Final answer:
The southern part of Spain's American empire was known as New Spain, which included present-day Mexico and parts of the southwestern United States. The United States gained Florida from Spain through the Adams-Onís Treaty, highlighting the challenging period for Spain in maintaining its New World Empire.
Step-by-step explanation:
The southern part of Spain's American empire was called New Spain. This region encompassed territories that include modern-day Mexico, Central America, and parts of the southwestern United States such as California, Arizona, New Mexico, and Texas. The capital of New Spain was Mexico City. In contrast, the Viceroyalty of Peru included territories that are now known as Peru, Chile, Bolivia, and Ecuador, with Lima as its capital city. Additionally, the Viceroyalty of New Granada was composed of areas that correspond to modern-day Venezuela, Colombia, Panama, and later Ecuador, governed from Bogota.
The Adams-Onís Treaty resulted in the United States acquiring Florida from Spain. This was significant as it reflected Spain's increasing difficulty in maintaining control over its New World Empire, particularly after fearing the loss of Florida amid growing revolutions in Latin America.
It's noteworthy that Spain was the country that established the first colonies in the Americas, bolstering its vast empire that at one point included Cuba, Puerto Rico, the Philippines, and Guam following Columbus's discovery in 1492.