On = about (what the book is about). A better synonym might be "how to do" (a compendious book about how to do ...) By = using the technique of (how to calculate using the techniques of completion and balancing)

Both are preposition of place. On is all about calculation of something. By the completion in balacing numbers. That means where the preposition point. There are two exacts point of view. Calculate for complete and balanced numbers.