For the same reason we check out mineral resources, sometimes at huge expense: in the hope of striking gold. Or oil, or other things which will give us money. In order to make money and increase military power. Stealing from distant lands was a lucrative business.
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Prince Henry helped lead Portugal in overseas exploration.
"Overseas exploration" means exploring places that are separated from your place of origin by an ocean or a sea, so to get there you have to go "over the sea."
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The possible explanation is that the Chinese thought that overseas exploration may violate Confucian principles. Another reason is that the Chinese wanted to preserve their traditions intact.
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