Jiāozhǐ, pronounced Kuchi in the Malay, became the "Cochin-China" of the Portuguese traders circa 1516, who so named it to distinguish it from the city and princely state of Cochin in India, their first headquarters in the Malabar Coast.
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The book Cíhǎi and the historian Nguyễn Văn Tố claim that both of the Zhǐ letters are correct.