The Persian Empire was a remarkably large and successful realm, at its peak sprawling across Central Asia, into NW India (including most of modern Pakistan), much of the Middle East, western coast of Arabia, Egypt, the Sinai, Anatolia, and northern Greece. The Persian pontoon bridge over the Danube was an impressive achievement by the imperial military engineers, and was done in order to attempt the conquest of the Scythian area north of the Black Sea. Alexander the Great's conquest of the Persian Empire went well, but his death at 32 led to a three-way split among his generals. The Seleucid Empire comprised much of the old Persian territory, but over time got carved into multiple ethnic kingdoms. Its tettering final remnant west of the Euphrates fell to the Romans about 64 BC.
The Han lasted roughly 400 years and while it was in contact with the Roman Empire, both of them experienced a 3rd c AD crisis, from which only Rome emerged reconstituted. Contact with the Hellenized Alexandrian successor states in Central Asia took place.
The Mongol Empire wasn't actually a single authority in control of much of the territory often bragged about by its advocates. It didn't establish durable control, and its duration was a bit more than 150 years, during which time its primary faction was subsumed into the deeper cultures of China, well established by the The Han Dynasty.
The Roman Empire began in Italy circa 500 BC with Rome's annexation of Ostia, and continued until Constantinople in 1453, a mere 39 years before Columbus set sail. After Roman expansion reached Anatolia, intermittent conflict with the Parthian Empire (a partly Hellenized successor to the Persian Empire) went on until the muzzie conquest of what's now Iran in the mid-7th c AD.
Charlemagne founded the mighty French kingdom of the Middle Ages, which led to France having the largest population in Europe by the end of the 18th century, and one of the largest in the world. The French Revolution and its purges and attacks by neighboring powers, followed by the Napoleonic Wars, whittled this down some, but France was the major rival of the Habsburgs in Europe before and after the French monarchy. France didn't get wrung out until both World Wars and, like Britain, the bloodletting from those conflicts led to the loss of much of their former overseas empire.
The Seljuk dynasty of Turks swung round into Anatolia and bit off pieces of Byzantine Anatolia, finally falling in its turn early in the 14th c. The Ottoman Empire emerged in Anatolia 1299 AD, reached its peak in the mid 16th c, and did pretty well through the mid 18th. Turkish groups have been dominant or shared dominance in Central Asia for a long while. Influence beyond their geographic limits have not been spectacular IMHO.
Habsburg Spain controlled more of the world's surface than any of its peers or probably any other political entity in history. The Habsburgs defeated the Ottoman Empire at Lepanto (sez here the largest Mediterranean naval engagement since Actium). The mines at Potosi were already being exploited prior to Spanish conquest, but the arrival of the Spanish juiced production; the estimates range from 25-35 percent of all the silver ever mined on Earth having come from Potosi. Yet that vast fortune came and went.
I like it. Good post.