Grimrock

I'm stuck somewhere in the Archives. There is a room with some flying monsters, and a lower area with green slimes. If you follow a few ladders you end up in a higher area just above the doorway you came in. There is a sign saying "Path of the Eagle" or something similar. What do you have to do here?

I've tried throwing Throwing Weapons to all the walls I could reach, thinking they can "fly", because there were some shuriken, but that wasn't it.
Dropping down serves no purpose either. There is one platform you can reach only this way, but it doesn't lead anywhere.

Any help is appreciated.

If that doesn't help:

Really? I though I tried that... Alright, thanks, I'll give it another go!

follow the highest path always. look down, and always stay where you would fall 2 levels instead of one.

spoiler for way back...

Odd, I assumed it meant this right from the start but whenever I walked off the edge I just plummeted like a stone...

Will try again!