pursue

1250–1300; Middle English pursuen < Anglo-French pursuer ≪ Latin prōsequī to pursue, follow, continue. See pro-¹, sue, prosecute

The current spelling of the English verb pursue dates from about 1300. It is one of several former spellings, including perseve, pursiew, pursuwe. The Middle English variants come from Anglo-French and Old French porsure, poursuire, porsivre (with many other spelling variants), ultimately from Latin prōsequi “to attend (with honors or compliments), go in pursuit of, follow with hostile intent, harry, examine or follow up (a subject or topic), continue,” which is the source of English prosecute
The many Latin meanings of prōsequi carry over into Old French and Middle English, and by the end of the Middle English period, the word pursue already had all of its current meanings. On the other hand, the word prosecute originally meant “to follow up, pursue, continue,” but shortly afterward, in the early 16th century, it took on its primary current meaning “to institute legal proceedings.”