early 14c., equite, "quality of being equal or fair, impartiality;" late 14c., "that which is equally right or just to all concerned," from Old French equite (13c.), from Latin aequitatem (nominative aequitas) "the uniform relation of one thing to others, equality, conformity, symmetry;" also "just or equitable conduct toward others," from aequus "even, just, equal" (see equal (adj.)).

In law, "fairness in the adjustment of conflicting interests; the settlement of controversies by the dictates of good conscience" (natural equity), late 14c., from Roman naturalis aequitas, the general principles of justice which corrected or supplemented the legal codes ("governed by benevolence, while justitia yields to another only what is strictly due," Lewis & Short).

Hence, in England and U.S., also "justice based on such principles, the system of jurisprudence as to what is fair and what is not," and "a court or jurisdiction in which these doctrines are applied" (1590s).

The Latin word also meant "a quiet, tranquil state of mind; moderation, evenness of temper."

The L. æquitas was somewhat influenced in meaning by being adopted as the ordinary rendering of Gr. ἐπιεικεια ...,which meant reasonableness and moderation in the exercise of one's rights, and the disposition to avoid insisting on them too rigorously. [OED]

From 1620s as "an equitable right, that to which one is justly entitled," especially a right recognized by courts of equity that is not provided for in the common or statute law (such as certain property rights of wives). Equities, "the ordinary shares of a limited company," carrying certain rights to assets and profits, is attested by 1904.

By 1980s it had taken on extended senses in sociology, e.g.: "allocating benefits in various policy fields in such a way as to provide groups, persons, and places with at least a minimum level of benefits so as to satisfy basic needs" [Stuart S. Nagel, "Equity as a Policy Goal," 1983].

early 15c., "equal in value, power, or effect," from Late Latin aequivalentem (nominative aequivalens) "equivalent," present participle of aequivalere "be equivalent," from Latin aequus "equal" (see equal (adj.)) + valere "be well, be worth" (from PIE root *wal- "to be strong"). As a noun from c. 1500, "that which is equal or corresponds to." Related: Equivalently.

"of doubtful signification, capable of being understood in different senses," c. 1600, with -al (1) + Late Latin aequivocus "of identical sound, of equal voice, of equal significance, ambiguous, of like sound," past participle of aequivocare, from aequus "equal" (see equal (adj.)) + vocare "to call," which is related to vox (genitive vocis) "voice" (from PIE root *wekw- "to speak"). Earlier in same sense was equivoque (late 14c.). Related: Equivocally (1570s).

late 14c., "the fallacy of using a word in different senses at different stages of the reasoning" (a loan-translation of Greek homonymia, literally "having the same name"), from Old French equivocation, from Late Latin aequivocationem (nominative aequivocatio), noun of action from aequivocus "of identical sound, of equal voice, of equal significance, ambiguous, of like sound," past participle of aequivocare, from aequus "equal" (see equal (adj.)) + vocare "to call," which is related to vox (genitive vocis) "voice" (from PIE root *wekw- "to speak").