https://maas.museum/observations/200...his-longitude/
James Cook had no chronometer on his 1st voyage but did on later voyages. The latest hi-tech was Lunar Distances. Polynesians surprised them by doing maths off the top of their head.
"These Polynesians.. .knowledge was .. extremely detailed, very accurate and in many respects superior to the instruments of the western navigators, such as Magellan and Cook, for whom the Pacific was a sea of constant surprises... western European sailors did not venture deep into their neighbourhood until the end of the Middle Ages. .they learned the art of dead reckoning, judging distance as they sailed to gain some sense of longitude: they appear to have found this easier to do than European sailors, who had to await the invention of the chronometer.. Tupaia , a Polynesian navigator who accompanied Captain Cook, astonished Cook's companions by his almost instinctive awareness of where the ship stood, without instruments or written records...just the super computer of the human brain. One of the most extraordinary methods of navigation was .a system known in the Carolina Islands as
etak...a relationship ..between the destination and another island in its vicinity; the method depended on placing this third point accurately in relation to the stars... powerful mental geometry , not to mention an astonishingly detailed, carefully memorised, mobile map of the heavens. _ D Abulafia 2019. "The Boundless Sea". Allen Lane. pp 5, 16-19. (Mediterranean History , Cambridge University).