The last time the United States bought a foreign territory — through a monetary transaction and not just a signed treaty — was in 1917, when the Virgin Islands were acquired from Denmark.

More than 100 years later, President Trump said he wanted to buy Greenland, the largest island in the world, from Denmark. Denmark has rejected that idea, but Mr. Trump is not the first president to attempt the purchase; Harry Truman tried in 1946, but Denmark wasn’t interested then, either.

In its 243-year history, the United States has purchased foreign land a number of times. Parts of present-day Arizona and New Mexico were bought from Mexico; Florida from Spain; and Alaska from Russia.

But that was centuries ago, during an era of exploration when powerful countries fought wars and negotiated treaties to claim land in the New World.

“That’s just not how it works anymore,” said Daniel Immerwahr, an associate professor of history at Northwestern University and the author of “How to Hide an Empire.”

At the turn of the 20th century, he said, there was a notion that the “frontier had come to an end” and there was little unclaimed land left.