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The fun thing about gunpowder is that, being a formula that was discovered by accident, you can plop its invention to almost any point in history, earlier or later than the historical date. Within the first century of gunpowder, you should be able to get basic rockets. Within the second, cannons. Within the third, hand cannons.

So, gunpowder is discovered, for our convenience, around AD 1, in the Roman Empire (Alexandria seems as good a place as any). This puts rockets in the Roman arsenal circa AD 100, cannons circa AD 200, and handcannons circa AD 300, if they follow the historical speed of progression. Given that adopting new weaponry was one of the Roman's strengths, if you think you can justify slightly faster speeds, I won't argue too strenuously against it.

So, with all of this in mind, what impacts might we see? Remember that, beyond the obvious military applications, gunpowder also encourages advancements in metallurgy, and it can be used in construction.
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