I think the jump you are referring to is in level 2. (the radio tower) Try setting your game to "always run". It should make the jumps easier. And then run and jump. When you want to walk up to the edge of a ledge without falling off, hold the shift key down in order to walk, not run.
You also might want to set your game to an easier setting. I think the default setting is harder.
Also, install the patch.