tact (n.)

1650s, "sense of touch or feeling" (with an isolated instance, tacþe from c. 1200), from Latin tactus "a touch, handling, sense of touch," from root of tangere "to touch" (from PIE root *tag- "to touch, handle").

The meaning "fineness of discernment in action or conduct, diplomacy, intuitive mental perception of what is best to do or say" is in English by 1804, noted at the time as a development in the French cognate tact. The Latin figurative sense was "influence, effect."