why private part of a class is considered as interface?

I'm reading Grady Booch's book third edition. In page 94, Booch said that:

We can furthur devide the interface of a class into four parts:

1. Public: a declaration that is accessible to all clients
2. Protected: a declaration that is accessible only to the class itself and its subclasses
3. Private: a declaration that is accessible only to the class itself
4. Package: a declaration that is accessible only by classes in the same package

I can understand why protected declaration can be considered a interface, becuase subclasses of a class is this class's client, too.

But I don't understand why the private declaration can be considered as interface. Please enlight me.