Online Etymology Dictionary

dexterity (n.) 1520s, from Middle French dexterit√© (16c.), from Latin dexteritatem (nominative dexteritas) “readiness, skillfulness, prosperity,” from dexter “skillful,” also “right (hand)” (source of Old French destre, Spanish diestro, etc.), from PIE root *deks- “on the right hand,” hence “south”