From my understanding, Europeans didn't realize that America was an altogether new continent until around 1502; when Amerigo Vespucci realized America wasn't India as what he saw there didn't match the stories he heard from sailors that went to India from the usual route around Africa (If possible I'd like this fact to be checked because I'm not very sure I understood it right).
What matters is that until 1502, everyone (even Columbus himself) was convinced that in 1492 the Columbus expedition just landed in India. That being said, why did Pope Julius II write the Treaty of Tordesillas (where he divided the world in two halves between the territories that could have been colonized by the Spanish and the Portuguese). Since by his knowledge America didn't exist, he said to Portugal "the territories to the east of Cape Verde Islands are yours" convinced there wasn't actually anything to the east of Cape Verde Islands (apart from India, whose existence was known since they always traded with them).
So, in the end my question is, how did they divide the world into two halves if they didn't know that the second half actually existed?
I am very sorry for my poor English but this is the best I could make, also thank you for the time you already spent reading this post and, possibly, to answer it. Good day.