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For us, it was easy to prove that Dido found the best possible solution to her problem. It was much harder for Dido, however. Not only did she have to do without magic pictures, but a lot less was known about mathematics in the time she lived.
Apart from being female, Dido had the best possible starting point for a mathematical career. She was a royal daughter and therefore had access to the best educators, and she didn't have to work like women of the lower classes. She was from Phoenicia, a nation of sailors and merchants. The Phoenicians had a lot of contact with the Egyptians and Babylonians, the leading nations in the sciences of that time.
But even with this starting point, Dido couldn't have known half as much about mathematics as we know today. The Phoenecians probably knew about the Pythagorean theorem and were able to solve algebraic problems. Their mathematical skills were very limited though. For example, you can clearly see this when you take into consideration that a kind of zero was first used 200 years after Dido. So she really must have been a mathematical talent to find the best possible solution for her problem.
