Final answer:
Hadrian's Rescript represented the unrestricted imperial authority with laws taking effect throughout the empire, contrasting with Trajan's military expansions and his involvement in practical governance and correspondence with the senate.
Step-by-step explanation:
The question concerns the differences between Hadrian's Rescript and Trajan's rule as Roman emperors. Hadrian's Rescript refers to the imperial proclamations that carried the force of law, differing from Trajan's more traditional administrative approaches. Hadrian's time marked a shift towards consolidation and cultural projects, such as the construction of the Pantheon and Hadrian's Wall, as opposed to Trajan's military expansions and pragmatic governance. Trajan was known for his military conquests, notably expanding the Roman Empire to its greatest size, but his successor Hadrian gave up Trajan's conquests in Mesopotamia, considering them unsustainable. Hadrian focused on establishing the cultural capital in Athens and building significant architectural works within the Empire.