Ancient greek "sans peine", so without pain, or without working hard at it ?
It's without "working hard at it" basicaly.
It's the principle of passive learning.
You go through the first half of the book by reading, pronuncing, listening to sentences (short sketches/stories). At this stage, you just observe the linguistic facts without trying to rationalise them. Then on each lesson you have some exercices of imitations (rephrasing mostly).
When you reach the first half of the book, you go on reading the second part and at the same time, you come back to the first lessons and now rationalise and draw grammatical laws from all you've read/learned before (they call that the "active learning). By the end of the book you've become well acquainted with the language.
I've been through the Modern Greek book, the Breton, German and tried to start the Chinese one. Unfortunately i'm a poorly organised one and it gets pretty difficult to stick to a tight schedule adding this to it, so i come and go to those books when i feel like... and it works pretty well actually.