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The Treaty of Tordesillas divided South America between Portugal and Spain. Portugal gained control of present-day Brazil, while Spain gained control of most of the rest of South America.
Portugal gained control over part of Brazil, and then argued that the line was not fair so it was moved so that they got full control of Brazil.
It's was England who gained control by defeating the French fleet of the cost of the Netherlands.
Portugal gained control of Brazil in the Americas. The future country of Brazil was claimed for Portugal in April 1500 by Pedro Álvares Cabral [ca. 1468 - ca. 1520]. Subsequently rival strongholds established by British, Dutch, French and Spanish settlers were overthrown successfully by Portugal.
Spain and Portugal, Portugal gaining what is today Brazil, Spain got the rest.
England gained control over the New Netherlands twice. The first time was in 1664, when four English frigates sailed into the colony's harbor and demanded its surrender. In 1673, a Dutch fleet of 21 ships returned to the colony and recaptured it. Despite this victory, the Netherlands' were defeated in Europe and surrendered New Netherlands to England in 1674 when they signed the Treaty of Westminster.
Portugal gained control of Brazil through the Treaty of Tordesillas. The Portuguese, along with help from native Brazilians, were able to keep out French and Dutch invaders.
Brazil
Spain lost control of the Netherlands. The Austrian Hapsburgs were less powerful, and German princes gained independence.
Angola and Mozambique