After the civil war (click here) that followed the death of Qin Shihuang in 210 B.C., China was reunited under the rule of the Han dynasty, which is divided into two major periods: the Western or Former Han (206 B.C.–9 A.D.) and the Eastern or Later Han (25–220 A.D.). The boundaries established by the Qin and maintained by the Han have more or less defined the nation of China up to the present day. The Western Han capital, Chang’an in present-day Shaanxi Province—a monumental urban center laid out on a north-south axis with palaces, residential wards, and two bustling market areas—was one of the two largest cities in the ancient world (Rome was the other)....
At no point in time does any expansion of China include Taiwan. It wasn't until WWII that those in power of the settlement with Japan decided China can do what it wanted in Pacific Ocean and the seas surrounding China. It was NOT The West's right to do that. Taiwan was already a part of The West and developed culture from The East, but, also The West.