Final answer:
Propertius lived and wrote under the reign and patronage of the Roman Emperor Augustus, who was known for his support of the arts and literature during the early Roman Empire.
Step-by-step explanation:
Propertius lived and wrote under the reign and patronage of Augustus. The historical context provided by references to prominent individuals such as Quintus Metellus Pius, Decimus Brutus, and Fulvius highlights the period of the early Roman Empire, during which Augustus, known for his significant reforms and being the founder of the Roman Principate, extended his support to literature and the arts. Propertius, belonging to that era, benefitted from this cultural renaissance and Augustus' patronage. The Senate's recognition of Augustus as the Princeps Senatus, the details about public services and homage to the Muses, all fit the cultural ambiance that Propertius would have experienced as a poet of that age.