Did any contemporaries ever refer to/address a Roman Emperor as "Emperor"?
I know that Augustus, the first emperor, was careful to avoid monarchical titles like "king" or "emperor" because he did not want to upset the Senate. Instead he used more innocuous titles like "first citizen" and "tribune." Presumably his successor emperors continued this tradition of side-stepping, but apparently somewhere in the course history we started referring to the rulers of Rome as "emperors."
Thinking about this led me to several questions:
When did people/emperors start calling Roman Emperors "emperor" instead of the more humble titles used by Augustus? What led to them giving up on the facade?
Before this point how would an Emperor react if someone addressed him as such to his face?
Did the title change work retroactively? i.e. would a writer of a later period refer to Augustus as "emperor" instead of "princeps"?
What did the rulers of the Byzantine Empire call themselves after the Western Empire was dissolved? Did they simply continue to be Roman Emperors of the Roman Empire?
Remember that 'emperor' is an English title, which is not directly analogous to the Latin imperator. When we say that Augustus became the first 'emperor', we are analysing a unique, and irreversible, combination of both political offices and personal status/influence that coalesced in a single figure, who simply could not be matched within the sphere of Republican Rome.
The title imperator is more specifically one associated with military power, and the concept of imperium, the right to put to use the power of the state, primarily through the army.
In the Greek East autokrator was used as a translation for imperator, but it does not have quite the same idea.
It's fairly common to refer to the period Augustus through to Domitian as the Principate because Augustus preserved the title princeps and maintained many of the trappings of Republicanism, as did his immediate successors. While Domitian did away with a lot of them, and the increasing 'easternness' of the Empire saw adoption of stylings more familiar to the Hellenic and even Persian world - which had less hang-ups about (divine) Monarchs.
In the east emperors tended to be referred to in Greek as basileus, which originally meant 'king', but in the imperial period tends to only refer to the Roman emperor(s); ironically, they took the Latin word rex (also 'king') into Greek to refer to kings.
So, really, I am saying that there wasn't really a 'word' for 'emperor', in Latin/Greek, there was a range of titles and terms, none of which exactly overlays our 'emperor'.