Proliferate is a back-formation of proliferation. That means that proliferation came first (we borrowed it from French in the 18th century) and was later shortened to form the verb proliferate. Ultimately these terms come from Latin. The French adjective prolifère ("reproducing freely") comes from the Latin noun proles and the Latin combining form -fer. Proles means "offspring" or "descendants," and -fer means "bearing." Both of these Latin forms gave rise to numerous other English words. Prolific and proletarian ultimately come from proles; aquifer and words ending in -ferous have their roots in -fer.