"quantity having magnitude and direction," 1846; earlier "line joining a fixed point and a variable point," 1704, from Latin vector "one who carries or conveys, carrier" (also "one who rides"), agent noun from past-participle stem of vehere "carry, convey" (from PIE root *wegh- "to go, move, transport in a vehicle"). Related: Vectorial.
1640s, "making or exhibiting a difference," from Medieval Latin differentialis, from Latin differentia "diversity, difference" (see difference). Related: Differentially. As a noun in mathematics, "an infinitesimal difference between two values of variable quantity," from 1704. Differential calculus is attested from 1702.
"of or pertaining to the Greek sea-god Proteus," 1590s, from Greek Prōteus, son of Oceanus and Tethys, who could change his form at will; hence, "readily assuming different shapes, exceedingly variable." His name is literally "first," from prōtos "first" (see proto-).