Which improvement in navigation technology allowed sailors to use celestial bodies to determine latitude?

For centuries Europeans and Arabs had sailed around its coasts using as reference the visible points of the littoral and their knowledge of the depths (probes) in different places. When, at the end of the 15th century, the Portuguese and Castilians began their more distant voyages of exploration and discovery, their navigation instruments were:

They knew the limitations and errors of navigating by esteem. They also knew that the magnetic declination was not constant but varied with place and time. They knew that the polar star was not located just above the celestial pole and knew how to correct the error introduced in the measurement of latitude by observing nearby stars (the "guards").

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