Thanks! I think I now recognize this from Spivak (Calculus), where much of the teaching is literally in the exercises. You are guided along, deriving/proving many things along the way, some incidental, some cumulative. (There's also important exposition in the exercises.)

A downside is you lose the thread if you skip exercises (e.g. do alternate ones) - the exercises are an integrated whole. But it's a lot to do all of them.

I hadn't gotten the impression that these helped show why exactly the axioms were choosen - though could well be there and I just didn't see it.