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Originally Posted by CRussel
Nearly that simple. You go through the longitude to get to the distance, though, since the longitude is actually more important. Your latitude is determined by the angle of a known star, the moon, or sun above the horizon and by the 1730s, this was measured using a sextant. (Many commercial captains today still use one regularly, even though GPS is far more precise. But then, I've been known to use a slide rule in recent memory.  ) Your longitude is determined by the difference in local noon v. Greenwich Mean Time noon.
The problem comes when you can't get a reliable sighting to determine exact local noon, or your latitude. Then you're down to dead reckoning, using the speed of the ship (literally done by tossing a weighted line over the side of the ship, and counting the number of knots in the rope in a given time), the compass heading, and a guess of the amount of current and "leeway" the ship is making.
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Dead reckoning is probably the method the Admiral was using in 1707 when the fleet of ships were wrecked. It sounds like you really needed both your latitude and longitude to be accurate or you were in deep trouble. And what form that trouble took could vary depending on where you were. It can't have been easy to live the life of a seaman back then.