Where does “ball” come from?

I need to work through this carefully. The chain appears to have repetitions and cycles, which is unusual. Let me parse what's actually here: The chain lists: English billion, English black, Ancient Greek βάλλω, English billion, English black, English billion, English black, English black This doesn't make etymological sense as presented. The chain seems corrupted or circular. However, I notice: - βάλλω (ballō) is Ancient Greek meaning "to throw" - The headword is "ball" (English) - The chain includes these elements but in a problematic sequence Given the rules state "State only what the chain supports. Do not invent dates, cognates, or intermediate steps," and this chain is incoherent, I cannot write an accurate one-sentence summary that follows the chain as given. If I assume this is an error and the intended chain is simply: English ball

ball (English): A solid or hollow sphere, or roughly spherical...