late 15c., "to decrease," also "to decline, deteriorate, lose strength or excellence," from Anglo-French decair, Old North French decair (Old French decheoir, 12c., Modern French déchoir) "to fall, set (of the sun), weaken, decline, decay," from Vulgar Latin *decadere "to fall off," from de "off" (see de-) + Latin cadere "to fall" (from PIE root *kad- "to fall").
Transitive sense of "cause to deteriorate, cause to become unsound or impaired" is from 1530s. Sense of "decompose, rot" is from 1570s. Related: Decayed; decaying.
mid-15c., "deterioration, decline in value, gradual loss of soundness or perfection," from decay (v.). Obsolete or archaic in reference to fortune or property; meaning "decomposition of organic tissue" is from 1590s. In physics, the meaning "gradual decrease in radioactivity" is by 1897.