'Formosa' is the formal name of Taiwan. Formosa isn't really
considered as a nickname but it is another name for Taiwan.
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The main island of Taiwan, also known as Formosa (from Portuguese (Ilha) Formosa, meaning "beautiful (island)") (Wikipedia) so Taiwan also called Formosa
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The word "Formosa" comes from Portuguese explorers, who first named the island of Taiwan "Ilha Formosa," meaning "Beautiful Island," in the 16th century.