It isn't vulgar to make known the roots of divulge. The preceding sentence contains two hints about the origins of the word. Divulge was borrowed into Middle English in the 15th century from Latin divulgare, a word that combines the prefix dis-, meaning "apart" or "in different directions," with vulgare, meaning "to make known." Vulgare, in turn, derives from the Latin noun vulgus, meaning "mob" or "common people." As you have no doubt guessed, English vulgar is another word that can be traced back to vulgus.