Prosecute
late Middle English (in prosecute (sense 2)): from Latin prosecut- ‘pursued, accompanied’, from the verb prosequi, from pro- ‘onward’ + sequi ‘follow’.
wiktionary
Borrowed from Latin prōsecūtus, perfect participle of prōsequor. Doublet of pursue, from Old French. Compare also persecute.
etymonline
prosecute (v.)
early 15c., prosecuten, "to follow up, pursue with a view to carry out or obtain" (some course or action), from Latin prosecutus, past participle of prosequi "follow after, accompany; chase, pursue; attack, assail, abuse," from pro- "forward" (see pro-) + sequi "follow" (from PIE root *sekw- (1) "to follow"). Meaning "bring to a court of law, seek to obtain by legal process" is recorded from 1570s. The Latin verb in Old French became prosequer, vulgarly porsuir, which passed to English as pursue.
