Part 2 of a 6-part BBC docuseries begins roughly at the end of the Roman Republic (the start of the Roman Empire).
History of Ancient Rome can be roughly divided into 4 phases:
1. The Roman Kingdom (753 BC–509 BC),
2. The Roman Republic (509 BC–27 BC),
3. The Western Roman Empire (TWRE) which for centuries included modern-day England and Wales, but never Scotland or Ireland (27 BC–00476 AD),
4. The Eastern Roman Empire (TERE) survived the fall of TWRE and lasted until 01453.
For context, The Scientific Revolution (which most scientists consider to have begun with The Copernican Revolution) began 90 years later in 01543 in Thorn, Royal Prussia, Poland (birthplace of Nicolaus Copernicus).
The region now called Poland was never a part of Ancient Rome (which never extended significantly north of The Black Sea in the European mainland), and Poland was one of the last regions of Europe to accept Christianity, which (having been embraced in 00313 when co-Emperors Constantine the Great and Licinius issued the Edict of Milan, providing for restitution to Christians injured during the persecutions), could arguably be considered to be an extension of Ancient Rome.
-TWRE lasted roughly 1,200 years in duration.
-Ancient Rome (including TERE) lasted rougly 2,206 years.
-If one considers Christianity to be an extension of Ancient Rome, then predominantly-Christian nations could arguably still be considered to be a part of a Roman civilization that has so far lasted 2,773 years.
The fall of TWRE was a 74-year-long period from about 00402 (when the capital of TWRE was forcibly moved from the city of Rome to the city of Ravenna), through 00410 (when the Sack of Rome occurred: Rome was sacked by the Visigoths under their king Alaric I), until about 00476 (when Odoacer conquered the Western Roman capital Ravenna, forced Emperor Romulus to abdicate, declared himself king of Italy, and The former Roman Senate sent former Emperor Zeno the imperial regalia of the Western Roman Empire).
See the wikipedia timeline for more detail.