Lieutenant James Cook, the first European to map the eastern coastline of Australia in 1770

In 1769, Lieutenant James Cook in command of HMS Endeavour, travelled to Tahiti to observe and record the transit of Venus. Cook also carried secret Admiralty instructions to locate the supposed Southern Continent.

Unable to find this continent, Cook decided to survey the east coast of New Holland, the only major part of that continent that had not been charted by Dutch navigators.

On 19 April 1770, Endeavour reached the east coast of New Holland and ten days later anchored at Botany Bay. Cook charted the coast to its northern extent and formally took possession of the east coast of New Holland on 21/22 August 1770 when on Possession Island off the west coast of Cape York Peninsula.

He noted in his journal that he could

land no more upon this Eastern coast of New Holland, and on the Western side I can make no new discovery the honour of which belongs to the Dutch Navigators and as such they may lay Claim to it as their property

but the Eastern Coast from the Latitude of 38 South down to this place I am confident was never seen or viseted by any European before us and therefore by the same Rule belongs to great Britain 

Credit: Wikipedia