early 15c., "conclusive, logical," also "following as an effect or result," from Old French consequent "following, resulting" and directly from Latin consequentem (nominative consequens) "following, consequent," present participle of consequi "to follow after," from assimilated form of com "with, together" (see con-) + sequi "to follow" (from PIE root *sekw- (1) "to follow"). Related: Consequently.
"a thing which follows from a cause," 1610s, from a more precise sense in logic, "that which follows logically from a premise" (late 14c.; compare antecedent), a sense now in consequence. For etymology, see consequent (adj.). Mathematical sense is from 1560s.
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