The Azores islands are a Portuguese archipelago in the North Atlantic Ocean, located about 1,500 km (930 mi) from Lisbon and about 3,900 km (2,400 mi) from the east coast of North America. 

There are conflicting records as to when they were discovered as stories have circulated even before the middle ages about a cluster of islands in the Atlantic Ocean. However, it was the Portuguese who laid claim to the islands in 1427 and colonized them in 1430. 

The islands were settled by a mixed group of people - Portuguese from the provinces, Madeirans, Moorish prisoners, enslaved Africans, French, Italians, Scots, English, Germans and Flemings were among the early settlers. There were petty criminals, Spanish clergy, Sephardic Jews, soldiers, government officials, European merchants and sugar cane growers.

The official colonization of the archipelago began in Santa Maria, where the first settlement was built. Settlers arrived from Portugal, in particular from the provinces of Algarve and Alentejo. By 1440, other settlements had developed along the river-valleys and coastal inlets of São Miguel, Terceira, Faial and Pico, supported by game and fishing. The availability of drinking water, along with fertile volcanic soils, made the islands attractive and easy to colonize, and the growing wheat market would support an export economy (along with various plant species that allowed the development of the dye industry in the colonies). Later, oranges were grown and exported to the British Isles.

The island of São Miguel was populated by 1444. Portuguese settlers came mostly from the regions of Estremadura, Alentejo and Algarve. The colonists spread themselves along the coastline in areas where conditions of accessibility and farming were best. The flourishing economy led to population expansion. In 1546, Ponta Delgada was made the capital of São Miguel and became the first city on the island.

Terceira was known as the island of Jesus Christ when it was settled by Portuguese navigators. Terceira's settlement was started on or about 1450 when its captaincy was granted to a Fleming, Jacome de Bruges, by Prince Henry the Navigator. The first settlements were situated in the areas of Porto Judeu and Praia da Vitoria and soon extended throughout the island.

Graciosa island was settled shortly afterward by settlers from Terceira.

Initially, Terceira's economy revolved around agriculture mainly through the production of grains, and the export of woad (a dye-yielding plant). The island began to play an important part in the history of navigation during the 15th and 16th centuries, as a port of call for the ships bringing the wealth of the Americas and for ships engaged in the East Indies trade. During this period Terceira was an emporium for the gold, silver, diamonds, and spices brought from other continents. This attracted the covetousness of French, English and Flemish corsairs who constantly attacked its coast for several centuries.

By the early 1800s, the population of Terceira was estimated to be between 40,000 and 50,000 inhabitants in three towns and 15 villages. Angra was the capital. 

The people of Terceira were held in great estimation, regarded as mild and benevolent and as superior in point of civilization to the inhabitants of the sister islands around. The men of Terceira were described as strong, well formed and with an agreeable expression of countenance; and the women more pleasing to the eye than those of the other islands.

To better understand the reasons behind the immigration of Portuguese from the Azores, one should try to perceive the nature of their birthplace. The inhabitants of these islands survived throughout centuries of disasters such as earthquakes which, time and again, destroyed their villages, often by complete burial. Additionally, they had to fight pirates who came from England and hid in the coves of the islands awaiting the Portuguese vessels on their way to Lisbon loaded with spices and skins from India. Crops were destroyed by strong winds; vines were attacked by illness, crippling wine production for European markets as well as destroying acres of oranges, once abundant in the Azores for export. These factors coupled with the fact that Azoreans were vastly ignored by the homeland, left the populace to their destiny of ignorance and illiteracy, exploited by the self-imposed aristocracy who, with a few exceptions, would worsen those conditions for their own economic and social benefit. In most cases, land was poorly divided, leaving the working population in a status of forever renting the land. They had to work in order to support their large families and pay fees and royalties. These fees took the form of shares of crops called for in the agreements and leases of the landlords.

Whilst the above are compelling reasons for migration, we have no definitive reason for the migration of our Cordeiro ancestors. Antonio Gonçalves Cordeiro was from São Pedro on the Island of Terceira. São Pedro is one of the five urban civil parishes of the municipality of Angra do Heroísmo, the historical capital of the Azores. The commercial port of early Angra also played an important role in the Portuguese East Indies trade beginning in the 15th Century. Hence, it is not unreasonable to suggest that our ancestors (either Antonio Gonçalves Cordeiro or his son, Manuel Gonçalves Cordeiro) may have been a trader or perhaps a person of status sent to Macau for work reasons.

Sources:
Wikipedia Azores
Azores.com
Azores Islands, Robert L. Santos, California State University