What exactly is augmenting path?

Question

When talking about computing network flows, the Algorithm Design Manual says:

Traditional network flow algorithms are based on the idea o

Answer 1

An augmenting path is a simple path - a path that does not contain cycles - through the graph using only edges with positive capacity from the source to the sink.

So the statement above is somehow obvious - if you can not find a path from the source to the sink that only uses positive capacity edges, then the flow can not be increased.

By the way the proof of that statement is not that easy.