[This is the text I'm using] (www.attalus.org/translate/caesars.html) and here is the passage in question. "Next came Claudius, at whom all the gods gazed, and admiring his greatness of soul granted the empire to his descendants, since they thought it just that the posterity of such a lover of his country should rule as long as possible."
That's a good question. The Historia Augusta, a deeply unreliable document, made the claim that Constantius Chlorus (the father of Constantine the Great and progenitor of the Constantinian dynasty) was the grand-nephew of Claudius II Gothicus, which implies it was a claim that the Constantinians (including Julian) were making at the time to make the Constantinians seem a bit less like upstarts and be attached by blood to a popular and militarily-successful emperor from a few generations back. Again, we have no idea if this blood relation between Claudius and the Constantinian Dynasty is actually true, but we do know that the Constantinians claimed it was true.