Actor – ORIGIN late Middle English (originally denoting an agent or administrator): from Latin, ‘doer, actor,’ from agere ‘do, act.’ The theater sense dates from the 16th cent.

Author – ORIGIN Middle English (in the sense ‘a person who invents or causes something’): from Old French autor, from Latin auctor, from augere ‘increase, originate, promote.’ The spelling with th arose in the 15th cent., and perhaps became established under the influence of authentic.

Authentic – ORIGIN late Middle English: via Old French from late Latin authenticus, from Greek authentikos ‘principal, genuine.’

Authority – ORIGIN Middle English: from Old French autorite, from Latin auctoritas, from auctor ‘originator, promoter.’

Then there’s the word augur. According to the Online Etymology Dictionary:

…augur, a religious official in ancient Rome who foretold events by interpreting omens, perhaps originally meaning “an increase in crops enacted in ritual,” in which case it probably is from Old L. augos (gen. augeris) “increase,” and is related to augere “increase” (see augment). The more popular theory is that it is from L. avis “bird,” since the flights, singing, and feeding of birds, along with entrails from bird sacrifices, were important objects of divination (cf. auspicious). In that case, the second element would be from garrire “to talk.” The verb is c.1600, from the noun.