Where does the flow of power come from for a Transmutation Circle to work? On the Full Metal Alchemist Wiki under the Category  Alchemy. It says this...


  The circle itself is a conduit which focuses and dictates the flow of
  power, tapping into the energies that already exist within the earth
  and matter. It represents the cyclical flow of the world's energies
  and phenomena and turns that power to manipulable ends.


But does this energy not come from a parallel world on the other side of the gate where alchemy took a different form of science? Did it not come from the lives of those who died in that world? Or is this different in FMA Brotherhood, because I am certain this is what Hohenhiem told Edward in the FMA Anime (2003).

Answers are appreciated. :)
Yes, It's different. The original FMA anime didn't wait around for the manga to catch up (like DBZ did), so it diverged instead.  

What you ended up with was 2 completely different endings, and 2 different explanations for why alchemy works:


In the original anime, the explanation was that It came from the other side of the gate.
In the manga and in brotherhood, it came from energy that was already in the earth.