@T.E.D. Seems like it would have been possible at any rate - signatures go as far back as writing itself - but they were mostly used on documents such as land deals or legal decrees. A "signed book" is not really a "signature" but actually an autograph and the concept of collecting autographs didn't really exist until the 16th century
(of course, autographs as in "books scribed by their author" were in great demand in antiquity but I don't think they would be "signed" beyond the author putting their name on it as normal for any book)
My presumption looking into this last week is that "Homer", if there indeed was a single such person, likely was not literate, and what we have are records of the oral epic poem transcribed by scribes.
Harvard being established since the 1600s...I can't find much information about this but imagine it's 1770s, tensions are high, and the American Revolution is brewing. With all the colonists mobilizing, I wonder if any British students or faculty at Harvard chose to join the Continental Army and ...