prosecute (v.)

late 13c., "follow with hostile intent, follow with a view of overtaking," from Anglo-French pursuer and directly from Old French poursuir (Modern French poursuivre), variant of porsivre "to chase, pursue, follow; continue, carry on," from Vulgar Latin *prosequare, from Latin prosequi "follow, accompany, attend; follow after, escort; follow up, pursue," from pro- "forward" (see pro-) + sequi "follow" (from PIE root *sekw- (1) "to follow").

The meaning "to proceed, to follow" (a path, etc.), usually figurative (in reference to a course of action, etc.), is from late 14c. This sense also was in Latin. The meaning "seek, seek to obtain" also is late 14c. Related: Pursued; pursuing. For sense, compare prosecute.

1560s, "the carrying out or following up of anything" (also literal, "action of pursuing, a following after," but this is obsolete), from French prosecution (late 13c.) and directly from Late Latin prosecutionem (nominative prosecutio) "a following," noun of action from past-participle stem of prosequi "to follow after; chase, pursue; attack, assail" (see prosecute). The meaning "legal action, the institution and carrying out of a suit at law" is from 1630s. Hence, transferred, "the party by whom legal proceedings are initiated" (1891).