comparison of mass," from Old French balance "balance, scales for weighing" (12c.), also in figurative sense; from Medieval Latin bilancia, from Late Latin bilanx, from Latin (libra) bilanx "(scale) having two pans," possibly from Latin bis "twice" (from PIE root *dwo- "two") + lanx "dish, plate, scale of a balance," which is of uncertain origin.

The accounting sense "arithmetical difference between the two sides of an account" is from 1580s; meaning "sum necessary to balance the two sides of an account" is from 1620s. Meaning "what remains or is left over" is by 1788, originally in commercial slang. Sense of "physical equipoise" is from 1660s; the meaning "general harmony between parts" is from 1732.

Many figurative uses are from Middle English image of the scales in the hands of personified Justice, Fortune, Fate, etc.; thus in (the) balance "at risk, in jeopardy or danger" (c. 1300). Balance of power in the geopolitical sense "distribution of forces among nations so that one may not dominate another" is from 1701. Balance of trade "difference between the value of exports from a country and the value of imports into it" is from 1660s.

balance (v.)

1570s, "be equal with," from balance (n.). Meaning "serve as a counterpoise to" is from 1590s; that of "bring or keep in equilibrium" is from 1630s; that of "keep oneself in equilibrium" is from 1833. Of accounts, "settle by paying what remains due," from 1580s. Related: Balanced; balancing.

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Definitions of balance
1
balance (n.)
a state of equilibrium;
balance (n.)
equality between the totals of the credit and debit sides of an account;
balance (n.)
harmonious arrangement or relation of parts or elements within a whole (as in a design); "in all perfectly beautiful objects there is found the opposition of one part to another and a reciprocal balance"- John Ruskin;
balance (n.)
equality of distribution;
balance (n.)
something left after other parts have been taken away;
he took what he wanted and I got the balance
Synonyms: remainder / residual / residue / residuum / rest
balance (n.)
the difference between the totals of the credit and debit sides of an account;
balance (n.)
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane;
Synonyms: symmetry / symmetricalness / correspondence
balance (n.)
a weight that balances another weight;
Synonyms: counterweight / counterbalance / counterpoise / equalizer / equaliser
balance (n.)
a wheel that regulates the rate of movement in a machine; especially a wheel oscillating against the hairspring of a timepiece to regulate its beat;
Synonyms: balance wheel
balance (n.)
a scale for weighing; depends on pull of gravity;
2
balance (v.)
bring into balance or equilibrium;
She has to balance work and her domestic duties
balance the two weights
Synonyms: equilibrate / equilibrize / equilibrise
balance (v.)
compute credits and debits of an account;
balance (v.)
hold or carry in equilibrium;
Synonyms: poise
balance (v.)
be in equilibrium;
3
Balance (n.)
(astrology) a person who is born while the sun is in Libra;
Synonyms: Libra
Balance (n.)
the seventh sign of the zodiac; the sun is in this sign from about September 23 to October 22;
Synonyms: Libra / Libra the Balance / Libra the Scales
From wordnet.princeton.edu