Historia Augusta, Hadrian 4:
The common opinion was that Trajan had it in mind to leave Neratius Priscus, not Hadrian, as his successor, and that many of his friends agreed with him in this, to the extent that he once told Priscus, “I commend the provinces to you, if anything fatal should ever happen to me.” And indeed, many assert that Trajan’s intention was to follow the example of Alexander of Macedon and die without a successor; and many also assert that on the verge of death, he wished to send a speech to the senate so that, in the event that something happened to him, the senate could provide an emperor for the Roman people; this speech was to be delivered with some names from which that same senate could select the best candidate.
Frequens sane opinio fuit Traiano id animi fuisse, ut Neratium Priscum, non Hadrianum successorem relinqueret, multis amicis in hoc consentientibus, usque eo ut Prisco aliquando dixerit: “commendo tibi provincias, si quid mihi fatale contigerit”. Et multi quidem dicunt Traianum in animo id habuisse, ut exemplo Alexandri Macedonis sine certo successo remoreretur, multi ad senatum eum orationem voluisse mittere petiturum, ut, si quid ei evenisset, principem Romanae rei publicae senatus daret, additis dum taxat nominibus ex quibus optimum idem senatus eligeret.
