It's only circular if you assume that "Capital" doesn't have a definition. It does: Capital is resources that can be invested into the generation of more resources. In order to meet that definition, resources need to have a few characteristics: They either need to be tools of production in of thenselves (like a factory, or a hammer), or they need to be able to be turned into tools (say, iron ore), and they need to be possessable (an RF band or an idea or land only becomes capital when a system ensures it can be possessed), and they need to transferrable (your face isn't capital, the rights to your likeness are).

"Private" in this case distinguishes the system from other where, say, only the state can own capital.