How did James Cook show that a great southern continent was not located in the South Pacific?

Captain James Cook systematically dismantled the long-held belief in a vast, habitable southern continent—often referred to as Terra Australis—through his extensive maritime expeditions in the 18th century.12

While philosophers and mapmakers had long argued that a large landmass must exist in the Southern Hemisphere to balance the continents of the north, Cook’s voyages provided the empirical evidence to disprove this theory. During his second voyage (1772–1775), Cook conducted a rigorous and methodical search of the southern oceans. He navigated the high latitudes of the Indian Ocean, the waters between New Zealand and Cape Horn, and the region between Cape Horn and the Cape of Good Hope.213

By sailing beyond latitude 70° S and completing the first west-to-east circumnavigation in high latitudes, Cook demonstrated that no such temperate southern continent existed. He concluded that any landmass in the far south was limited to the frozen, inhospitable regions of Antarctica, effectively proving that the fabled Terra Australis of the mapmakers was a myth.21