1. How should a European colonial power apply the principles of the Treaty of Tordesillas when establishing new territorial claims in the late 15th or early 16th century?
By respecting the demarcation line established by the treaty and asserting claims only within their designated sphere.
Explication
The Treaty of Tordesillas established a demarcation line that divided the world into Spanish and Portuguese spheres of influence. Applying its principles means respecting this line and asserting claims only within the designated area, which was the intended purpose of the treaty. Negotiating new lines or disregarding it would be contrary to its principles, and claiming territories outside the demarcation line without agreement would violate the treaty.