"Britain, a former part of the Roman Empire, began rising to prominence in the late 1700's." - p.19
'Began rising to prominence in the late 1700s'???
First British Empire (1583-1783)
Main article: English colonial empire
In 1578, Queen Elizabeth I granted a patent to Humphrey Gilbert for discovery and overseas exploration.  That year, Gilbert sailed for the West Indies with the intention of engaging in piracy and establishing a colony in North America, but the expedition was aborted before it had crossed the Atlantic.   In 1583 he embarked on a second attempt, on this occasion to the island of Newfoundland whose harbour he formally claimed for England, although no settlers were left behind. Gilbert did not survive the return journey to England, and was succeeded by his half-brother, Walter Raleigh, who was granted his own patent by Elizabeth in 1584. Later that year, Raleigh founded the colony of Roanoke on the coast of present-day North Carolina, but lack of supplies caused the colony to fail. 
In 1603, King James VI of Scotland ascended to the English throne and in 1604 negotiated the Treaty of London, ending hostilities with Spain. Now at peace with its main rival, English attention shifted from preying on other nations' colonial infrastructure to the business of establishing its own overseas colonies.  The British Empire began to take shape during the early 17th century, with the English settlement of North America and the smaller islands of the Caribbean, and the establishment of private companies, most notably the English East India Company, to administer colonies and overseas trade. This period, until the loss of the Thirteen Colonies after the American War of Independence towards the end of the 18th century, has subsequently been referred to as the "First British Empire". 
The early 17th century is, of course, the early 1600s.