Verifying the signature of a transaction seems circular

Question

I'm reading Mastering Ethereum. Around page 116 it says;

"to verify the signature one must have the signature (r and s), the serialized transaction, and the public key that corresponds to the private key used to create the signature."

But then it says that the public key is not sent with the transaction, that it is derived from the signature, and on page 120 has the math to do this.

This logic seems circular. What am I missing? Thanks.

Answer 1

Public key can be recovered from serialized transaction and digital signature. Lower 20 bytes of the public key hash should be equal to address of the wallet.