'Pursue' and 'prosecute' are the same Latin verb — one came through French sound changes, one through scholarship.
To follow or chase someone or something; to continue or proceed along a path or route; to seek to attain or accomplish a goal.
From Anglo-Norman 'pursuer,' from Old French 'porsivre / poursuir' (to follow after, to chase), from Latin 'prosequi' (to follow forward, to accompany, to pursue, to narrate at length), a compound of 'pro-' (forward, along, in front of) + 'sequi' (to follow). The Latin 'sequi' is the direct reflex of PIE *sekw- (to follow, to accompany), one of the most productive roots in the family. The same root produced Sanskrit 'sacate' (he follows
The phrase 'pursuit of happiness' in the American Declaration of Independence uses 'pursuit' in a sense closer to its Latin root than modern casual usage suggests. Jefferson's 'pursuit' meant active, purposeful following — not mere chasing, but the deliberate and sustained following of a goal. The word's etymology (to follow forward) captures