Why is it called a "long" or "short" position in the financial markets?

Is there a convincing explanation why it’s called going “long” if you buy a share on the stock market, and going “short” when you sell a share that you don’t own?

As far as I can tell, it’s a terminology choice made so long ago that everyone’s forgotten.

“Short” comes from your having been short of the shares you sold and I suspect “long” came from needing a word to distinguish it from “short.”