What diseases could doctors cure in the 19th century?

I have reached the chapter in which Lady Arabella is sick. She had fallen out with Dr Thorne, so she started using Dr Fillgrave. That made me start wondering what sorts of serious disease a skilled physician could cure that a less skilful physician could not. Lady Arabella has a dangerous condition, but it is apparently not one of those common infectious diseases we had back then. If Lady Arabella had cancer, Dr Thorne could not have cured that. I wonder what diseases doctors could cure back then. They must have been able to cure some or nobody would have called them out.