On the subject of Ancient Gunpowder and other such weapons, I wonder if Gunpowder or a effective equialent could arise in Ancient Greece and change the face of warfare in the region.
Air Cannons: Ctesibius (282-22BC) is regarded as the father of the science of compressed air, creating many pump machines, and it is even said thathe created a sort of air cannon. Are these claims possible? If so bound by physics is it possible to be improved upon and what military applications are possible? Perhaps Air Guns?
Greek Fire: Greek fire was invented in 7th century, by a certain Lebanese Christian, but such forms of flamethrower weaponry have previously been used, is it possible that the Greek Fire formula becomes more widespread amongst the various powers?
Everything Archimedes: Archimedes is the most well known inventor from Claws to Heat Rays, is it possible that if he survived that he could have invented more and his weapons become more in use? One fictional book (the Lost Legion by H. Warner Munn) postulates that he worked on steam and hydraulics, where in the book a hydraulic gun was created to sucess (before it exploded, and in the words of the book itself the death of the Roman Legionaire-Would-Be-Inventor was a good thing because it forestalled the Steam Revolution and saved many lives). How would Steam Power effect the Roman Empire I wonder....
Polybolos: The Repeating Balista, what if its Driven Chain was used for smaller versions of itself in the form of Repeating Crossbows>?