This is one of Somtow’s early books, and in a 1983 edition (first, I think) from before he began publishing as SP Somtow. Really, the man is incredibly, ridiculously multitalented. It’s actually the first of three in this world, but I had to go looking to find that out, and I’ll count myself absurdly lucky if I find the others any time soon.
It’s an alternate-history job, set in a world where the Roman Empire develops steam power under the Julio-Claudians and can therefore expand across the Atlantic, into the lands of the Apaxae, Comanxii, and so forth.
Our viewpoint character, Titus Papinianus, is the Commander of the Thirty-Fourth Legion—-not this Papinianus, but presumably a relative. “Papinian” is Somtow’s middle name. The Aquila of the title (“actually some barbaric tongue-twister, but it means eagle”) is the war-chief of a band of Lacotii auxiliaries, bought for the arena and then sent off by Domitian to aid the Thirty-Fourth in Cappadocia.
That’s the first book of Aquila, originally published on its own; the books after that deal with Titus’s experiences as Governor of Terra Nova, sent to find a route to the Chinish Empire by Domitian and then by Trajan. First south, to the land of the Olmechii, and then west and north to the land of the Kwakiutl, which must clearly be the land they seek given the combination of giant bones littering the land (the remains of silkworms, as in the scientiae fictiones of P. Iosephus Agricola) and the discovery of a scroll which is “a dictionary of the Chinook speech! Now what else could that mean, but that we have here a transcription into Egyptian letters of the Chinish tongue?”
There’s a bit of racial stereotyping going on, which is sort of inevitable in SF of this era, but it’s countered by comments about the problems with imperial projects.
 No, it sounds more like Herbert to me too, but I may be missing something. There are a lot of these littering the text, such as the Judean Asimianus and his epic poem Fundatio.