This technically is not next on the list, but I have now read Sir Thomas Heath's translation of Apollonius of Perga's work On Conic Sections. Cambridge University Press still has this book in print, though in paperback only. For a hardcover edition, you will need to go scrounging through the used book listings once again. Like Heath's other translations, it is as approachable as Greek math is going to get. And Heath has relied much more heavily here on modern notation than in his other translations. This is largely because Apollonius' proofs are extremely large even with modern notation. I imagine nothing but the original textual descriptions would be an extremely tough nut for the modern reader to crack.
Between the first and second edition of the Great Books of the Western World, Apollonius was one of the few authors dropped. Mortimer J. Adler is said to have regretted the removal of Apollonius. However, having read Apollonius, I can understand why it was removed. His Conics is an extremely focused book. Since the Great Books reader has already read a ton of geometry, the novelty of the Greek methodology will have already lost its appeal by this point in the list. If you are not really into cones and the various ways to slice them up, this book is really not for you. Since it is not officially on the list and I was bored out of my mind, I have to confess that I mostly skimmed after the first quarter of the book. So my recommendation is to just stick to the second edition reading list and skip Apollonius unless you are a truly devote mathematician. For everyone else, maybe consider putting it on your list for the second round of reading where you catch up on all those related books you discovered through reading the existing list.