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How did arithmetic help astronomers determine latitude and longitude?

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arithmetic A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”

Arithmetic and mathematical tables were essential to astronomers and navigators for determining latitude and longitude by converting celestial observations into geographic coordinates.

Latitude

To determine latitude, navigators measured the elevation angle of a celestial body—such as the polestar or the Sun—above the horizon using instruments like the quadrant, astrolabe, or sextant. Because these bodies do not always align perfectly with the Earth's axis, navigators used arithmetic to apply necessary corrections based on almanacs and astronomical tables.123

Longitude

Determining longitude was historically more complex, requiring precise timekeeping and advanced calculations. Astronomers developed ephemerides—tables detailing the day-to-day positions of celestial bodies—to facilitate these computations. One primary method involved measuring "lunar distances," or the angular displacement of the Moon from other celestial objects. This required tedious arithmetic and highly accurate tables, such as those published in the Nautical Almanac, to translate observed angles and time into longitude.423

These techniques relied on trigonometry, which evolved from early geometric models into a system of numerical tables for calculating angular positions.56