"Purchase" doesn't really mean anything, because being property isn't a quality of an object that can be analyzed. What being property means is dictated by anyone with the means to enforce their preferred meaning.

The definition of owning a book doesn't include the right to read it out loud, for example. I may own a small piece of land in the city, but I'm told that I must build a single-family home or grassy field on it rather than a parking lot, skyscraper, or open sewer.

The problem is that property rights are defined by people with the most property in a way that expands their control over that property.