How can the transaction history be checked when new addresses are generated?

How can the transaction history be checked when new addresses are generated?

When a new transaction is executed via a Bitcoin-client, the sender will have a different address than the ones used in previous transactions. I also know that all the full nodes in the Bitcoin network maintain a ledger, which is basically a history off all Bitoin transactions ever made so the nodes can check the integrity of the system and the current amount of bitcoins people have available in their wallets. How is it even possible to check all the transactions when there are constantly new addresses being generated? You can't even link a current transaction to the previous. Is there something I'm missing?

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