Which books of Polybius’s Histories have survived complete?

Of the 40 books that comprise the Histories by the Greek historian Polybius, only Books I through V have survived in their complete form.1

The remaining portions of the work are known today through various excerpts, including those preserved in a 10th-century collection of passages from Greek historians that were rediscovered and published between the 16th and 19th centuries. The 40th book of the original work served as an index.1