Why did James Cook call the mainland Australia?

Australia means “southern land”, and James Cook, when he rediscovered this continent for Europeans, was sure that there was no more southern continent, so he made a choice in favor of this name. The British navigator was confident in the absence of a more southerly land because he repeatedly wanted to swim to this extreme point, but he could not overcome the storm zone and in his homeland said that there was only ice and water near the South Pole.