1690s, "moving or situated in different directions from a common point," from Modern Latin divergentem (nominative divergens), present participle of divergere "go in different directions," from assimilated form of dis- "apart" (see dis-) + vergere "to bend, turn, tend toward" (from PIE root *wer- (2) "to turn, bend").
General sense of "separating or separated from one another, following different courses or directions" is from 1801. Figurative sense of "deviating from something taken as a standard" is from 1839. Related: Divergently.