Third Kingdom: the waist/leggings of bronze. Also described as a four headed leopard with eagles wings.

Was the Greek army known for being swift and powerful? Alexander the so-called "Great," was a mighty king. Kings are set up and removed by God, are they not? Yet, he is so-called "Great." If you look at him from man's eyes alone, perhaps he was. Secular history would surely bill him accordingly, and does for that matter.

Each procession in the statue, and each beast in the progression of stream of time, the previous kingdom wasn't totally annihilated.  Rather that the previous kingdoms were taken over and with the new guy at the head, giving preference to that which is favorable.  So, the Babylonian philosophies and the philosophies of the Medes and Persians were not cut off, but rather took on modified appearances and infused into the next link of the chain.