Do you have any books? would be Har du några böcker?
The thing here is that while you can say Have you no books? in English (also an accepted answer), the most natural way to translate this Swedish sentence is Don't you have any books? And vice versa, if you translate that back into Swedish, it is possible to say Har du inte några böcker? but we prefer the construction with inga.
Other than that, no normally translates as ingen/inget/inga and not translates as inte. But it doesn't work out like that in cases like this one, because of the difference between några-inga and some-any-none.