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..... and another thing.

"....(Cook) consulted the British Nautical Almanac to determine at what time the angular distance would be the same if observed from Greenwich."

From this, I understand the idea is that Captain Cook measures the angular distance from the Polynesian Islands (or wherever) and then uses the Nautical Almanac to compute the time at which he would have seen the same angular distance, had been standing at Greenwich Observatory. This would then have been the time at which he made his observation in the Polynesian Islands (or wherever).

Did I get that right?

Geoffrey Kolbe